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Journal articles on the topic 'Nonlinear econometric'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Andersen, Torben G. "SIMULATION-BASED ECONOMETRIC METHODS." Econometric Theory 16, no. 1 (February 2000): 131–38. http://dx.doi.org/10.1017/s0266466600001080.

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The accessibility of high-performance computing power has always influenced theoretical and applied econometrics. Gouriéroux and Monfort begin their recent offering, Simulation-Based Econometric Methods, with a stylized three-stage classification of the history of statistical econometrics. In the first stage, lasting through the 1960's, models and estimation methods were designed to produce closed-form expressions for the estimators. This spurred thorough investigation of the standard linear model, linear simultaneous equations with the associated instrumental variable techniques, and maximum likelihood estimation within the exponential family. During the 1970's and 1980's the development of powerful numerical optimization routines led to the exploration of procedures without closed-form solutions for the estimators. During this period the general theory of nonlinear statistical inference was developed, and nonlinear micro models such as limited dependent variable models and nonlinear time series models, e.g., ARCH, were explored. The associated estimation principles included maximum likelihood (beyond the exponential family), pseudo-maximum likelihood, nonlinear least squares, and generalized method of moments. Finally, the third stage considers problems without a tractable analytic criterion function. Such problems almost invariably arise from the need to evaluate high-dimensional integrals. The idea is to circumvent the associated numerical problems by a simulation-based approach. The main requirement is therefore that the model may be simulated given the parameters and the exogenous variables. The approach delivers simulated counterparts to standard estimation procedures and has inspired the development of entirely new procedures based on the principle of indirect inference.

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2

Peng, Jiangyan, and Qiying Wang. "WEAK CONVERGENCE TO STOCHASTIC INTEGRALS UNDER PRIMITIVE CONDITIONS IN NONLINEAR ECONOMETRIC MODELS." Econometric Theory 34, no. 5 (October 26, 2017): 1132–57. http://dx.doi.org/10.1017/s0266466617000408.

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Limit theory with stochastic integrals plays a major role in time series econometrics. In earlier contributions on weak convergence to stochastic integrals, the literature commonly uses martingale and semi-martingale structures. Liang, Phillips, Wang, and Wang (2016) (see also Wang (2015), Chap. 4.5) currently extended weak convergence to stochastic integrals by allowing for a linear process or a α-mixing sequence in innovations. While these martingale, linear process and α-mixing structures have wide relevance, they are not sufficiently general to cover many econometric applications that have endogeneity and nonlinearity. This paper provides new conditions for weak convergence to stochastic integrals. Our frameworks allow for long memory processes, causal processes, and near-epoch dependence in innovations, which have applications in a wide range of econometric areas such as TAR, bilinear, and other nonlinear models.

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3

Franke, Jurgen, Benedikt M. Potscher, and Ingmar R. Prucha. "Dynamic Nonlinear Econometric Models: Asymptotic Theory." Journal of the American Statistical Association 94, no. 446 (June 1999): 652. http://dx.doi.org/10.2307/2670192.

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4

de Jong, Robert M. "DYNAMIC NONLINEAR ECONOMETRIC MODELS—ASYMPTOTIC THEORY." Econometric Theory 16, no. 1 (February 2000): 127–30. http://dx.doi.org/10.1017/s0266466600001079.

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Benedikt Pötscher and Ingmar Prucha are two exceptional econometricians who combine an extraordinary knowledge of the statistics and econometrics literature with great analytical skills. Both are excellent mathematicians, and the comment that can be heard among mathematicians that econometricians are “self-made mathematicians” definitely does not apply to them. Therefore, given the task of writing an overview of asymptotic theory for minimization estimators for dependent processes, one could hardly imagine a better choice of writers for such a task. The result is a remarkable book that deserves to receive attention from an audience that is broader than experts in the field only.

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5

Mariano and Brown. "Stochastic Prediction in Dynamic Nonlinear Econometric Systems." Annales de l'inséé, no. 59/60 (1985): 267. http://dx.doi.org/10.2307/20076566.

