Journal articles: 'Residual autocorrelation'

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Dash, Mihir. "Beta Estimation in Indian Stock Markets - Some Issues." Asian Journal of Finance & Accounting 7, no. 2 (2015): 23. http://dx.doi.org/10.5296/ajfa.v7i2.6751.

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This study examines the reliability of the OLS beta estimates in Indian stock markets by considering the residual characteristics of the market model regressions. The statistics used include the coefficient of determination (R2), the F-test for significance of the regression coefficient, the Durbin-Watson test for serial autocorrelation, the residual autocorrelation function, the Kolmogorov-Smirnov and Shapiro-Wilk tests for normality of the residuals, the presence of outliers, and White’s test for heteroskedasticity.The results of the study indicate some serious issues afflicting beta estimation in Indian stock markets, including: non-normality of stock returns and of residuals, extreme standardized residual values, heteroskedasticity, residual autocorrelation, and low R2. Thus, the simple market model is likely to result in biased estimates for beta in Indian stock markets.

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Franses, Philip Hans. "Testing for residual autocorrelation in growth curve models." Technological Forecasting and Social Change 69, no. 2 (2002): 195–204. http://dx.doi.org/10.1016/s0040-1625(01)00148-2.

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Fasso, Alessandro. "Residual Autocorrelation Distribution in the Validation Data Set." Journal of Time Series Analysis 21, no. 2 (2000): 143–53. http://dx.doi.org/10.1111/1467-9892.00178.

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Brüggemann, Ralf, Helmut Lütkepohl, and Pentti Saikkonen. "Residual autocorrelation testing for vector error correction models." Journal of Econometrics 134, no. 2 (2006): 579–604. http://dx.doi.org/10.1016/j.jeconom.2005.07.006.

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Dutkowski, Gregory W., João Costa e Silva, Arthur R. Gilmour, Hubert Wellendorf, and Alexandre Aguiar. "Spatial analysis enhances modelling of a wide variety of traits in forest genetic trials." Canadian Journal of Forest Research 36, no. 7 (2006): 1851–70. http://dx.doi.org/10.1139/x06-059.

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Spatial analysis of progeny trial data improved predicted genetic responses by more than 10% for around 20 of the 216 variables tested, although, in general, the gains were more modest. The spatial method partitions the residual variance into an independent component and a two-dimensional spatially autocorrelated component and is fitted using REML. The largest improvements in likelihood were for height. Traits that exhibit little spatial structure (stem counts, form, and branching) did not respond as often. The spatial component represented up to 50% of the total residual variance, usually subsuming design-based blocking effects. The autocorrelation tended to be high for growth, indicating a smooth environmental surface, it tended to be small for measures of health, indicating patchiness, and otherwise the autocorrelation was intermediate. Negative autocorrelations, indicating competition, were present in only 10% of diameter measurements for the largest diameter square planted trials, and between nearest trees with rectangular planting at smaller diameters. Bimodal likelihood surfaces indicate that competition may be present, but not dominant, in other cases. Modelling of extraneous effects yielded extra genetic gain only in a few trials with severely asymmetric autocorrelations. Block analysis of resolvable incomplete-block or row–column designs was better than randomized complete-block analysis, but spatial analysis was even better.

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DEWIANTARI, NI KADEK YUNI, I. WAYAN SUMARJAYA, and G. K. GANDHIADI. "PETA KENDALI EWMA RESIDUAL PADA DATA BERAUTOKORELASI." E-Jurnal Matematika 8, no. 1 (2019): 64. http://dx.doi.org/10.24843/mtk.2019.v08.i01.p236.

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Control charts with autocorrelation can be overcome by creating control chart with residuals from the best forecasting model. EWMA control chart is a alternative to the Shewhart control chart when detecting small shifts. The purpose of this study is to make the best forecasting model to obtain residual, and see the stability of the rupiah exchange rate against US dollar using EWMA control chart with residual. The best model of the case is ARIMA (1,1,1). The results of the EWMA residual control chart with ? = 0.1 there is a pattern that makes the process unstable.

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Adams, Douglas E., and Randall J. Allemang. "Residual frequency autocorrelation as an indicator of non-linearity." International Journal of Non-Linear Mechanics 36, no. 8 (2001): 1197–211. http://dx.doi.org/10.1016/s0020-7462(00)00090-1.

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Marazzi, Alfio, and Victor J. Yohai. "Robust Box–Cox transformations based on minimum residual autocorrelation." Computational Statistics & Data Analysis 50, no. 10 (2006): 2752–68. http://dx.doi.org/10.1016/j.csda.2005.04.007.

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Bazilevsky, M. P. "Research of New Criteria for Detecting First-order Residuals Autocorrelation in Regression Models." Mathematics and Mathematical Modeling, no. 3 (August 3, 2018): 13–25. http://dx.doi.org/10.24108/mathm.0318.0000102.

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When estimating regression models using the least squares method, one of its prerequisites is the lack of autocorrelation in the regression residuals. The presence of autocorrelation in the residuals makes the least-squares regression estimates to be ineffective, and the standard errors of these estimates to be untenable. Quantitatively, autocorrelation in the residuals of the regression model has traditionally been estimated using the Durbin-Watson statistic, which is the ratio of the sum of the squares of differences of consecutive residual values to the sum of squares of the residuals. Unfortunately, such an analytical form of the Durbin-Watson statistic does not allow it to be integrated, as linear constraints, into the problem of selecting informative regressors, which is, in fact, a mathematical programming problem in the regression model. The task of selecting informative regressors is to extract from the given number of possible regressors a given number of variables based on a certain quality criterion.The aim of the paper is to develop and study new criteria for detecting first-order autocorrelation in the residuals in regression models that can later be integrated into the problem of selecting informative regressors in the form of linear constraints. To do this, the paper proposes modular autocorrelation statistic for which, using the Gretl package, the ranges of their possible values and limit values were first determined experimentally, depending on the value of the selective coefficient of auto-regression. Then the results obtained were proved by model experiments using the Monte Carlo method. The disadvantage of the proposed modular statistic of adequacy is that their dependencies on the selective coefficient of auto-regression are not even functions. For this, double modular autocorrelation criteria are proposed, which, using special methods, can be used as linear constraints in mathematical programming problems to select informative regressors in regression models.

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Bennis, Saad, and Pierre Bruneau. "Comparaison de méthodes d'estimation des débits journaliers." Canadian Journal of Civil Engineering 20, no. 3 (1993): 480–89. http://dx.doi.org/10.1139/l93-062.

