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1

Shapor, Maria Alexandrovna, and Rafael Rubenovich Gevogyan. "Features of the vector autoregression models application in macroeconomic research." Mezhdunarodnaja jekonomika (The World Economics), no. 8 (August 10, 2021): 634–49. http://dx.doi.org/10.33920/vne-04-2108-05.

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In this paper, we analyzed articles by foreign authors that use various vector autoregression models to calculate the impact of qualitative indicators on the economic processes of countries or a group of countries. In particular, the article analyzed the classical model of vector autoregression (VAR), panel model of autoregressive (PVAR), Bayesian model of autoregressive (BVAR), structural model of autoregressive (SVAR), and the global model of autoregressive (GVAR). Among the works using vector autoregressive models, the main emphasis is on financial indicators. Moreover, articles with non-trivial variables are rare. This is because financial macroeconomic variables in most cases have a direct impact on economic processes in the country. The analysis of financial indicators and the results obtained can play a significant role in the development of economic strategies in different states, since the results obtained with the help of vector autoregression models are usually quite accurate. The studied articles analyze the data of both developed and developing states or groups of states in different periods. The studied articles were classified according to several criteria, which were selected by the author to structure the work. Note that among the works using vector autoregressive models, the main emphasis is on financial indicators. Moreover, articles with non-trivial variables are rare. This is since financial macroeconomic variables in most cases have a direct impact on economic processes in the country. The analysis of financial indicators and the results obtained can play a significant role in the development of economic strategies in different states, since the results obtained with the help of vector autoregression models are usually quite accurate. In the conclusion of this study, the author presented conclusions based on the analysis of autoregressive models.
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Gurrib, Muhammad I., and Syed Z. Ahmad. "Saudi Arabia’s Inflation Agenda: A Vector Autoregressive Framework." International Journal of Trade, Economics and Finance 1, no. 1 (2010): 63–67. http://dx.doi.org/10.7763/ijtef.2010.v1.12.

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3

Lee, Youngsoo. "Interest rate and housing market: MS-VAR approach." Journal of Housing and Urban Finance 6, no. 1 (June 2021): 5–22. http://dx.doi.org/10.38100/jhuf.2021.6.1.5.

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4

Dufour, Jean-Marie. "Unbiasedness of Predictions from Etimated Vector Autoregressions." Econometric Theory 1, no. 3 (December 1985): 387–402. http://dx.doi.org/10.1017/s0266466600011270.

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Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds: specifically, if a vector autoregression of arbitrary finite order is fitted to a sample from any process in this class, the fitted model will produce unbiased forecasts, in the sense that the prediction errors have distributions symmetric about zero. Different numbers of lags may be used for each variable in each autoregression and variables may even be missing, without unbiasedness being affected. This property is exact in finite samples. Similarly, the residuals from the same autoregressions have distributions symmetric about zero.
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5

Wujung, Vukenkeng Andrew, and Mukete Emmanuel Mbella. "Entrepreneurship and poverty reduction in Cameroon: A Vector Autoregressive approach." Archives of Business Research 2, no. 5 (September 30, 2014): 1–11. http://dx.doi.org/10.14738/abr.25.345.

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6

Liao, Zhipeng, and Peter C. B. Phillips. "AUTOMATED ESTIMATION OF VECTOR ERROR CORRECTION MODELS." Econometric Theory 31, no. 3 (March 13, 2015): 581–646. http://dx.doi.org/10.1017/s026646661500002x.

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Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics. As such they offer considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. The paper develops the new methods, derives their limit theory, discusses implementation, reports simulations, and presents an empirical illustration with macroeconomic aggregates.
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7

Saikkonen, Pentti. "Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes." Econometric Reviews 18, no. 3 (January 1999): 235–57. http://dx.doi.org/10.1080/07474939908800444.

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8

Härdle, W., A. Tsybakov, and L. Yang. "Nonparametric vector autoregression." Journal of Statistical Planning and Inference 68, no. 2 (May 1998): 221–45. http://dx.doi.org/10.1016/s0378-3758(97)00143-2.