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6

Andrews, Donald W. K., and C. John McDermott. "Nonlinear Econometric Models with Deterministically Trending Variables." Review of Economic Studies 62, no. 3 (July 1995): 343. http://dx.doi.org/10.2307/2298032.

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7

Schineller, Lisa M. "A Nonlinear Econometric Analysis of Capital Flight." International Finance Discussion Paper 1997, no. 594 (October 1997): 1–38. http://dx.doi.org/10.17016/ifdp.1997.594.

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8

Andrews, Isaiah, and Anna Mikusheva. "A Geometric Approach to Nonlinear Econometric Models." Econometrica 84, no. 3 (2016): 1249–64. http://dx.doi.org/10.3982/ecta12030.

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9

Schwiebert, Jörg. "A detailed decomposition for nonlinear econometric models." Journal of Economic Inequality 13, no. 1 (November 29, 2014): 53–67. http://dx.doi.org/10.1007/s10888-014-9291-x.

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10

Andrews, Donald W. K., and Ray C. Fair. "Inference in Nonlinear Econometric Models with Structural Change." Review of Economic Studies 55, no. 4 (October 1988): 615. http://dx.doi.org/10.2307/2297408.

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11

Padoan, Pier Carlo. "Nonlinear simulation analysis in continuous time econometric models." Computers & Mathematics with Applications 24, no. 8-9 (October 1992): 57–65. http://dx.doi.org/10.1016/0898-1221(92)90187-m.

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12

Ibragimov, Rustam, and Peter C. B. Phillips. "REGRESSION ASYMPTOTICS USING MARTINGALE CONVERGENCE METHODS." Econometric Theory 24, no. 4 (April 4, 2008): 888–947. http://dx.doi.org/10.1017/s0266466608080365.

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Weak convergence of partial sums and multilinear forms in independent random variables and linear processes and their nonlinear analogues to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and conceptually simple method for obtaining such forms of convergence. The method relies on the fact that the econometric quantities of interest involve discrete time martingales or semimartingales and shows how in the limit these quantities become continuous martingales and semimartingales. The limit theory itself uses very general convergence results for semimartingales that were obtained in the work of Jacod and Shiryaev (2003, Limit Theorems for Stochastic Processes). The theory that is developed here is applicable in a wide range of econometric models, and many examples are given. %One notable outcome of the new approach is that it provides a unified treatment of the asymptotics for stationary, explosive, unit root, and local to unity autoregression, and also some general nonlinear time series regressions. All of these cases are subsumed within the martingale convergence approach, and different rates of convergence are accommodated in a natural way. Moreover, the results on multivariate extensions developed in the paper deliver a unification of the asymptotics for, among many others, models with cointegration and also for regressions with regressors that are nonlinear transforms of integrated time series driven by shocks correlated with the equation errors. Because this is the first time the methods have been used in econometrics, the exposition is presented in some detail with illustrations of new derivations of some well-known existing results, in addition to the provision of new results and the unification of the limit theory for autoregression.

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13

Zhou, Hong Yan. "Nonlinear Econometric Model of Electronic Products and its Application." Applied Mechanics and Materials 596 (July 2014): 114–18. http://dx.doi.org/10.4028/www.scientific.net/amm.596.114.

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Digital product development is very rapid, this paper use engineering method to establish electronic product development model, and use Shift-share method to analysis decompose the economic capacity of the electronics industry, with the high level of industrial economic quantity Comparative analysis of the overall strength of the digital industry. Shift-share model with a comprehensive economic assessment, and put forward development proposals of corresponding electronic products.

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14

Chang, Yoosoon, Joon Y. Park, and Peter C. B. Phillips. "Nonlinear econometric models with cointegrated and deterministically trending regressors." Econometrics Journal 4, no. 1 (June 1, 2001): 1–36. http://dx.doi.org/10.1111/1368-423x.00054.