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The aim of the first part of our research, described in this paper, was to compare daily streamflow estimation techniques and models. A general application software named DebEst was developed for the purpose. The Saint-François River basin was used as a physical test area because of the availability of several hydrometric stations in this region. All techniques and models used gave good results. However, principal component analysis and multiple regression applied to deterministic models gave better results than ARIMA models. The least square recursive algorithm was more flexible than the other techniques, although discrepancies sometimes appeared because of incorrect weighting of measuring and modelling noise. Results improved significantly when seasonal models were used and when the variation of parameters was taken into account as a function of flow. All techniques described yielded autocorrelated residuals, at least for the first three time lags. The amplitude of the residual autocorrelation function was reduced by seasonal models although it still remained high. In the second part of our research, the Kalman filter technique will be used in conjunction with the methods described above to extract residual information and generate truly independent residuals. Key words: missing streamflow record, principal components, least squares, recursive parameter estimation, residual autocorrelation. [Journal translation]

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Wenning, Zachary, and Emily Valenci. "A Monte Carlo Simulation Study on the Power of Autocorrelation Tests for ARMA Models." American Journal of Undergraduate Research 16, no. 3 (2019): 59–67. http://dx.doi.org/10.33697/ajur.2019.030.

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It is often the case when assessing the goodness of fit for an ARMA time series model that a portmanteau test of the residuals is conducted to assess residual serial correlation of the fitted ARMA model. Of the many portmanteau tests available for this purpose, one of the most famous and widely used is a variant of the original Box-Pierce test, the Ljung-Box test. Despite the popularity of this test, however, there are several other more modern portmanteau tests available to assess residual serial autocorrelation of the fitted ARMA model. These include two portmanteau tests proposed by Monti and Peña and Rodríguez. This paper focuses on the results of a power analysis comparing these three different portmanteau tests against different fits of ARMA - derived time series, as well as the behavior of the three different test statistics examined when applied to a real-world data set. We confirm that for situations in which the moving average component of a fitted ARMA model is underestimated or when the sample size is small, the portmanteau test proposed by Monti is a viable alternative to the Ljung-Box test. We show new evidence that the Peña and Rodríguez may also be a viable option for testing for residual autocorrelation for data with small sample sizes. KEYWORDS: Time Series; Monte Carlo; ARMA Models; Power; Simulation; Autocorrelation Tests; Portmanteau Tests; Monti; Ljung-Box; Peña and Rodríguez

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Wang, Hai Yu. "The Detection Method of Small Shifts Based on Stationary Autocorrelated Process." Applied Mechanics and Materials 235 (November 2012): 227–32. http://dx.doi.org/10.4028/www.scientific.net/amm.235.227.

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When control charts are used to monitor a process, a standard assumption is that observations from the process at different times are independent random variables. However, the independence assumption is often not reasonable for processes of interest in many applications because the dynamics of the process product autocorrelation in the process observations. The presence of significant autocorrelation in the process observations can have a large impact on traditional control charts developed under the independence assumption. A method of monitoring little shifts in stationary autocorrelated process is discussed in this paper. At first, auto-regressive moving-average model is used to fit stationary autocorrelated process. Then, process autocorrelation can be removed by residual method, and exponentially weighted moving average charts are constructed to monitor little shifts of process mean and variance. Comparing with other methods, we can illustration that this EWMA residuals charts have better efficiency for stationary autocorrelated processes.

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Bennis, Saad, and Pierre Bruneau. "Amélioration de méthodes d'estimation des débits journaliers." Canadian Journal of Civil Engineering 20, no. 3 (1993): 490–99. http://dx.doi.org/10.1139/l93-063.

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The aim of the research described in this paper was to improve results obtained with conventional daily streamflow estimation methods. The technique requires a robust filter such as the Kalman filter. An explanation of the general filtering algorithm is first given, followed by illustration of how the robust-filter technique can be combined with daily streamflow estimation methods to improve performance. In particular, missing data estimates were more precise with the robust filter, and independent residuals with autocorrelation functions close to zero were obtained. The Saint-François River basin was used as a physical test area. Key words: Kalman filter, missing streamflow record, persistence, extrapolation, noise covariance matrix, residual autocorrelation. [Journal translation]

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Razavi, Mehrdad, Thomas J. Grabowski, Sonya Mehta, and Lizann Bolinger. "The source of residual temporal autocorrelation in fMRI time series." NeuroImage 13, no. 6 (2001): 228. http://dx.doi.org/10.1016/s1053-8119(01)91571-x.

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Li, W. K., and Philip L. H. Yu. "On the residual autocorrelation of the autoregressive conditional duration model." Economics Letters 79, no. 2 (2003): 169–75. http://dx.doi.org/10.1016/s0165-1765(02)00303-8.

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MONTI, ANNA CLARA. "A proposal for a residual autocorrelation test in linear models." Biometrika 81, no. 4 (1994): 776–80. http://dx.doi.org/10.1093/biomet/81.4.776.

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Huo, Lijuan, Tae-Hwan Kim, Yunmi Kim, and Dong Jin Lee. "A residual-based test for autocorrelation in quantile regression models." Journal of Statistical Computation and Simulation 87, no. 7 (2016): 1305–22. http://dx.doi.org/10.1080/00949655.2016.1262371.

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Gruzdev, A. N. "Аccounting for autocorrelation in a linear regression problem on an example of analysis of atmospheric column NO2 content". Известия Российской академии наук. Физика атмосферы и океана 55, № 1 (2019): 73–82. http://dx.doi.org/10.31857/s0002-351555173-82.

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A method is proposed for taking into account a serial correlation (an autocorrelation) of data in a linear regression problem, which allows accounting for the autocorrelation on long scales. A residual series is presented as an autoregressive process of an order, k, that can be much larger than 1, and the autocorrelation function of the processes is calculated by solving the system of the Yule–Walker equations. Given the autocorrelation function, the autocorrelation matrix is constructed which enters the formulas for estimates of regression coefficients and their errors. The efficiency of the method is demonstrated on the base of the multiple regression analysis of data of 26-year measurements of the column NO2 contents at the Zvenigorod Research Station of the Institute of Atmospheric Physics. Estimates of regression coefficients and their errors depend on the autoregression order k. At first the error increases with increasing k. Then it approaches its maximum and thereafter begins to decrease. In the case of NO2 at the Zvenigorod Station the error more than doubled in its maximum compared to the beginning value. The decrease in the error after approaching the maximum stops if k approaches the value such that the autoregressive process of this order allows accounting for important features of the autocorrelation function of the residual series. Estimates have been obtained of seasonally dependent linear trends and effects on NO2 of nature factors such that the 11-year solar cycle, the quasi-biennial oscillation, the North Atlantic Oscillation and other.