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9

Lanne, Markku, and Pentti Saikkonen. "NONCAUSAL VECTOR AUTOREGRESSION." Econometric Theory 29, no. 3 (November 12, 2012): 447–81. http://dx.doi.org/10.1017/s0266466612000448.

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In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of particular importance in economic applications that currently use only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. Therefore, we propose a procedure for discriminating between causality and noncausality. The methods are illustrated with an application to interest rate data.
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10

Zhu, Xuening, Rui Pan, Guodong Li, Yuewen Liu, and Hansheng Wang. "Network vector autoregression." Annals of Statistics 45, no. 3 (June 2017): 1096–123. http://dx.doi.org/10.1214/16-aos1476.

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11

Dhrymes, Phoebus J. "Autoregressive Errors in Singular Systems of Equations." Econometric Theory 10, no. 2 (June 1994): 254–85. http://dx.doi.org/10.1017/s0266466600008410.

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We consider a system of m general linear models, where the system error vector has a singular covariance matrix owing to various “adding up” requirements and, in addition, the error vector obeys an autoregressive scheme. The paper reformulates the problem considered earlier by Berndt and Savin [8] (BS), as well as others before them; the solution, thus obtained, is far simpler, being the natural extension of a restricted least-squares-like procedure to a system of equations. This reformulation enables us to treat all parameters symmetrically, and discloses a set of conditions which is different from, and much less stringent than, that exhibited in the framework provided by BS.Finally, various extensions are discussed to (a) the case where the errors obey a stable autoregression scheme of order r; (b) the case where the errors obey a moving average scheme of order r; (c) the case of “dynamic” vector distributed lag models, that is, the case where the model is formulated as autoregressive (in the dependent variables), and moving average (in the explanatory variables), and the errors are specified to be i.i.d.
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12

Euán, Carolina, and Ying Sun. "Bernoulli vector autoregressive model." Journal of Multivariate Analysis 177 (May 2020): 104599. http://dx.doi.org/10.1016/j.jmva.2020.104599.

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13

Davis, Richard A., Pengfei Zang, and Tian Zheng. "Sparse Vector Autoregressive Modeling." Journal of Computational and Graphical Statistics 25, no. 4 (October 1, 2016): 1077–96. http://dx.doi.org/10.1080/10618600.2015.1092978.

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14

Luukkonen, Ritva, Antti Ripatti, and Pentti Saikkonen. "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes." Journal of Business & Economic Statistics 17, no. 2 (April 1999): 195. http://dx.doi.org/10.2307/1392475.

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15

Luukkonen, Ritva, Antti Ripatti, and Pentti Saikkonen. "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes." Journal of Business & Economic Statistics 17, no. 2 (April 1999): 195–204. http://dx.doi.org/10.1080/07350015.1999.10524810.

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16

Johansen, Soren. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models." Econometrica 59, no. 6 (November 1991): 1551. http://dx.doi.org/10.2307/2938278.

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17

Franchi, Massimo, and Paolo Paruolo. "Cointegration, Root Functions and Minimal Bases." Econometrics 9, no. 3 (August 17, 2021): 31. http://dx.doi.org/10.3390/econometrics9030031.

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This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of polynomial vectors over complex scalars, (ii) as a free module of polynomial vectors over scalar polynomials, or finally (iii) as a vector space of rational vectors over rational scalars. Third, it shows that a canonical set of root functions can be used as a basis of the various notions of cointegrating space. Fourth, it reviews results on how to reduce polynomial bases to minimal order—i.e., minimal bases. The application of these results to Vector AutoRegressive processes integrated of order 2 is found to imply the separation of polynomial cointegrating vectors from non-polynomial ones.
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18

Buldygin, V. V., and V. A. Koval. "Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes." gmj 8, no. 2 (June 2001): 221–30. http://dx.doi.org/10.1515/gmj.2001.221.

