Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form

In this article, we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests by a Monte Carlo experiment and compare these to the most widely used linear test. Our tests appear to be well-sized and have reasonably good power properties.

[1]  Saday Sadayappan,et al.  Research Papers , 2020, 2020 Research on Equity and Sustained Participation in Engineering, Computing, and Technology (RESPECT).

[2]  Jennifer L. Castle,et al.  A low-dimension portmanteau test for non-linearity , 2010 .

[3]  Almut E. D. Veraart.  INFERENCE FOR THE JUMP PART OF QUADRATIC VARIATION OF ITÔ SEMIMARTINGALES , 2008, Econometric Theory.

[4]  Timo Terasvirta,et al.  Multivariate GARCH Models , 2008 .

[5]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[6]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[7]  Craig Hiemstra,et al.  Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation , 1994 .

[8]  L. Evans,et al.  Pierce and Haugh on characterizations of causality: A re-examination☆ , 1983 .

[9]  Timo Teräsvirta,et al.  A SIMPLE VARIABLE SELECTION TECHNIQUE FOR NONLINEAR MODELS , 2001 .

[10]  Jie Zhu.  FIEGARCH-M and and International Crises: A Cross-Country Analysis , 2008 .

[11]  D. Peel,et al.  Advertising and Aggregate Consumption , 1975 .

[12]  L. Godfrey,et al.  REGRESSION EQUATIONS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

[13]  Timo Teräsvirta,et al.  Another look at Swedish business cycles, 1861–1988 , 1999 .

[14]  Jim Malley,et al.  A non-parametric approach to non-linear causality testing , 1996 .

[15]  Timo Teräsvirta,et al.  Testing linearity against smooth transition autoregressive models , 1988 .

[16]  Bent Nielsen,et al.  An Analysis of the Indicator Saturation Estimator as a Robust Regression Estimator , 2008 .

[17]  Jie Zhu.  Pricing Volatility of Stock Returns With Volatile and Persistent Components , 2007 .

[18]  R. Tschernig,et al.  A simple variable selection technique for nonlinearmodelsGianluigi Rech , , 1999 .

[19]  Michael Sorensen,et al.  Parametric Inference for Discretely Sampled Stochastic Differential Equations , 2008 .

[20]  Kellen Petersen August.  Real Analysis , 2009 .

[21]  Jane L. Harvill,et al.  Miscellanea. A note on tests for nonlinearity in a vector time series , 1999 .

[22]  J. Miller,et al.  Extracting a common stochastic trend: Theory with some applications , 2009 .

[23]  Peter Christoffersen,et al.  Volatility Components, Affine Restrictions and Non-Normal Innovations , 2008 .

[24]  G. Rangarajan,et al.  Multiple Nonlinear Time Series with Extended Granger Causality , 2004 .

[25]  Larry D. Haugh,et al.  The characterization of instantaneous causality: A comment , 1979 .

[26]  James G. MacKinnon,et al.  Graphical Methods for Investigating the Size and Power of Hypothesis Tests , 1998 .

[27]  OpenStaxCollege.  Test of Independence , 2013 .

[28]  Richard Schmalensee,et al.  Advertising and aggregate consumption: an analysis of causality , 1980 .

[29]  Jie Zhu.  Testing for Expected Return and Market Price of Risk in Chinese A-B Share Market: A Geometric Brownian Motion and Multivariate GARCH Model Approach , 2008 .

[30]  S Boccaletti,et al.  Reconstructing embedding spaces of coupled dynamical systems from multivariate data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form , 2008 .

[32]  Jing Li,et al.  Testing Granger Causality in the presence of threshold effects , 2006 .

[33]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[34]  Peter F. Christoffersen,et al.  Option Valuation with Long-Run and Short-Run Volatility Components , 2008 .

[35]  Parameterizing Unconditional Skewness in Models for Financial Time Series , 2008 .

[36]  Dag Tjøstheim,et al.  MULTIPLE BILINEAR TIME SERIES MODELS , 1987 .

[37]  T. Breusch.  TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR MODELS , 1978 .

[38]  Timo Terasvirta,et al.  Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure , 2008 .

[39]  Tom Engsted,et al.  An Iterated GMM Procedure for Estimating the Campbell-Cochrane Habit Formation Model, with an Application to Danish Stock and Bond Returns , 2008 .