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Martellosio, Federico. "POWER PROPERTIES OF INVARIANT TESTS FOR SPATIAL AUTOCORRELATION IN LINEAR REGRESSION." Econometric Theory 26, no. 1 (2009): 152–86. http://dx.doi.org/10.1017/s0266466609090641.

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This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.

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Zhang, Feng Wang, Wen Gang Che, Bei Bei Xu, and Jing Zhi Xu. "The Research of ARMA Model in CPI Time Series." Applied Mechanics and Materials 347-350 (August 2013): 3099–103. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.3099.

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The changing trend of CPI to a certain extent reflects the degree of inflation, which has a great significance on macro-control and research on national economic. ARMA model is one of the simple and practical models in financial time series analysis with relatively high forecast accuracy. The paper utilizing Eviews software, through the statistical analysis of CPI from the year of 1995 to 2008 monthly in China, through the ADF unit root test [, by dint of the autocorrelation function ACF diagram [ and partial autocorrelation function PACF diagram [ to identify the model consequently establish the model, through the residual serial correlation test of the residuals of the model to select the correct model [. The predications of the model showed that the ARMA model is valid and forecast accuracy is relatively high

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Mainali, Janardan, Heejun Chang, and Yongwan Chun. "A review of spatial statistical approaches to modeling water quality." Progress in Physical Geography: Earth and Environment 43, no. 6 (2019): 801–26. http://dx.doi.org/10.1177/0309133319852003.

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We review different regression models related to water quality that incorporate spatial aspects in their model. Spatial aspects refer to the location of different sites and are usually characterized by the distance between different points and directions by which they are related to each other. We focus on spatial lag and error, spatial eigenvector-based, geographically weighted regression, and spatial-stream-network-based models. We evaluated different studies using these methods based on how they dealt with clustering (spatial autocorrelation) of response variables, incorporated those clustering in the error (residual spatial autocorrelation), used multi-scale processes, and improved the model performance. The water-quality-based regression modeling approaches are shifting from straight-line distance-based spatial relations to upstream–downstream relations. Calculation of spatial autocorrelation and residual spatial autocorrelation was dependent upon the type of spatial regression used. The weights matrix is used as available in the software and most of the studies did not attempt to modify it. Different scale processes like certain distance from rivers versus consideration of entire watersheds are dealt with separately in most of the studies. Generally, the capacity of the predictor variables to predict the response variable significantly improves when spatial regressions are used. We identify new research directions in terms of spatial considerations, weights matrix construction, inclusion of multi-scale processes, and identification of predictor variables in such models.

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No, Taehyun, and Taewook Lee. "Wild bootstrap Ljung-Box test for residual autocorrelation in vector autoregressive models." Journal of the Korean Data And Information Science Society 31, no. 3 (2020): 477–85. http://dx.doi.org/10.7465/jkdi.2020.31.3.477.

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Magnussen, Steen, Johannes Breidenbach, and Fransisco Mauro. "The challenge of estimating a residual spatial autocorrelation from forest inventory data." Canadian Journal of Forest Research 47, no. 11 (2017): 1557–66. http://dx.doi.org/10.1139/cjfr-2017-0247.

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Estimates of stand averages are needed by forest management for planning purposes. In forest enterprise inventories supported by remotely sensed auxiliary data, these estimates are typically derived exclusively from a model that does not consider stand effects in the study variable. Variance estimators for these means may seriously underestimate uncertainty, and confidence intervals may be too narrow when a model used for computing a stand mean omits a nontrivial stand effect in one or more of the model parameters, a nontrivial spatial distance dependent autocorrelation in the model residuals, or both. In simulated sampling from 36 populations with stands of different sizes and differing with respect to (i) the correlation between a study variable (Y) and two auxiliary variables (X), (ii) the magnitude of stand effects in the intercept of a linear population model linking X to Y, and (iii) a first-order autoregression in Y and X, we learned that none of the tested designs provided reliable estimates of the within-stand autocorrelation among model residuals. More-reliable estimates were possible from stand-wide predictions of Y. The anticipated bias in an estimated autoregression parameter had a modest influence on estimates of variance and coverage of nominal 95% confidence intervals for a synthetic stand mean.

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de Oliveira Silva, Renan, Eliane da Silva Christo, and Kelly Alonso Costa. "Analysis of Residual Autocorrelation in Forecasting Energy Consumption through a Java Program." Advanced Materials Research 962-965 (June 2014): 1753–56. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.1753.

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The study of forecasting of energy in Brazil is important for future planning, as the country has experienced crises of energy supply. And a model developed in java is an affordable and efficient tool to be used both in Brazil and in other countries. Time series analysis is highly important in many different application areas, for it allows description and modeling of a variable of interest’s behavior, thus enabling the forecasting of its future values, which serves as support for decision making. When the data used in regression analysis comprises time series, the dependency between the observations grants a dynamic quality to the regression model. In this situation, it is common to come across a problem known as residual autocorrelation, which invalidates the assumptions made about the term of error in the classical linear regression models. This paper presents a program created in Java by implementing the method of Cochrane-Orcutt for the correction of residual autocorrelation. And the application is made in the Brazilian energy final consumption forecasting.

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Alsharif, Mohammed, Mohammad Younes, and Jeong Kim. "Time Series ARIMA Model for Prediction of Daily and Monthly Average Global Solar Radiation: The Case Study of Seoul, South Korea." Symmetry 11, no. 2 (2019): 240. http://dx.doi.org/10.3390/sym11020240.