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Abstract The problems of almost sure convergence to zero and almost sure boundedness of operator-normed sums of different sequences of random vectors are studied. The sequences of independent random vectors, orthogonal random vectors and the sequences of vector-valued martingale-differences are considered. General results are applied to the problem of asymptotic behaviour of multidimensional autoregression processes.
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19

Chen, Cathy W. S., and L. M. Chiu. "Ordinal Time Series Forecasting of the Air Quality Index." Entropy 23, no. 9 (September 4, 2021): 1167. http://dx.doi.org/10.3390/e23091167.

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This research models and forecasts daily AQI (air quality index) levels in 16 cities/counties of Taiwan, examines their AQI level forecast performance via a rolling window approach over a one-year validation period, including multi-level forecast classification, and measures the forecast accuracy rates. We employ statistical modeling and machine learning with three weather covariates of daily accumulated precipitation, temperature, and wind direction and also include seasonal dummy variables. The study utilizes four models to forecast air quality levels: (1) an autoregressive model with exogenous variables and GARCH (generalized autoregressive conditional heteroskedasticity) errors; (2) an autoregressive multinomial logistic regression; (3) multi-class classification by support vector machine (SVM); (4) neural network autoregression with exogenous variable (NNARX). These models relate to lag-1 AQI values and the previous day’s weather covariates (precipitation and temperature), while wind direction serves as an hour-lag effect based on the idea of nowcasting. The results demonstrate that autoregressive multinomial logistic regression and the SVM method are the best choices for AQI-level predictions regarding the high average and low variation accuracy rates.
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20

Balatskiy, E. V., and M. A. Yurevich. "Inflation Forecasting: The Practice of Using Synthetic Procedures." World of new economy 12, no. 4 (June 3, 2019): 20–31. http://dx.doi.org/10.26794/2220-6469-2018-12-4-20-31.

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The article contains a review of inflation forecasting models, including the most popular class of models as one-factor models: random walk, direct autoregression, recursive autoregression, stochastic volatility with an unobserved component and of the integrated model of autoregression with moving average. Also, we discussed the possibilities of various modifications of models based on the Phillips curve (including the “triangle model”), vector autoregressive models (including the factor-extended model of B. Bernanke’s vector autoregression), dynamic general equilibrium models and neural networks. Further, we considered the comparative advantages of these classes of models. In particular, we revealed a new trend in inflation forecasting, which consists of the introduction of synthetic procedures for private forecasts accounting obtained by different models. An important conclusion of the study is the superiority of expert assessments in comparison with all available models. We have shown that in the conditions of a large number of alternative methods of inflation modelling, the choice of the adequate approach in specific conditions (for example, for the Russian economy of the current period) is a non-trivial procedure. Based on this conclusion, the authors substantiate the thesis that large prognostic possibilities are inherent in the mixed strategies of using different methodological approaches, when implementing different modelling tools at different stages of modelling, in particular, the multifactorial econometric model and the artificial neural network.
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21

Kalliovirta, Leena, Mika Meitz, and Pentti Saikkonen. "Gaussian mixture vector autoregression." Journal of Econometrics 192, no. 2 (June 2016): 485–98. http://dx.doi.org/10.1016/j.jeconom.2016.02.012.

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22

Lanne, Markku, and Jani Luoto. "Noncausal Bayesian Vector Autoregression." Journal of Applied Econometrics 31, no. 7 (January 8, 2016): 1392–406. http://dx.doi.org/10.1002/jae.2497.

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23

Feifei, Wang, Zhu Xuening, and Pan Rui. "Generalized network vector autoregression." SCIENTIA SINICA Mathematica 51, no. 8 (July 9, 2020): 1253. http://dx.doi.org/10.1360/scm-2018-0839.

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24

Grynkiv, Galyna, and Lars Stentoft. "Stationary Threshold Vector Autoregressive Models." Journal of Risk and Financial Management 11, no. 3 (August 5, 2018): 45. http://dx.doi.org/10.3390/jrfm11030045.