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15

Lilien, David M. "Econometric software reliability and nonlinear estimation in EViews: comment." Journal of Applied Econometrics 15, no. 1 (January 2000): 107–10. http://dx.doi.org/10.1002/(sici)1099-1255(200001/02)15:1<107::aid-jae554>3.0.co;2-4.

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16

Kunz, Johannes S., and Rainer Winkelmann. "An Econometric Model of Healthcare Demand With Nonlinear Pricing." Health Economics 26, no. 6 (April 4, 2016): 691–702. http://dx.doi.org/10.1002/hec.3343.

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17

Liao, Ruofan, Paravee Maneejuk, and Songsak Sriboonchitta. "Beyond Deep Learning: An Econometric Example." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, Supp01 (August 28, 2020): 31–38. http://dx.doi.org/10.1142/s0218488520400036.

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In the past, in many areas, the best prediction models were linear and nonlinear parametric models. In the last decade, in many application areas, deep learning has shown to lead to more accurate predictions than the parametric models. Deep learning-based predictions are reasonably accurate, but not perfect. How can we achieve better accuracy? To achieve this objective, we propose to combine neural networks with parametric model: namely, to train neural networks not on the original data, but on the differences between the actual data and the predictions of the parametric model. On the example of predicting currency exchange rate, we show that this idea indeed leads to more accurate predictions.

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18

Christopeit, Norbert. "WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE." Econometric Theory 25, no. 5 (October 2009): 1180–207. http://dx.doi.org/10.1017/s0266466608090476.

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We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

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19

Wolak, Frank A. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models." Econometric Theory 5, no. 1 (April 1989): 1–35. http://dx.doi.org/10.1017/s0266466600012238.

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This paper considers a general nonlinear econometric model framework that contains a large class of estimators defined as solutions to optimization problems. For this framework we derive several asymptotically equivalent forms of a test statistic for the local (in a way made precise in the paper) multivariate nonlinear inequality constraints test H: h(β) ≥ 0 versus K: β ∈ RK. We extend these results to consider local hypotheses tests of the form H: h1(β) ≥ 0 and h2(β) = 0 versus K: β ∈ RK. For each test we derive the asymptotic distribution for any size test as a weighted sum of χ2-distributions. We contrast local as opposed to global inequality constraints testing and give conditions on the model and constraints when each is possible. This paper also extends the well-known duality results in testing multivariate equality constraints to the case of nonlinear multivariate inequality constraints and combinations of nonlinear inequality and equality constraints.

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20

Wachowiak, Mark P., Renata Wachowiak-Smolíková, and Dušan Smolík. "Parameter estimation of nonlinear econometric models using particle swarm optimization." Ekonomická revue - Central European Review of Economic Issues 13, no. 1 (December 31, 2010): 193–200. http://dx.doi.org/10.7327/cerei.2010.12.01.

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21

Bucci, Andrea. "Realized Volatility Forecasting with Neural Networks." Journal of Financial Econometrics 18, no. 3 (2020): 502–31. http://dx.doi.org/10.1093/jjfinec/nbaa008.

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Abstract In the last few decades, a broad strand of literature in finance has implemented artificial neural networks as a forecasting method. The major advantage of this approach is the possibility to approximate any linear and nonlinear behaviors without knowing the structure of the data generating process. This makes it suitable for forecasting time series which exhibit long-memory and nonlinear dependencies, like conditional volatility. In this article, the predictive performance of feed-forward and recurrent neural networks (RNNs) was compared, particularly focusing on the recently developed long short-term memory (LSTM) network and nonlinear autoregressive model process with eXogenous input (NARX) network, with traditional econometric approaches. The results show that RNNs are able to outperform all the traditional econometric methods. Additionally, capturing long-range dependence through LSTM and NARX models seems to improve the forecasting accuracy also in a highly volatile period.