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Forecasting solar radiation has recently become the focus of numerous researchers due to the growing interest in green energy. This study aims to develop a seasonal auto-regressive integrated moving average (SARIMA) model to predict the daily and monthly solar radiation in Seoul, South Korea based on the hourly solar radiation data obtained from the Korean Meteorological Administration over 37 years (1981–2017). The goodness of fit of the model was tested against standardized residuals, the autocorrelation function, and the partial autocorrelation function for residuals. Then, model performance was compared with Monte Carlo simulations by using root mean square errors and coefficient of determination (R2) for evaluation. In addition, forecasting was conducted by using the best models with historical data on average monthly and daily solar radiation. The contributions of this study can be summarized as follows: (i) a time series SARIMA model is implemented to forecast the daily and monthly solar radiation of Seoul, South Korea in consideration of the accuracy, suitability, adequacy, and timeliness of the collected data; (ii) the reliability, accuracy, suitability, and performance of the model are investigated relative to those of established tests, standardized residual, autocorrelation function (ACF), and partial autocorrelation function (PACF), and the results are compared with those forecasted by the Monte Carlo method; and (iii) the trend of monthly solar radiation in Seoul for the coming years is analyzed and compared on the basis of the solar radiation data obtained from KMS over 37 years. The results indicate that (1,1,2) the ARIMA model can be used to represent daily solar radiation, while the seasonal ARIMA (4,1,1) of 12 lags for both auto-regressive and moving average parts can be used to represent monthly solar radiation. According to the findings, the expected average monthly solar radiation ranges from 176 to 377 Wh/m2.

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Park, No-Wook. "Time-Series Mapping of PM10Concentration Using Multi-Gaussian Space-Time Kriging: A Case Study in the Seoul Metropolitan Area, Korea." Advances in Meteorology 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/9452080.

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This paper presents space-time kriging within a multi-Gaussian framework for time-series mapping of particulate matter less than 10 μm in aerodynamic diameter (PM10) concentration. To account for the spatiotemporal autocorrelation structures of monitoring data and to model the uncertainties attached to the prediction, conventional multi-Gaussian kriging is extended to the space-time domain. Multi-Gaussian space-time kriging presented in this paper is based on decomposition of the PM10concentrations into deterministic trend and stochastic residual components. The deterministic trend component is modelled and regionalized using the temporal elementary functions. For the residual component which is the main target for space-time kriging, spatiotemporal autocorrelation information is modeled and used for space-time mapping of the residual. The conditional cumulative distribution functions (ccdfs) are constructed by using the trend and residual components and space-time kriging variance. Then, the PM10concentration estimate and conditional variance are empirically obtained from the ccdfs at all locations in the study area. A case study using the monthly PM10concentrations from 2007 to 2011 in the Seoul metropolitan area, Korea, illustrates the applicability of the presented method. The presented method generated time-series PM10concentration mapping results as well as supporting information for interpretations, and led to better prediction performance, compared to conventional spatial kriging.

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Thorson, James T., Olaf P. Jensen, and Elise F. Zipkin. "How variable is recruitment for exploited marine fishes? A hierarchical model for testing life history theory." Canadian Journal of Fisheries and Aquatic Sciences 71, no. 7 (2014): 973–83. http://dx.doi.org/10.1139/cjfas-2013-0645.

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Recruitment often varies substantially in fish populations, and residual variability may have serial autocorrelation due to environmental effects even after accounting for a stock–recruitment relationship. However, the likely magnitude of variability and autocorrelation in recruitment has yet to be formally estimated. We therefore developed a hierarchical model for recruitment variability and autocorrelation and applied it to data for 154 fish populations. Results were similar when using either the Ricker or Beverton–Holt stock–recruitment model, and showed that autocorrelated recruitment has a marginal standard deviation of 0.74 (SD = 0.35) and a mean autocorrelation of 0.43 (SD = 0.28) when predicting for an unobserved taxonomic order. Estimates differed somewhat among taxonomic orders and stocks, and also supported a hypothesized positive relationship between age at maturity and autocorrelation in recruitment. Our results can be used as a Bayesian prior for recruitment variability in models for data-poor stocks and to distinguish recruitment from other process errors in models for data-rich stocks. Estimates can also be used in the design of future simulation models and management strategy evaluations and in theoretical research regarding life history variation.

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Yu, Jian Li, and Rui Fang Zhou. "Process Monitoring and Adjustment Based on Optimal RBF Network." Applied Mechanics and Materials 336-338 (July 2013): 1286–91. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.1286.

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Modern complex manufacturing process output data showed high autocorrelation, resulting in the output of the process to deviate from the design target , or that false alarms increasd in traditional control chart in monitoring process. Statistical Process Control (SPC) and Automatic process control (APC) are main methods of industrial processes. Study based on the optimization of radial basis (Radial Basis Funtion RBF) neural network integrated SPC/APC quality control model, the forecast MMSE controller based on optimal radial basis function networks were utilized to adjut process of productive process output, and residual control charts were utilized to monitor process output after adjustment. Results show that optimal RBF network can improve forecast accuracy and adjustment effect, eliminate effectively process output autocorrelation. The residual control chart will in steady state and with small fluctuation. Intergrated SPC/APC quality control model based on optimal radial basis function can eliminate process fluctuation effectively and guaranteeproduct stable quality in process quality control.

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Pereira, Adriele Aparecida, Tales Jesus Fernandes, Myriane Stella Scalco, and Augusto Ramalho De Morais. "MODELAGEM NÃO LINEAR DO CRESCIMENTO EM ALTURA DO CAFEEIRO IRRIGADO E NÃO IRRIGADO EM DIFERENTES DENSIDADES." IRRIGA 1, no. 1 (2018): 140. http://dx.doi.org/10.15809/irriga.2016v1n1p140-149.

