A Simple Specification Procedure for the Transition Function in Persistent Nonlinear Time Series Models

A simple procedure for the specification of the transition function describing the regime switch in nonlinear autoregressive models is proposed. This procedure is based on auxiliary regressions of unit root tests and is applicable to a variety of transition functions. In contrast to other procedures, complicated and computer-intense estimation of the candidate models is not necessary. Our approach entirely relies on OLS estimation of auxiliary regressions instead. We use standard information criteria for the selection of the unknown transition function. Our Monte Carlo simulations reveal that the approach works well in practice. Empirical applications to the S&P500 price-earnings ratio and the US interest spread highlight the merits of our suggested procedure.

[1]  Howell Tong,et al.  Threshold Models in Time Series Analysis-30 Years On , 2011 .

[2]  D. McMillan.  Bubbles in the dividend–price ratio? Evidence from an asymmetric exponential smooth-transition model , 2007 .

[3]  David E. Rapach,et al.  Valuation ratios and long-horizon stock price predictability , 2005 .

[4]  Lutz Kilian,et al.  Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions? , 1999 .

[5]  Heather M. Anderson,et al.  Transaction Costs and Nonlinear Adjustment Towards Equilibrium in the US Treasury Bill Market , 1997 .

[6]  Claudia Grote,et al.  Testing for Cointegration in a Double-LSTR Framework , 2015 .

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

[8]  R. Shiller,et al.  Valuation Ratios and the Long-Run Stock Market Outlook , 1998 .

[9]  Rickard Sandberg,et al.  Linearity Testing in Time-Varying Smooth Transition Autoregressive Models under Unknown Degree of Persistency , 2010 .

[10]  B. Hansen,et al.  Inference in TAR Models , 1997 .

[11]  David I. Harvey,et al.  Testing for Time Series Linearity , 2007 .

[12]  Hyeongwoo Kim,et al.  A Century of Purchasing Power Parity Confirmed: The Role of Nonlinearity , 2010 .

[13]  Mototsugu Shintani,et al.  Testing for a Unit Root Against Transitional Autoregressive Models , 2016 .

[14]  M. Lettau,et al.  Reconciling the Return Predictability EvidenceThe Review of Financial Studies: Reconciling the Return Predictability Evidence , 2008 .

[15]  David E. Rapach,et al.  The out-of-sample forecasting performance of nonlinear models of real exchange rate behavior , 2006 .

[16]  R. Tschernig,et al.  Nonlinear Interest Rate Dynamics and Implications for the Term Structure , 1996 .

[17]  Rehim Kiliĉ.  Linearity Tests and Stationarity , 2004 .

[18]  Mark P. Taylor,et al.  Why is it so Difficult to Beat the Random Walk Forecast of Exchange Rates? , 2001 .

[19]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[20]  Diana Adler.  Non Linear Time Series A Dynamical System Approach , 2016 .

[21]  Gawon Yoon.  Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models , 2010 .

[22]  Zacharias Psaradakis,et al.  Selecting nonlinear time series models using information criteria , 2009 .

[23]  George Kapetanios,et al.  Testing for a unit root in the nonlinear STAR framework , 2003 .

[24]  R. Sollis.  A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries , 2009 .

[25]  Kerk L. Phillips,et al.  What is the shape of real exchange rate nonlinearity? , 2013 .

[26]  Timo Teräsvirta,et al.  Smooth transition autoregressive models - A survey of recent developments , 2000 .

[27]  Bruce E. Hansen,et al.  THRESHOLD AUTOREGRESSION WITH A UNIT ROOT , 2001 .

[28]  T. Teräsvirta,et al.  Time-Varying Smooth Transition Autoregressive Models , 2003 .

[29]  Stijn Van Nieuwerburgh,et al.  Reconciling the Return Predictability Evidence , 2006 .

[30]  T. Teräsvirta.  Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models , 1994 .

[31]  Robinson Kruse,et al.  Unit roots, nonlinearities and structural breaks , 2012 .

[32]  J. Stock,et al.  Testing for Common Trends , 1988 .

[33]  Chi Young Choi,et al.  How Useful are Tests for Unit-Root in Distinguishing Unit-Root Processes from Stationary but Non-Linear Processes? , 2007 .