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22

Zhou, Huan, Shaojian Qu, Qinglu Yuan, and Shilei Wang. "Spatial Effects and Nonlinear Analysis of Energy Consumption, Financial Development, and Economic Growth in China." Energies 13, no. 18 (September 22, 2020): 4982. http://dx.doi.org/10.3390/en13184982.

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Energy consumption is of great significance to the sustainable development of the economy. Due to the spatial heterogeneity of low-carbon growth in regional economies, the relationship between energy consumption and economic growth is complicated. However, a few researches have been published about spatial spillover effects and non-linearity of energy consumption and financial development on regional economic growth in China. Based on the panel data of 30 provinces in China from 2007 to 2017, this paper analyzes the spatial spillover effects and threshold effects of energy consumption and financial development on regional economic growth by using spatial and nonlinear econometric methods. The main conclusions are as follows. Spatial econometric methods show that financial development and energy consumption are two factors of production input to promote China’s economic growth. Meanwhile, energy consumption and financial development have spillover effects on regional economic growth. Additionally, the nonlinear econometric method finds that with increasing financial development, the impact of energy consumption on economic growth is segmented. Therefore, relevant policies should be implemented to enhance the role of finance in energy consumption to promote low-carbon growth of China’s economy.

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23

Roljic, Lazo. "An expert system for national economy model simulations." Yugoslav Journal of Operations Research 12, no. 2 (2002): 247–69. http://dx.doi.org/10.2298/yjor0202247r.

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There are some fundamental economic uncertainties. We cannot forecast economic events with a very high scientific precision. It is very clear that there does not exist a unique 'general' model, which can yield all answers to a wide range of macroeconomic issues. Therefore, we use several different kinds of models on segments of the macroeconomic problem. Different models can distinguish/solve economy desegregation, time series analysis and other subfactors involved in macroeconomic problem solving. A major issue becomes finding a meaningful method to link these econometric models. Macroeconomic models were linked through development of an Expert System for National Economy Model Simulations (ESNEMS). ESNEMS consists of five parts: (1) small-scale short-term national econometric model, (2) Methodology of Interactive Nonlinear Goal Programming (MINGP), (3) data-base of historical macro-economic aggregates, (4) software interface for interactive communications between a model and a decision maker, and (5) software for solving problems. ESNEMS was developed to model the optimum macro-economic policy of a developing country (SFRY-formerly Yugoslavia). Most econometric models are very complex. Optimizing of the economic policy is typically defined as a nonlinear goal programming problem. To solve/optimize these models, a new methodology, MINGP, was developed as a part of ESNEMS. MINGP is methodologically based on linear goal programming and feasible directions method. Using Euler's Homogeneous Function Theorem, MINGP linearizes nonlinear homogeneous functions. The highest priorities in minimizing the objective function are the growth of gross domestic product and the decrease of inflation. In the core of the optimization model, MINGP, there is a small-scale econometric model. This model was designed through analysis of the causal relations in the SFRY's social reproduction process of the past 20 years. The objective of the econometric model is to simulate potential short term (one-year) national economic policies. Ex-ante simulation and optimization of economic policy for 1986 showed that, in SFRY, non-consistent macro-economic policy was resolute and led to both slower economic development and more rapid growth of inflation.

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24

Masry, Elias, and Dag Tjøstheim. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality." Econometric Theory 11, no. 2 (February 1995): 258–89. http://dx.doi.org/10.1017/s0266466600009166.

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We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

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25

Robinson, P. M. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models." Econometrica 59, no. 3 (May 1991): 755. http://dx.doi.org/10.2307/2938227.

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26

Pötscher, Benedikt M., and Ingmar R. Prucha. "Basic structure of the asymptotic theory in dynamic nonlinear econometric models." Econometric Reviews 10, no. 3 (January 1991): 253–325. http://dx.doi.org/10.1080/07474939108800209.

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27

Blueschke, D., V. Blueschke-Nikolaeva, and R. Neck. "Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects." Computational Economics 42, no. 1 (November 1, 2012): 107–18. http://dx.doi.org/10.1007/s10614-012-9351-x.