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MODELAGEM NÃO LINEAR DO CRESCIMENTO EM ALTURA DO CAFEEIRO IRRIGADO E NÃO IRRIGADO EM DIFERENTES DENSIDADES ADRIELE APARECIDA PEREIRA1; TALES JESUS FERNANDES2; MYRIANE STELLA SCALCO3 E AUGUSTO RAMALHO DE MORAIS4 1Licenciada em Matemática, Mestre, DEX/UFLA, Lavras-MG, e-mail: adrieleapvga@yahoo.com.br2Licenciado em Matemática, Doutor, Prof. DEX/UFLA, Lavras-MG, e-mail: tales.jfernandes@dex.ufla.br3Engenheira Agrônoma, Doutora, DAG/UFLA, Lavras-MG, e-mail: msscalco@dag.ufla.br4Engenheiro Agrônomo, Doutor, Prof. DEX/UFLA, Lavras-MG, e-mail: armorais@dex.ufla.br 1 RESUMO Heterogeneidade de variâncias e autocorrelação residual são características inerentes à dados de crescimento ao longo do tempo que se não considerados nas análises podem conduzir a resultados imprecisos. Este estudo teve por objetivo comparar os ajustes dos modelos Logístico e Gompertz, considerando os métodos de mínimos quadrados: ordinários e generalizados. Os dados utilizados referem-se à altura de plantas do cafeeiro, submetidas aos regimes de irrigação Si (testemunha), 60 kPa e 140 kPa, nas densidades de plantio 2500 e 5000 plantas ha-1. Segundo o desvio padrão residual e a análise de resíduos, o ajuste do modelo Gompertz pelo método de mínimos quadrados generalizados, que incorpora a heterogeneidade de variâncias e autocorrelação residual na modelagem, apresentou os melhores resultados para todos os dados analisados, sendo indicado para modelar o crescimento em altura do cafeeiro ao longo do tempo. Os ajustes referentes às plantas irrigadas apresentaram as maiores estimativas para a altura assintótica, confirmando que a irrigação da lavoura proporciona maior crescimento das plantas. Palavras-Chave: Autocorrelação residual, Gompertz, Heterocedasticidade. PEREIRA, A. A.; FERNANDES, T. J.; SCALCO, M. S.; MORAIS, A. R. de MODELING NONLINEAR GROWTH IN HEIGHT COFFEE WITH AND WITHOUT IRRIGATION IN DIFFERENT DENSITIES 2 ABSTRACT Heterogeneity of variance and residual autocorrelation characteristics are inherent in the growth data over time that is not considered in the analysis may lead to inaccurate results. This study aimed to compare the settings of the Logistic and Gompertz models, considering the methods of least squares: ordinary and generalized. The data used refer to the height of the coffee plants, subjected to irrigation systems Si (non irrigated), 60 kPa and 140 kPa, the planting densities in 2500 and 5000 plants ha-1. According to the residual standard deviation and the residual analysis, the fit of the Gompertz model by generalized least squares method, which incorporates the heterogeneity of residual variance and autocorrelation in modeling, showed the best results for all data analyzed, suitable for modeling the growth in height of the coffee over time. The adjustments related to the irrigated plants had the highest estimates for the asymptotic height, confirming that the crop irrigation provides greater plant growth. Keywords: Residual autocorrelation, Gompertz, Heteroscedasticity.

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Matsyura, О. V., М. V. Matsyura та А. А. Zimaroyeva. "ВИКОРИСТАННЯ ПРОГРАМИ «SIMPLY TAGGING» ДЛЯ ПРОГНОЗУВАННЯ ГУСТОТИ ПТАХІВ У ГНІЗДОВИХ БІОТОПАХ". Biological Bulletin of Bogdan Chmelnitskiy Melitopol State Pedagogical University 2, № 2 (2012): 94. http://dx.doi.org/10.15421/20122_25.

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For the analysis of long-term observations data on dynamics of bird populations the most suitable methods could be the stochastic processes. Abundance (density) of birds is calculated on the integrated area of studied habitats. Using the method of autocorrelation the correlogram of changes in number of birds drawn during the study period in all the area. After that, the calculation of the autocorrelation coefficients and partial autocorrelation are performed. The most appropriate model is the mixed autoregressive moving average (ARIMA). Ecological significance of autoregressive parameters is to display the frequency of changes in the number of birds in the seasonal and long-term aspects. The sliding average is one of the simplest methods, which allows reject the random fluctuations of the empirical regression line. Validation of the model could be conducted on truncated data series (10 years). The forecast is calculated for the next two years and compared with empirical data. Calculation of correlation coefficients between the real data and the forecast is performed using non-parametric Spearman correlation coefficient. The residual rows of selected models are estimated by residual correlogram. The constructed model can be used to analyze and forecast the number of birds in breeding biotopes. Keywords: analysis, density, indirect methods, birds, Simply Tagging.

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Crase, Beth, Adam C. Liedloff, and Brendan A. Wintle. "A new method for dealing with residual spatial autocorrelation in species distribution models." Ecography 35, no. 10 (2012): 879–88. http://dx.doi.org/10.1111/j.1600-0587.2011.07138.x.

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McCord, Michael James, John McCord, Peadar Thomas Davis, Martin Haran, and Paul Bidanset. "House price estimation using an eigenvector spatial filtering approach." International Journal of Housing Markets and Analysis 13, no. 5 (2019): 845–67. http://dx.doi.org/10.1108/ijhma-09-2019-0097.

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Purpose Numerous geo-statistical methods have been developed to analyse the spatial dimension and composition of house prices. Despite these advances, spatial filtering remains an under-researched approach within house price studies. This paper aims to examine the spatial distribution of house prices using an eigenvector spatial filtering (ESF) procedure, to analyse the local variation and spatial heterogeneity. Design/methodology/approach Using 2,664 sale transactions over the one year period Q3 2017 to Q3 2018, an eigenvector spatial filtering approach is applied to evaluate spatial patterns within the Belfast housing market. This method consists of using geographical coordinates to specify eigenvectors across geographic distance to determine a set of spatial filters. These convey spatial structures representative of different spatial scales and units. The filters are incorporated as predictors into regression analyses to alleviate spatial autocorrelation. This approach is intuitive, given that detection of autocorrelation in specific filters and within the regression residuals can be markers for exclusion or inclusion criteria. Findings The findings show both robust and effective estimator consistency and limited spatial dependency – culminating in accurately specified hedonic pricing models. The findings show that the spatial component alone explains 14.6 per cent of the variation in property value, whereas 77.6 per cent of the variation could be attributed to an interaction between the structural characteristics and the local market geography expressed by the filters. This methodological step reduced short-scale spatial dependency and residual autocorrelation resulting in increased model stability and reduced misspecification error. Originality/value Eigenvector-based spatial filtering is a less known but suitable statistical protocol that can be used to analyse house price patterns taking into account spatial autocorrelation at varying (different) spatial scales. This approach arguably provides a more insightful analysis of house prices by removing spatial autocorrelation both objectively and subjectively to produce reliable, yet understandable, regression models, which do not suffer from traditional challenges of serial dependence or spatial mis-specification. This approach offers property researchers and policymakers an intuitive but comprehensible approach for producing accurate price estimation models, which can be readily interpreted.

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SILVA, Walleff Silva, Felipe Augusto FERNANDES, Fabiana Rezende MUNIZ, Joel Augusto MUNIZ, and Tales Jesus FERNANDES. "EUCALYPTUS GRANDIS X EUCALYPTUS UROPHYLLA GROWTH CURVE IN DIFFERENT SITE CLASSIFICATIONS, CONSIDERING RESIDUAL AUTOCORRELATION." REVISTA BRASILEIRA DE BIOMETRIA 39, no. 1 (2021): 122–38. http://dx.doi.org/10.28951/rbb.v39i1.511.