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This paper examines the steady state properties of the Threshold Vector Autoregressive model. Assuming that the trigger variable is exogenous and the regime process follows a Bernoulli distribution, necessary and sufficient conditions for the existence of stationary distribution are derived. A situation related to so-called “locally explosive models”, where the stationary distribution exists though the model is explosive in one regime, is analysed. Simulations show that locally explosive models can generate some of the key properties of financial and economic data. They also show that assessing the stationarity of threshold models based on simulations might well lead to wrong conclusions.
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25

Kalli, Maria, and Jim E. Griffin. "Bayesian nonparametric vector autoregressive models." Journal of Econometrics 203, no. 2 (April 2018): 267–82. http://dx.doi.org/10.1016/j.jeconom.2017.11.009.

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26

Li, Xuedi, Jie Ma, Zhu Chen, and Haitao Zheng. "Linkage Analysis among China’s Seven Emissions Trading Scheme Pilots." Sustainability 10, no. 10 (September 23, 2018): 3389. http://dx.doi.org/10.3390/su10103389.

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This paper focuses on the time-varying correlation among China’s seven emissions trading scheme markets. Correlation analysis shows a weak connection among these markets for the whole sample period, which spans from 9 June 2014 to 30 June 2017. The return rate series of the seven markets show the characteristics of a fat-tailed and skewed distribution, and the Vector Autoregression (VAR) residuals present a significant Autoregressive Conditional Heteroscedasticity (ARCH) effect. Therefore, we adopt Vector Autoregression Generalized ARCH model with Dynamic Conditional Correlation (VAR-DCC-GARCH) to capture the time-varying correlation coefficients. The results of the VAR-DCC-GARCH show that the conditional correlation coefficients fluctuate fiercely over time. At some points, the different markets present a significant correlation with the value of the even peaks of the coefficient at 0.8, which indicates that these markets are closely connected. However, the connection between each market does not last long. According to the actual situation of China’s regional carbon emission markets, policy factors may explain most of the temporary, significant co-movement among markets.
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Gupta, Shashi, Himanshu Choudhary, and D. R. Agarwal. "Hedging Efficiency of Indian Commodity Futures." Paradigm 21, no. 1 (June 2017): 1–20. http://dx.doi.org/10.1177/0971890717700529.

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This article examines the hedge ratio and hedging effectiveness in agricultural (castor seed, guar seed) and non-agricultural (copper, nickel, gold, silver, natural gas and crude oil) commodities traded in National Commodity and Derivative Exchange (NCDEX) and Multi Commodity Exchange (MCX), respectively. Constant and dynamic hedge ratios are estimated by using ordinary least square (OLS), vector autoregression (VAR), vector error correction model (VECM) and vector autoregressive-multivariate generalized autoregressive conditional heteroskedasticity model (VAR-MGARCH). The results of constant as well as dynamic hedge ratios reveal that the Indian futures market provides higher hedging effectiveness in case of precious metal (65–75 per cent) compared to industrial metal and energy commodities (less than 50 per cent). Hedging effectiveness for castor seed and natural gas is even lower than 10 per cent. This study concluded that VECM and VAR-MGARCH both are providing higher hedging although VECM is providing the highest hedge ratio. It has been found that the next to near month futures provide better hedging effectiveness as compared to near month futures for crude oil and silver. It is recommended that the policy makers should pay attention towards the number of delivery centres, standard of quality of underlying assets and transaction costs in spot market.
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Jiang, Han, Yajie Zou, Shen Zhang, Jinjun Tang, and Yinhai Wang. "Short-Term Speed Prediction Using Remote Microwave Sensor Data: Machine Learning versus Statistical Model." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/9236156.