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28

Nakashima, Kiyotaka. "AN EXTREMELY-LOW-INTEREST-RATE POLICY AND THE SHAPE OF THE JAPANESE MONEY DEMAND FUNCTION." Macroeconomic Dynamics 13, no. 5 (October 8, 2009): 553–79. http://dx.doi.org/10.1017/s1365100509080225.

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This paper explores the shape of the Japanese money demand function in relation to the historical path of the Bank of Japan's policy rate by employing Saikkonen and Choi's [Econometric Theory 20, 301–340 (2004)] cointegrating smooth transition model. The nonlinear model provides a unified econometric framework, not only for pursuing the time profile of interest elasticity, but also to test the linearity of the Japanese money demand function. The test results for the linearity of the Japanese money demand function provide evidence of nonlinearity with a semilog model and linearity with a double-log model. Using a nonlinear semilog model, the analysis also finds that Japanese money demand comprises three regimes and that the interest semielasticity began to increase in the early 1990s when the Bank of Japan set the policy rate below 3%.

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29

Richards, Timothy J., Paul M. Patterson, and Pieter Van Ispelen. "Modeling Fresh Tomato Marketing Margins: Econometrics and Neural Networks." Agricultural and Resource Economics Review 27, no. 2 (October 1998): 186–99. http://dx.doi.org/10.1017/s106828050000650x.

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This study compares two methods of estimating a reduced form model of fresh tomato marketing margins: an econometric and an artificial neural network (ANN) approach. Model performance is evaluated by comparing out-of-sample forecasts for the period of January 1992 to December 1994. Parameter estimates using the econometric model fail to reject a dynamic, imperfectly competitive, uncertain relative price spread margin specification, but misspecification tests reject both linearity and log-linearity. This nonlinearity suggests that an inherently nonlinear method, such as a neural network, may be of some value. The neural network is able to forecast with approximately half the mean square error of the econometric model, but both are equally adept at predicting turning points in the time series.

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30

RICHARDS, GORDON R. "FRACTALITY IN A MACROECONOMIC MODEL: NONLINEAR OSCILLATION AROUND A LONG-TERM EQUILIBRIUM." Fractals 10, no. 02 (June 2002): 235–51. http://dx.doi.org/10.1142/s0218348x02001063.

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Recent studies have established that macroeconomic time series exhibit fractal properties. Empirical tests here demonstrate that interest rates, exchange rates, output and prices all show evidence of a non-integer fractal dimension. Several classes of volatility models widely used in econometrics can give rise to fractality. In the paradigm proposed here, fractality results from multiplicative relationships between residual noise terms in simultaneous equation systems. The emergence of fractality in a large-scale econometric model is analyzed. The model uses well-established structural equations, so that all variables converge toward their equilibrium paths in the long run. The forecasted paths are then embedded in noise, and the model is re-simulated at a higher frequency. The simultaneity of the model equations causes the embedding noise to take on fractal properties. Multi-scaling demonstrates that the model simulations reproduce the fractal properties of the real-world time series reasonably well. Finally, it is possible to forecast at short horizons using an algorithm that exploits two aspects of fractality, scaling symmetries and intermittency. Ratios of rates of change capture proximate symmetries. A logit regression is used to predict the conditional probability of extreme events.

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31

Kharin, S. V. "Price transmission on agricultural markets: methodological approaches." Agricultural Science Euro-North-East 22, no. 1 (February 17, 2021): 7–20. http://dx.doi.org/10.30766/2072-9081.2021.22.1.07-20.

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The phenomenon of price transmission on various agricultural markets has attracted the attention of scientists in the 21-st century. Empirical studies of price relationships at various market levels can be found in recent publications. In this scientific review the survey was carried out as to the existing empirical literature on price transmission in agricultural markets of European, Asian, North and South American countries. The paper also presents the analysis of the most important methodological approaches, which are very heterogeneous in the aspects of econometric models, asymmetry types and empirical results. The article provides a detailed analysis of applied research in the field of the linear and nonlinear concepts of cointegration, also the most popular econometric price transmission models have been assessed in the light of the main advantages and disad-vantages with a special focus on autoregressive models with distributed lags, error correction models, nonlinear models with switching regimes and vector autoregressive models. In recent years nonlinear and nonparametric methodological approaches and techniques have become widely used in applied research of market integration and price transmission.