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Brazil is a major producer in the timber sector, mainly with the use of wood from species of the genus Eucalyptus, with 26.1% of planted forests located in Minas Gerais. Researchers and manufacturers have been searching for techniques with the objective of making full use of these forests, with a primary focus on greater growth. A modeling of growth curves is an alternative for the estimation of oral production andan important aid tool for the researcher's decision making. Growth curves are commonly studied by nonlinear regression models, which have important assumptions that if not met should be added to the model. The present work aims to select among nonlinear Logistic, Gompertz and von Bertalany regression models the most suitable to describe the growth in wood volume of Eucalyptus urophylla x Eucalyptus grandis hybrids in three Forest Site categories, including whether assumption deviations are required. Methods were executed by the Gauss-Newton iterative method implemented in nls() and it gnls() functions of the R software. Determination coecient, Akaike information criterion (AICc) and Residual Standard Deviation (RSD) were used as selection evaluators of the best model. The results demonstrate that for all site categories, the Gompertz model with addition of autoregressive parameters AR (1) is the most appropriate to describe the growth in wood volume of Eucalyptus urophylla x Eucalyptus grandis hybrids. The addition of the rst-order autoregressive parameter does not aect the quality of t, but it is the correct procedure. Site I, which presents the largest trees according to pre-dened variations, recorded 308 m3/ha of wood volume, followed by 286 m3/ha and 263 m3/ha for Sites II and III, respectively. The time for Site III to reach the maximum point of volume growth is between the fourth and sixth year, while the other sites are more precocious, reaching this point between the second and third year.

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Bramowicz, M., S. Kulesza, P. Czaja, and W. Maziarz. "Application of the Autocorrelation Function and Fractal Geometry Methods for Analysis of MFM Images." Archives of Metallurgy and Materials 59, no. 2 (2014): 451–57. http://dx.doi.org/10.2478/amm-2014-0075.

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Abstract Presented work is focused on the use of correlation methods for numerical analysis of magnetic stray field over the surface of materials. Obtained results extend our previous findings about application of the autocorrelation function and the fractal analysis for characterization of magnetic surfaces. Several domain images are recorded at various tip-sample gaps (i.e. the lift heights), and then their average widths were extrapolated down to the zero distance in order to estimate the width seen right on the surface. Apart from that, fractal parameters were derived from autocorrelation function, which turned out to be sensitive to the lift height, and might constitute universal measure (the critical lift height), above which the MFM signal became dominated by thermal noises and non-magnetic residual interactions.

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Liu, Xin, Zuolin Xiao, and Rui Liu. "A Spatio-Temporal Bayesian Model for Estimating the Effects of Land Use Change on Urban Heat Island." ISPRS International Journal of Geo-Information 8, no. 12 (2019): 522. http://dx.doi.org/10.3390/ijgi8120522.

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The urban heat island (UHI) phenomenon has been identified and studied for over two centuries. As one of the most important factors, land use, in terms of both composition and configuration, strongly influences the UHI. As a result of the availability of detailed data, the modeling of the residual spatio-temporal autocorrelation of UHI, which remains after the land use effects have been removed, becomes possible. In this study, this key statistical problem is tackled by a spatio-temporal Bayesian hierarchical model (BHM). As one of the hottest areas in China, southwest China is chosen as our study area. Results from this study show that the difference of UHI levels between different cities in southwest China becomes large from 2000 to 2015. The variation of the UHI level is dominantly driven by temporal autocorrelation, rather than spatial autocorrelation. Compared with the composition of land use, the configuration has relatively minor influence upon UHI, due to the terrain in the study area. Furthermore, among all land use types, the water body is the most important UHI mitigation factor at the regional scale.

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Guo, Ye Cai, Zhi Chao Zhang, Fang Xu, and Shi Jie Guo. "Variable Step-Size Wavelet Vector Machine Blind Equalization Algorithm." Applied Mechanics and Materials 121-126 (October 2011): 4892–96. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.4892.

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In order to overcome the contradiction of the CMA with a constant step-size between the convergence rate and the residual mean square error(MSE), on the basis of analyzing the idea of variable step-size, the feature of Support Vector Machine(SVM) and Wavelet Transform, a Variable step-size Wavelet transform Support vector machine Constant Modulus blind equalization Algorithm (VWSCMA) is proposed. In the proposed algorithm, the variable step-size is used to solve the contradiction between the convergence rate and the residual MSE, SVM is employed to optimize the weight vector of equalizer, and wavelet transform is used to reduce the autocorrelation of input signals of equalizer. Simulation results show that the proposed algorithm can effectively overcome the contradiction between the convergence rate and the residual error and has good equalization performance.

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Ammann, Lorenz, Fabrizio Fenicia, and Peter Reichert. "A likelihood framework for deterministic hydrological models and the importance of non-stationary autocorrelation." Hydrology and Earth System Sciences 23, no. 4 (2019): 2147–72. http://dx.doi.org/10.5194/hess-23-2147-2019.

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Abstract. The widespread application of deterministic hydrological models in research and practice calls for suitable methods to describe their uncertainty. The errors of those models are often heteroscedastic, non-Gaussian and correlated due to the memory effect of errors in state variables. Still, residual error models are usually highly simplified, often neglecting some of the mentioned characteristics. This is partly because general approaches to account for all of those characteristics are lacking, and partly because the benefits of more complex error models in terms of achieving better predictions are unclear. For example, the joint inference of autocorrelation of errors and hydrological model parameters has been shown to lead to poor predictions. This study presents a framework for likelihood functions for deterministic hydrological models that considers correlated errors and allows for an arbitrary probability distribution of observed streamflow. The choice of this distribution reflects prior knowledge about non-normality of the errors. The framework was used to evaluate increasingly complex error models with data of varying temporal resolution (daily to hourly) in two catchments. We found that (1) the joint inference of hydrological and error model parameters leads to poor predictions when conventional error models with stationary correlation are used, which confirms previous studies; (2) the quality of these predictions worsens with higher temporal resolution of the data; (3) accounting for a non-stationary autocorrelation of the errors, i.e. allowing it to vary between wet and dry periods, largely alleviates the observed problems; and (4) accounting for autocorrelation leads to more realistic model output, as shown by signatures such as the flashiness index. Overall, this study contributes to a better description of residual errors of deterministic hydrological models.

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Indrawati, Luvera Deva Intan, Rina Dwi Indriana, and Irham Nurwidyanto. "Comparative Results of Regional and Residual Anomalies with the Upward Continuation, Moving Average, and Polynomial Methods for Magnetic Data." Journal of Physics and Its Applications 2, no. 2 (2020): 90–93. http://dx.doi.org/10.14710/jpa.v2i2.7673.