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Recently, a number of short-term speed prediction approaches have been developed, in which most algorithms are based on machine learning and statistical theory. This paper examined the multistep ahead prediction performance of eight different models using the 2-minute travel speed data collected from three Remote Traffic Microwave Sensors located on a southbound segment of 4th ring road in Beijing City. Specifically, we consider five machine learning methods: Back Propagation Neural Network (BPNN), nonlinear autoregressive model with exogenous inputs neural network (NARXNN), support vector machine with radial basis function as kernel function (SVM-RBF), Support Vector Machine with Linear Function (SVM-LIN), and Multilinear Regression (MLR) as candidate. Three statistical models are also selected: Autoregressive Integrated Moving Average (ARIMA), Vector Autoregression (VAR), and Space-Time (ST) model. From the prediction results, we find the following meaningful results: (1) the prediction accuracy of speed deteriorates as the prediction time steps increase for all models; (2) the BPNN, NARXNN, and SVM-RBF can clearly outperform two traditional statistical models: ARIMA and VAR; (3) the prediction performance of ANN is superior to that of SVM and MLR; (4) as time step increases, the ST model can consistently provide the lowest MAE comparing with ARIMA and VAR.
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29

Durbin, J. "Approximate distributions of Student's t-statistics for autoregressive coefficients calculated from regression residuals." Journal of Applied Probability 23, A (1986): 173–85. http://dx.doi.org/10.2307/3214351.

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We consider a multiple regression model in which the regressors are Fourier cosine vectors. These regressors are intended as approximations to ‘slowly changing' regressors of the kind often found in time series regression applications. The errors in the model are assumed to be generated by a special type of autoregressive model defined so that the regressors are eigenvectors of the quadratic forms occurring in the exponent of the probability density of the errors. This autoregression is intended as an approximation to the usual stationary autoregression. Both approximations are adopted for the sake of mathematical convenience.Student's t-statistics are constructed for the autoregressive coefficients in a manner analogous to ordinary regression. It is shown that these statistics are distributed as Student's t to the first order of approximation, that is with errors in the density of order T−1/2, where T is the sample size, while the squares of the statistics are distributed as the square of Student's t to the second order of approximation, that is with errors in the density of order Τ–1.
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30

Durbin, J. "Approximate distributions of Student's t-statistics for autoregressive coefficients calculated from regression residuals." Journal of Applied Probability 23, A (1986): 173–85. http://dx.doi.org/10.1017/s0021900200117061.

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We consider a multiple regression model in which the regressors are Fourier cosine vectors. These regressors are intended as approximations to ‘slowly changing' regressors of the kind often found in time series regression applications. The errors in the model are assumed to be generated by a special type of autoregressive model defined so that the regressors are eigenvectors of the quadratic forms occurring in the exponent of the probability density of the errors. This autoregression is intended as an approximation to the usual stationary autoregression. Both approximations are adopted for the sake of mathematical convenience. Student's t-statistics are constructed for the autoregressive coefficients in a manner analogous to ordinary regression. It is shown that these statistics are distributed as Student's t to the first order of approximation, that is with errors in the density of order T −1/2, where T is the sample size, while the squares of the statistics are distributed as the square of Student's t to the second order of approximation, that is with errors in the density of order Τ –1.
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31

Pradhan, Kailash. "The Hedging Effectiveness of Stock Index Futures: Evidence for the S&P CNX Nifty Index Traded in India." South East European Journal of Economics and Business 6, no. 1 (April 1, 2011): 111–23. http://dx.doi.org/10.2478/v10033-011-0010-2.

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The Hedging Effectiveness of Stock Index Futures: Evidence for the S&P CNX Nifty Index Traded in IndiaThis study evaluates optimal hedge ratios and the hedging effectiveness of stock index futures. The optimal hedge ratios are estimated from the ordinary least square (OLS) regression model, the vector autoregression model (VAR), the vector error correction model (VECM) and multivariate generalized autoregressive conditional heteroskedasticity (M-GARCH) models such as VAR-GARCH and VEC-GARCH using the S&P CNX Nifty index and its futures index. Hedging effectiveness is measured in terms of within sample and out of sample risk-return trade-off at various forecasting horizons. The analysis found that the VEC-GARCH time varying hedge ratio provides the greatest portfolio risk reduction and generates the highest portfolio returns.
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LAZARIU, VICTORIA, CHENGXUAN YU, and CRAIG GUNDERSEN. "FORECASTING WOMEN, INFANTS, AND CHILDREN CASELOADS: A COMPARISON OF VECTOR AUTOREGRESSION AND AUTOREGRESSIVE INTEGRATED MOVING AVERAGE APPROACHES." Contemporary Economic Policy 29, no. 1 (January 2011): 46–55. http://dx.doi.org/10.1111/j.1465-7287.2010.00203.x.