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32

Teräsvirta, Timo. "Mathematical and Quantitative Methods: Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series." Journal of Economic Literature 51, no. 4 (December 1, 2013): 1190–92. http://dx.doi.org/10.1257/jel.51.4.1183.r4.

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Timo Terasvirta of Aarhus University reviews, “Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series” by Andrew C. Harvey. The Econlit abstract of this book begins: “Presents a theory for a class of nonlinear time series models that can deal with dynamic distributions, with an emphasis on models in which the conditional distribution of an observation may be heavy-tailed and the location and/or scale changes over time. Discusses statistical distributions and asymptotic theory; location; scale; location/scale models for nonnegative variables; dynamic kernel density estimation and time-varying quantiles; multivariate models, correlation, and association; and further directions in dynamic models. Harvey is Professor of Econometrics at the University of Cambridge and Fellow of Corpus Christi College, the Econometric Society, and the British Academy.”

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Enders, Walter, and Gary A. Hoover. "The Nonlinear Relationship between Terrorism and Poverty." American Economic Review 102, no. 3 (May 1, 2012): 267–72. http://dx.doi.org/10.1257/aer.102.3.267.

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In spite of the common wisdom that poverty breeds terrorism, econometric tests usually find that terrorism is influenced by population and various measures of democratic freedom, but not per capita GDP. Unlike previous studies, we use a data set containing separate measures of domestic and transnational terrorism and estimate models allowing for a nonlinear relationship between terrorism and poverty. When we account for the nonlinearities in the data and distinguish between the two types of terrorist events, we find that poverty has as a very strong influence on domestic terrorism and a small, but significant, effect on transnational terrorism.

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Andrews, Donald W. K. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers." Econometrica 55, no. 6 (November 1987): 1465. http://dx.doi.org/10.2307/1913568.

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35

Hall, S. G. "Estimating the uncertainty of the simulation properties of large nonlinear econometric models." Applied Economics 18, no. 9 (September 1986): 985–93. http://dx.doi.org/10.1080/00036848600000055.

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Blueschke-Nikolaeva, V., D. Blueschke, and R. Neck. "Optimal control of nonlinear dynamic econometric models: An algorithm and an application." Computational Statistics & Data Analysis 56, no. 11 (November 2012): 3230–40. http://dx.doi.org/10.1016/j.csda.2010.10.030.

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37

Liang, Hanying, Peter C. B. Phillips, Hanchao Wang, and Qiying Wang. "WEAK CONVERGENCE TO STOCHASTIC INTEGRALS FOR ECONOMETRIC APPLICATIONS." Econometric Theory 32, no. 6 (July 24, 2015): 1349–75. http://dx.doi.org/10.1017/s0266466615000274.

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Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on functional weak convergence. In establishing such convergence, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications involve a cointegration framework where endogeneity and nonlinearity play major roles and complicate the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I (1) and I (0) time series that simplifies the asymptotics and our limit results for such covariances hold for linear process, long memory, and mixing variates in the innovations. These results extend earlier findings in the literature, are relevant in many applications, and involve simple conditions that facilitate practical implementation. A nonlinear extension of FM regression is used to illustrate practical application of the methods.

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38

Sandberg, Rickard. "CONVERGENCE TO STOCHASTIC POWER INTEGRALS FOR DEPENDENT HETEROGENEOUS PROCESSES." Econometric Theory 25, no. 3 (June 2009): 739–47. http://dx.doi.org/10.1017/s0266466608090270.