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Geophysics programing of regional and residual anomaly separation on Magnetic data has been carried out with the results compared with the upward continuation method in the OasisMontaj software. Separation of anomalies with moving average and polynomial methods is processed using Matlab programming. The orders used in the polynomial method are first-order, second-order and third-order. Comparison is done by calculating the match value. The chosen matching method is autocorrelation. Correlation of residual magnetic anomalies resulting from upward continuation (Magpick) to moving averages, 1st-order polynomials, 2nd-order polynomials and 3rd-order polynomials. Correlation values obtained for the moving average method are 0.9604, first order polynomial 0.9072, 2nd order polynomial 0.9482 and third order polynomial 0.6057. The moving average and second order polynomial methods can be used as a substitute method if we do not use the upward continuation method.

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Resende, Guilherme Mendes. "Spatial Dimensions of Economic Growth in Brazil." ISRN Economics 2013 (January 31, 2013): 1–19. http://dx.doi.org/10.1155/2013/398021.

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The contribution of this paper is to explore time and spatial scale dimensions of economic growth in Brazil using alternative panel data techniques to provide a measure of the extent of spatial autocorrelation (in kilometres) over three decades (1970–2000) as well as discussing the determinants of economic growth at a variety of geographic scales (minimum comparable areas, micro-regions, meso-regions, and states). The magnitude and statistical significance of growth determinants such as schooling, population density, population growth, and transportation costs are dependent on the scale of analysis. Moreover, the extent of residual spatial autocorrelation showed that it seems to vary across spatial scales. Indeed, spatial autocorrelation seems to be bounded at the state level and it shows positive and statistically significant values across distances of more than 1,500 kilometres at the other three spatial scales. Among other results, the study suggests that the nonspatial panel data techniques are not able to deal with spatially correlated omitted variables across different spatial scales, except for the state level where nonspatial panel data models seem to be appropriate to investigate growth determinants and convergence process in the Brazilian states case.

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SIN, CHOR-YIU. "QMLE OF A STANDARD EXPONENTIAL ACD MODEL: ASYMPTOTIC DISTRIBUTION AND RESIDUAL CORRELATION." Annals of Financial Economics 09, no. 02 (2014): 1440009. http://dx.doi.org/10.1142/s2010495214400090.

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Since the seminal work by Engle and Russell, (1998), numerous studies have applied their standard/linear ACD(m,q) model (autoregressive conditional duration model of orders m and q) to fit the irregular spaced transaction data. Recently, Araichi et al. (2013) also applied the ACD model to claims in insurance. Many of these papers assume that the standardized error follows a standard exponential distribution. In this paper, we derive the asymptotic distribution of the quasi-maximum likelihood estimator (QMLE) when a standard exponential distribution is used. In other words, we provide robust standard errors for an ACD model. Applying this asymptotic theory, we then derive the asymptotic distribution of the corresponding residual autocorrelation.

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Ubierna, Andrés, and Santiago Velilla. "A goodness-of-fit process for ARMA models based on a modified residual autocorrelation sequence." Journal of Statistical Planning and Inference 137, no. 9 (2007): 2903–19. http://dx.doi.org/10.1016/j.jspi.2006.10.006.

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Baek, Eun Kyeng, and John M. Ferron. "Multilevel models for multiple-baseline data: modeling across-participant variation in autocorrelation and residual variance." Behavior Research Methods 45, no. 1 (2012): 65–74. http://dx.doi.org/10.3758/s13428-012-0231-z.

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Lin, Ge, and Tonglin Zhang. "Loglinear Residual Tests of Moran's I Autocorrelation and their Applications to Kentucky Breast Cancer Data." Geographical Analysis 39, no. 3 (2007): 293–310. http://dx.doi.org/10.1111/j.1538-4632.2007.00705.x.

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Gilcher, Mario, Thorsten Ruf, Christoph Emmerling, and Thomas Udelhoven. "Remote Sensing Based Binary Classification of Maize. Dealing with Residual Autocorrelation in Sparse Sample Situations." Remote Sensing 11, no. 18 (2019): 2172. http://dx.doi.org/10.3390/rs11182172.

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In order to discuss potential sustainability issues of expanding silage maize cultivation in Rhineland-Palatinate, spatially explicit monitoring is necessary. Publicly available statistical records are often not a sufficient basis for extensive research, especially on soil health, where risk factors like erosion and compaction depend on variables that are specific to every site, and hard to generalize for larger administrative aggregates. The focus of this study is to apply established classification algorithms to estimate maize abundance for each independent pixel, while at the same time accounting for their spatial relationship. Therefore, two ways to incorporate spatial autocorrelation of neighboring pixels are combined with three different classification models. The performance of each of these modeling approaches is analyzed and discussed. Finally, one prediction approach is applied to the imagery, and the overall predicted acreage is compared to publicly available data. We were able to show that Support Vector Machine (SVM) classification and Random Forests (RF) were able to distinguish maize pixels reliably, with kappa values well above 0.9 in most cases. The Generalized Linear Model (GLM) performed substantially worse. Furthermore, Regression Kriging (RK) as an approach to integrate spatial autocorrelation into the prediction model is not suitable in use cases with millions of sparsely clustered training pixels. Gaussian Blur is able to improve predictions slightly in these cases, but it is possible that this is only because it smoothes out impurities of the reference data. The overall prediction with RF classification combined with Gaussian Blur performed well, with out of bag error rates of 0.5% in 2009 and 1.3% in 2016. Despite the low error rates, there is a discrepancy between the predicted acreage and the official records, which is 20% in 2009 and 27% in 2016.

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Shi, Feng, Yong-Seon Song, Jacobo Asorey, et al. "HIR4: cosmological signatures imprinted on the cross-correlation between a 21-cm map and galaxy clustering." Monthly Notices of the Royal Astronomical Society 499, no. 4 (2020): 4613–25. http://dx.doi.org/10.1093/mnras/staa2914.