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33

Elbourne, Adam, and Jakob de Haan. "Modeling Monetary Policy Transmission in Acceding Countries: Vector Autoregression Versus Structural Vector Autoregression." Emerging Markets Finance and Trade 45, no. 2 (March 2009): 4–20. http://dx.doi.org/10.2753/ree1540-496x450201.

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34

Nielsen, Bent. "ANALYSIS OF COEXPLOSIVE PROCESSES." Econometric Theory 26, no. 3 (October 7, 2009): 882–915. http://dx.doi.org/10.1017/s0266466609990144.

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A vector autoregressive model allowing for unit roots as well as an explosive characteristic root is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Cointegrating and coexplosive vectors can be found that eliminate these common factors. The likelihood ratio test for a simple hypothesis on the coexplosive vectors is analyzed. The method is illustrated using data from the extreme Yugoslavian hyperinflation of the 1990s.
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35

Li, Yuanyuan, and Dietmar Bauer. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size." Econometrics 8, no. 3 (September 17, 2020): 38. http://dx.doi.org/10.3390/econometrics8030038.

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In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size. We deal with unrestricted OLS estimators (in the model formulated in levels as well as in vector error correction form) as well as with two stage estimation (2SI2) in the vector error correction model (VECM) formulation. Our main results are analogous to the I(1) case: We show that the long VAR approximation leads to consistent estimates of the long and short run dynamics. Furthermore, tests on the autoregressive coefficients follow standard asymptotics. The pseudo likelihood ratio tests on the cointegrating ranks (using the Gaussian likelihood) used in the 2SI2 algorithm show under the null hypothesis the same distributions as in the case of data generating processes following finite order VARs. The same holds true for the asymptotic distribution of the long run dynamics both in the unrestricted VECM estimation and the reduced rank regression in the 2SI2 algorithm. Building on these results we show that if the data is generated by an invertible VARMA process, the VAR approximation can be used in order to derive a consistent initial estimator for subsequent pseudo likelihood optimization in the VARMA model.
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36

Zarepour, M., and S. M. Roknossadati. "MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS." Econometric Theory 24, no. 3 (January 22, 2008): 677–95. http://dx.doi.org/10.1017/s0266466608080286.

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We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases.
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37

Harris, David. "Principal Components Analysis of Cointegrated Time Series." Econometric Theory 13, no. 4 (February 1997): 529–57. http://dx.doi.org/10.1017/s0266466600005995.

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This paper considers the analysis of cointegrated time series using principal components methods. These methods have the advantage of requiring neither the normalization imposed by the triangular error correction model nor the specification of a finite-order vector autoregression. An asymptotically efficient estimator of the cointegrating vectors is given, along with tests forcointegration and tests of certain linear restrictions on the cointegrating vectors. An illustrative application is provided.
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38

Tsuji, Chikashi. "Exploring Return Transmission in Asian Stock Markets." Journal of Management Research 11, no. 4 (October 8, 2019): 48. http://dx.doi.org/10.5296/jmr.v11i4.15533.