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Building on work of Hansen (1992, Econometric Theory 8, 489–501), we show weak convergence for power transformations of integrated processes, with possibly serially correlated and heterogeneously distributed increments, to stochastic power integrals. The theory is applicable when testing the unit root or cointegration hypothesis in nonlinear systems by regression-based test statistics.

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Kapetanios, George. "TESTING FOR EXOGENEITY IN THRESHOLD MODELS." Econometric Theory 26, no. 1 (August 13, 2009): 231–59. http://dx.doi.org/10.1017/s0266466609090665.

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Most work in the area of nonlinear econometric modeling is based on a single equation and assumes exogeneity of the explanatory variables. Recently, work by Caner and Hansen (2004) and Psaradakis, Sola, and Spagnolo (2005) has considered the possibility of estimating nonlinear models by methods that take into account endogeneity but provide no tests for exogeneity. This paper examines the problem of testing for exogeneity in nonlinear threshold models. We suggest new Hausman-type tests and discuss the use of the bootstrap to improve the properties of asymptotic tests. The theoretical properties of the tests are discussed and an extensive Monte Carlo study is undertaken.

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40

Jiang, Yu Ying, and Yong Ming Zhang. "Statistical Inference for a Kind of Nonlinear Regression Model." Advanced Materials Research 616-618 (December 2012): 2149–52. http://dx.doi.org/10.4028/www.scientific.net/amr.616-618.2149.

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As we all know, statistical inference of linear models has been a hot topic of statistical and econometric research. However, in many practical problems, the variable of interest and covariates are often nonlinear relationship. The performance of the statistical inference using linear models model can be very poor. In this paper, the statistical inference of a nonlinear regression model under some additional restricted conditions is investigated. The restricted estimator for the unknown parameter is proposed. Under some mild conditions, the asymptotic normality of the proposed estimator is established on the basis of Lagrange multiplier and hence can be used to construct the asymptotic confidence region of the regression parameter.

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41

Antônio, Cordeiro de Santana, Lima de Santana Ádamo, Miguel Amin Mário, and Nilson. "Evaluation of nonlinear econometric models to estimate the wood volume of amazon forests." African Journal of Agricultural Research 12, no. 6 (February 9, 2017): 382–88. http://dx.doi.org/10.5897/ajar2016.11897.

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Lakshmi, P., and S. Visalakshmi. "Exploring the usage of econometric techniques in nonlinear machine learning and data mining." International Journal of Mathematics in Operational Research 9, no. 3 (2016): 349. http://dx.doi.org/10.1504/ijmor.2016.078825.

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Lakshmi, P., and S. Visalakshmi. "Exploring the usage of econometric techniques in nonlinear machine learning and data mining." International Journal of Mathematics in Operational Research 9, no. 3 (2016): 349. http://dx.doi.org/10.1504/ijmor.2016.10000130.

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44

Pollard, D. "Comment on basic structure of the asymptotic theory in dynamic nonlinear econometric models." Econometric Reviews 10, no. 3 (January 1991): 337–44. http://dx.doi.org/10.1080/07474939108800212.

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Miazhynskaia, Tatiana, Sylvia Frühwirth-Schnatter, and Georg Dorffner. "Neural Network Models for Conditional Distribution Under Bayesian Analysis." Neural Computation 20, no. 2 (February 2008): 504–22. http://dx.doi.org/10.1162/neco.2007.3182.

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We use neural networks (NN) as a tool for a nonlinear autoregression to predict the second moment of the conditional density of return series. The NN models are compared to the popular econometric GARCH(1,1) model. We estimate the models in a Bayesian framework using Markov chain Monte Carlo posterior simulations. The interlinked aspects of the proposed Bayesian methodology are identification of NN hidden units and treatment of NN complexity based on model evidence. The empirical study includes the application of the designed strategy to market data, where we found a strong support for a nonlinear multilayer perceptron model with two hidden units.

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Lieberman, Offer. "ASYMPTOTIC THEORY OF STATISTICAL INFERENCE FOR TIME SERIES." Econometric Theory 18, no. 4 (May 17, 2002): 993–99. http://dx.doi.org/10.1017/s0266466602004103.