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ABSTRACT We explore the cosmological multitracer synergies between an emission-line galaxy distribution from the Dark Energy Spectroscopic Instrument and a Tianlai Project 21-cm intensity map. We use simulated maps generated from a particle simulation in the light-cone volume (Horizon Run 4), sky-trimmed and including the effects of foreground contamination, its removal and instrument noise. We first validate how the foreground residual affects the recovered 21-cm signal by putting different levels of foreground contamination into the 21-cm maps. We find that the contamination cannot be ignored in the angular autocorrelation power spectra of H i even when it is small, but it has no influence on the accuracy of the angular cross-correlation power spectra between H i and galaxies. In the foreground-cleaned map case, as information is lost in the cleaning procedure, there is also a bias in the cross-correlation power spectrum. However, we found that the bias from the cross-correlation power spectrum is scale-independent, which is easily parametrized as part of the model, while the offset in the H i autocorrelation power spectrum is non-linear. In particular, we tested that the cross-correlation power also benefits from the cancellation of the bias in the power spectrum measurement that is induced by the instrument noise, which changes the shape of the autocorrelation power spectra but leaves the cross-correlation power spectra unaffected. We then modelled the angular cross-correlation power spectra to fit the baryon acoustic oscillation feature in the broad-band shape of the angular cross-correlation power spectrum, including contamination from the residual foreground and the effect of instrument noise. We forecast a constraint on the angular diameter distance DA for the Tianlai Pathfinder redshift 0.775 &lt; z &lt; 1.03, giving a distance measurement with a precision of 2.7 per cent at that redshift.

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Holmberg, Henrik, and Erling Häggström Lundevaller. "A test for robust detection of residual spatial autocorrelation with application to mortality rates in Sweden." Spatial Statistics 14 (November 2015): 365–81. http://dx.doi.org/10.1016/j.spasta.2015.07.001.

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Keele, Luke, and Nathan J. Kelly. "Dynamic Models for Dynamic Theories: The Ins and Outs of Lagged Dependent Variables." Political Analysis 14, no. 2 (2006): 186–205. http://dx.doi.org/10.1093/pan/mpj006.

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A lagged dependent variable in an OLS regression is often used as a means of capturing dynamic effects in political processes and as a method for ridding the model of autocorrelation. But recent work contends that the lagged dependent variable specification is too problematic for use in most situations. More specifically, if residual autocorrelation is present, the lagged dependent variable causes the coefficients for explanatory variables to be biased downward. We use a Monte Carlo analysis to assess empirically how much bias is present when a lagged dependent variable is used under a wide variety of circumstances. In our analysis, we compare the performance of the lagged dependent variable model to several other time series models. We show that while the lagged dependent variable is inappropriate in some circumstances, it remains an appropriate model for the dynamic theories often tested by applied analysts. From the analysis, we develop several practical suggestions on when and how to use lagged dependent variables on the right-hand side of a model.

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David, Hassan Camil, Rodrigo Otávio Veiga Miranda, John Welker, Luan Demarco Fiorentin, Ângelo Augusto Ebling, and Pedro Henrique Belavenutti Martins da Silva. "STRATEGIES FOR STEM MEASUREMENT SAMPLING: A STATISTICAL APPROACH OF MODELLING INDIVIDUAL TREE VOLUME." CERNE 22, no. 3 (2016): 249–60. http://dx.doi.org/10.1590/01047760201622032155.

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ABSTRACT The aim of this paper was to evaluate different criteria for stem measurement sampling and to identify the criterion with best performance for developing individual tree volume equations. Data were collected in eucalyptus stands 58 to 65 months old. Schumacher-Hall model was applied using five sampling criteria with nine variations (45 in total): 1) number of trees per diameter class, being (a) fixed number, (b) proportional to the diameter class of the sample, or (c) proportional to the standard deviation of the sample; and 2) the width of the diameter class, which ranged from 1.0 up to 5.0 cm. We used the equations generated from each of the five sampling criteria to estimate stem volume of trees reserved for validation. This allowed us to obtain standard errors of estimates from this data-set. In addition, residuals of volume estimates were examined by means of statistical tests of bias, autocorrelation and heteroscedasticity. Better performances of volume equations occurred when smaller diameter class widths were used, i.e., when the sample size increased. There was no clear trend in increasing/decreasing residual autocorrelation and/or heteroscedasticity. Both methods of sampling proportional to the frequency of diameter class had the best performances, inclusive using only 36 trees. The ones where choice of trees was proportional to the standard deviation had the worst. In conclusion, the selection proportional to the frequency of the diameter class, under the condition that at least two trees per class are sampled, provides models statistically better than all the other criteria.

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Pitman, Marshall K., Russell F. Briner, and John E. McEnroe. "The Impact Of FASB Statement No. 34s Disclosures On Stock Prices." Journal of Applied Business Research (JABR) 3, no. 1 (2011): 1. http://dx.doi.org/10.19030/jabr.v3i1.6541.

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This study provides empirical evidence that the disclosures required by FASB Statement No. 34 has an impact on common stock prices in the initial year of release, 1980, but not in subsequent year. Weekly data for 123 NYSE sample companies were used to estimate the regression coefficients via the GMM using a GLS with a lag of 3 due to the presence of autocorrelation. Statistical analysis of the average residual indicated that it was significantly different from zero. The evidence of this study supports the hypothesis that FASB 34 affected the capital market equilibrium via users reactions to the required disclosures.

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Xiao, Zhuolei, Yerong Zhang, Kaixuan Zhang, Dongxu Zhao, and Guan Gui. "GARLM: Greedy Autocorrelation Retrieval Levenberg–Marquardt Algorithm for Improving Sparse Phase Retrieval." Applied Sciences 8, no. 10 (2018): 1797. http://dx.doi.org/10.3390/app8101797.

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The goal of phase retrieval is to recover an unknown signal from the random measurements consisting of the magnitude of its Fourier transform. Due to the loss of the phase information, phase retrieval is considered as an ill-posed problem. Conventional greedy algorithms, e.g., greedy spare phase retrieval (GESPAR), were developed to solve this problem by using prior knowledge of the unknown signal. However, due to the defect of the Gauss–Newton method in the local convergence problem, especially when the residual is large, it is very difficult to use this method in GESPAR to efficiently solve the non-convex optimization problem. In order to improve the performance of the greedy algorithm, we propose an improved phase retrieval algorithm, which is called the greedy autocorrelation retrieval Levenberg–Marquardt (GARLM) algorithm. Specifically, the proposed GARLM algorithm is a local search iterative algorithm to recover the sparse signal from its Fourier transform magnitude. The proposed algorithm is preferred to existing greedy methods of phase retrieval, since at each iteration the problem of minimizing the objective function over a given support is solved by using the improved Levenberg–Marquardt (ILM) method and matrix transform. A local search procedure such as the 2-opt method is then invoked to get the optimal estimation. Simulation results are given to show that the proposed algorithm performs better than the conventional GESPAR algorithm.

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Journal articles on the topic 'Residual autocorrelation'

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