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This paper investigates the return transmission between four Asian stock markets in Japan, China, Korea, and Taiwan. Specifically, applying a vector autoregression (VAR) model, this study derives the following interesting findings and interpretations. First, our results reveal that (1) rapid cross-country and autoregressive return transmission between the four Asian stock markets recently decreased, and (2) recently, the effects from the Japanese stock market to the other three Asian stock markets became weaker. Furthermore, our results clarify that (3) the return transmission effect from the Chinese stock market to the other three Asian stock markets is generally weak, also meaning that the Chinese stock market evolves autonomously.
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39

Wang, Lei, and Shanshan Ding. "Vector autoregression and envelope model." Stat 7, no. 1 (2018): e203. http://dx.doi.org/10.1002/sta4.203.

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Zhu, Huafeng, Xingfa Zhang, Xin Liang, and Yuan Li. "On a vector double autoregressive model." Statistics & Probability Letters 129 (October 2017): 86–95. http://dx.doi.org/10.1016/j.spl.2017.05.002.

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41

Fischer, A., and Heinz Luck. "Vector Autoregressive Modelling Of Fire Signals." Fire Safety Science 4 (1994): 727–38. http://dx.doi.org/10.3801/iafss.fss.4-727.

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42

Mussard, Stéphane, and Oumar Hamady Ndiaye. "Vector autoregressive models: A Gini approach." Physica A: Statistical Mechanics and its Applications 492 (February 2018): 1967–79. http://dx.doi.org/10.1016/j.physa.2017.11.111.

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43

de Waele, S., and P. M. T. Broersen. "Order selection for vector autoregressive models." IEEE Transactions on Signal Processing 51, no. 2 (February 2003): 427–33. http://dx.doi.org/10.1109/tsp.2002.806905.

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44

Saikkonen, Pentti, and HELMUT Lütkepohl. "Infinite-Order Cointegrated Vector Autoregressive Processes." Econometric Theory 12, no. 5 (December 1996): 814–44. http://dx.doi.org/10.1017/s0266466600007179.

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Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.
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45

Broersen, P. M. T. "Vector Autoregressive Order Selection in Practice." IEEE Transactions on Instrumentation and Measurement 58, no. 8 (August 2009): 2565–73. http://dx.doi.org/10.1109/tim.2009.2015631.

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46

Ni, Shawn, and Dongchu Sun. "Bayesian Estimates for Vector Autoregressive Models." Journal of Business & Economic Statistics 23, no. 1 (January 2005): 105–17. http://dx.doi.org/10.1198/073500104000000622.

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47

Lütkepohl, Helmut. "Estimation of structural vector autoregressive models." Communications for Statistical Applications and Methods 24, no. 5 (September 30, 2017): 421–41. http://dx.doi.org/10.5351/csam.2017.24.5.421.

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48

Fong, P. W., W. K. Li, C. W. Yau, and C. S. Wong. "On a mixture vector autoregressive model." Canadian Journal of Statistics 35, no. 1 (March 2007): 135–50. http://dx.doi.org/10.1002/cjs.5550350112.

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49

Meyer, Marco, and Jens-Peter Kreiss. "On the Vector Autoregressive Sieve Bootstrap." Journal of Time Series Analysis 36, no. 3 (September 17, 2014): 377–97. http://dx.doi.org/10.1111/jtsa.12090.

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50

Chapman, David, Mark A. Cane, Naomi Henderson, Dong Eun Lee, and Chen Chen. "A Vector Autoregressive ENSO Prediction Model." Journal of Climate 28, no. 21 (October 30, 2015): 8511–20. http://dx.doi.org/10.1175/jcli-d-15-0306.1.

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Abstract The authors investigate a sea surface temperature anomaly (SSTA)-only vector autoregressive (VAR) model for prediction of El Niño–Southern Oscillation (ENSO). VAR generalizes the linear inverse method (LIM) framework to incorporate an extended state vector including many months of recent prior SSTA in addition to the present state. An SSTA-only VAR model implicitly captures subsurface forcing observable in the LIM residual as red noise. Optimal skill is achieved using a state vector of order 14–17 months in an exhaustive 120-yr cross-validated hindcast assessment. It is found that VAR outperforms LIM, increasing forecast skill by 3 months, in a 30-yr retrospective forecast experiment.
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