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Modern time series econometrics involves a diversity of models. In addition to the more traditional vector autoregressive (VAR) and autoregressive moving average (ARMA) systems, cointegration and unit root models are in widespread use for macroeconomic data, nonlinear and non-Gaussian models are popular for financial data, and long memory models are becoming more common in both macroeconomic and financial applications. Much econometric thought relates to issues of estimation and hypothesis testing, and so, in the absence of a usable finite sample theory (as is the case for the models just mentioned), an enormous amount of effort has been given to developing adequate asymptotics for statistical inference. There is often a lag between the introduction of a new model and the development of an asymptotic theory. In consequence, applied econometricians sometimes have to estimate time series models for which no asymptotic theory is available. For instance, multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models have been in use in empirical research for a while, and practitioners have been using asymptotic normality of estimators in this model even though a theoretical justification is not available.

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Yue, Yiding, Lei He, and Guanchun Liu. "Modeling and Application of a New Nonlinear Fractional Financial Model." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/325050.

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The paper proposes a new nonlinear dynamic econometric model with fractional derivative. The fractional derivative is defined in the Jumarie type. The corresponding discrete financial system is considered by removing the limit operation in Jumarie derivative’s. We estimate the coefficients and parameters of the model by using the least squared principle. The new approach to financial system modeling is illustrated by an application to model the behavior of Japanese national financial system which consists of interest rate, investment, and inflation. The empirical results with different time step sizes of discretization are shown, and a comparison of the actual data against the data estimated by empirical model is illustrated. We find that our discrete financial model can describe the actual data that include interest rate, investment, and inflation accurately.

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Bi, Chao, and Jingjing Zeng. "Nonlinear and Spatial Effects of Tourism on Carbon Emissions in China: A Spatial Econometric Approach." International Journal of Environmental Research and Public Health 16, no. 18 (September 11, 2019): 3353. http://dx.doi.org/10.3390/ijerph16183353.

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Reducing carbon emissions is crucial to the sustainable development of tourism. However, there are no consistent conclusions about the nexus between tourism and carbon emissions. Considering the possible nonlinear and spatial effects of tourism on carbon emissions, this paper employed spatial econometric models combined with quadratic terms of explanatory variables to explore the nexus between them using Chinese provincial panel data from 2003 to 2016. The main results are as follows: (1) There is a significant inverse U-shaped relationship between tourism development and carbon emissions. In the provinces whose tourism receipts are relatively low, the effects of tourism on carbon emissions are positive but decrease gradually as the tourism receipts increase and then shifts to negative and continues decreasing gradually when the tourism receipts beyond the critical value. (2) For the geographical proximity and industrial relevance, one province’s tourism development not only affects its carbon emissions but also affects its neighbors’ carbon emissions through spatial lag effect (indirect effect) which is also inverse U-shaped. (3) Carbon reduction policies, sustainable education, and transportation infrastructure all have significant moderating effects on the relationship between tourism and carbon emissions, but the moderating effect of the management efficiency of tourism is not statistically significant. Furthermore, improvements to the sustainable education and transportation infrastructure not only strengthen the direct negative effect of tourism on carbon emissions but also strengthen the indirect negative effect of tourism on carbon emissions. This study not only advances the existing literature but is also of considerable interest to policymakers.

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Blueschke, D., V. Blueschke-Nikolaeva, and I. Savin. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach." Journal of Economic Dynamics and Control 37, no. 4 (April 2013): 821–37. http://dx.doi.org/10.1016/j.jedc.2012.12.003.

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Borjigin, Sumuya, Yating Yang, Xiaoguang Yang, and Leilei Sun. "Econometric testing on linear and nonlinear dynamic relation between stock prices and macroeconomy in China." Physica A: Statistical Mechanics and its Applications 493 (March 2018): 107–15. http://dx.doi.org/10.1016/j.physa.2017.10.033.

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