Smooth Transition Models: Extensions and Outlier Robust Inference

textabstractThe dynamic properties of many economic time series variables can be characterised as state-dependent or regime-switching. A popular model to describe this type of non-linear behaviour is the smooth transition model, which accommodates two regimes facilitating a gradual transition from one regime to the other. The first part of this thesis considers three extensions of the basic smooth transition model. Models are developed which allow for more than two regimes, for time-varying properties in conjunction with regime-switching behaviour, and for modeling several time series jointly. Particular emphasis is placed on the inter-related issues of specification and inference in such models. The second part of the thesis concerns the influence of atypical observations on testing procedures for smooth transition non-linearity and on the estimation of smooth transition models. Traditional methods that are used for these purposes are found to be very sensitive to such outliers. Therefore, outlier robust testing procedures and estimation methods are developed

[1]  M. Hashem Pesaran,et al.  A floor and ceiling model of US output , 1997 .

[2]  Does Seasonality Influence the Dating of Business Cycle Turning Points , 1999 .

[3]  J. Gooijer,et al.  Some recent developments in non-linear time series modelling, testing, and forecasting☆ , 1992 .

[4]  T. Fomby,et al.  Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series , 1994 .

[5]  Gregory D. Hess,et al.  Measuring and Comparing Business-Cycle Features , 1997 .

[6]  T. Teräsvirta,et al.  Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models , 1992 .

[7]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[8]  Andre Lucas,et al.  Unit Root Tests Based on M Estimators , 1995, Econometric Theory.

[9]  Elvezio Ronchetti,et al.  Robustness Aspects of Model Choice , 1997 .

[10]  Peter R. Locke,et al.  Index arbitrage and nonlinear dynamics between the S&P 500 futures and cash , 1996 .

[11]  P. Franses,et al.  Nonlinear Error-Correction Models for Interest Rates in The Netherlands , 1997 .

[12]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[13]  Alan M. Taylor,et al.  Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited , 1997 .

[14]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[15]  B. Falk.  Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle , 1986, Journal of Political Economy.

[16]  David A. Hsieh,et al.  A heteroscedasticity-consistent covariance matrix estimator for time series regressions , 1983 .

[17]  R. Tsay.  Outliers, Level Shifts, and Variance Changes in Time Series , 1988 .

[18]  K. Kroner,et al.  Arbitrage, Cointegration, and Testing the Unbiasedness Hypothesis in Financial Markets , 1995, Journal of Financial and Quantitative Analysis.

[19]  D. Peel,et al.  Transactions Costs and Nonlinear Adjustment in Real Exchange Rates; An Empirical Investigation , 1997, Journal of Political Economy.

[20]  Nathan S. Balke.  Detecting Level Shifts in Time Series , 1993 .

[21]  Shang-Jin Wei,et al.  "The Bigger They are, the Harder They Fall": How Price Differences Across U.S. Cities are Arbitraged , 1997 .

[22]  J. Stock,et al.  The NAIRU, Unemployment and Monetary Policy , 1997 .

[23]  P. O'Connell.  Market frictions and real exchange rates , 1998 .

[24]  Daniel E. Sichel.  Are Business Cycles Asymmetric? A Correction , 1989, Journal of Political Economy.

[25]  P. Franses,et al.  SETS, arbitrage activity, and stock price dynamics , 2000 .

[26]  George Sofianos.  Index Arbitrage Profitability , 1993 .

[27]  R. Martin,et al.  Leave‐K‐Out Diagnostics for Time Series , 1989 .

[28]  Timo Teräsvirta,et al.  POWER OF THE NEURAL NETWORK LINEARITY TEST , 1993 .

[29]  R. Tsay.  Testing and modeling multivariate threshold models , 1998 .

[30]  Clive W. J. Granger,et al.  Long memory series with attractors , 2001 .

[31]  Michael D. Boldin.  A Check on the Robustness of Hamilton's Markov Switching Model Approach to the Economic Analysis of the Business Cycle , 1996 .

[32]  Rob J Hyndman,et al.  Computing and Graphing Highest Density Regions , 1996 .

[33]  R. Tsay.  Nonlinearity tests for time series , 1986 .

[34]  Paul Newbold,et al.  Unit roots and smooth transitions , 1998 .

[35]  Philip Hans Franses,et al.  Time Series Models for Business and Economic Forecasting , 1998 .

[36]  N. Ravishanker,et al.  Reallocation Outliers in Time Series , 1993 .

[37]  M. Otto,et al.  Outliers in Time Series , 1972 .

[38]  M. Hashem Pesaran,et al.  A Simple Nonparametric Test of Predictive Performance , 1992 .

[39]  Andre Lucas,et al.  Testing for ARCH in the presence of additive outliers , 1999 .

[40]  Philip Rothman,et al.  FURTHER EVIDENCE ON THE ASYMMETRIC BEHAVIOR OF UNEMPLOYMENT RATES OVER THE BUSINESS CYCLE , 1991 .

[41]  James M. Nason,et al.  Nonparametric exchange rate prediction , 1990 .

[42]  S. Kirk Elwood,et al.  Is the persistence of shocks to output asymmetric , 1998 .

[43]  N. Kaldor,et al.  A Model of the Trade Cycle , 1940 .

[44]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[45]  D. Peel,et al.  A note on some properties of the ESTAR model , 1998 .

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

[47]  Allan D. Brunner.  Conditional Asymmetries in Real GNP: A Seminonparametric Approach , 1990 .

[48]  R. Verbrugge.  Investigating Cyclical Asymmetries , 1997 .

[49]  Marco Bianchi,et al.  Unemployment Persistence: Does the Size of the Shock Matter? , 1996 .

[50]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[51]  Milton Friedman,et al.  THE “PLUCKING MODEL” OF BUSINESS FLUCTUATIONS REVISITED , 1993 .

[52]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[53]  J. Wooldridge.  A Unified Approach to Robust, Regression-Based Specification Tests , 1990, Econometric Theory.

[54]  Salih N. Neftçi.  Are Economic Time Series Asymmetric over the Business Cycle? , 1984, Journal of Political Economy.

[55]  M. Hashem Pesaran,et al.  A generalization of the non-parametric Henriksson-Merton test of market timing , 1994 .

[56]  Y. Shin,et al.  Generalized Impulse Response Analysis in Linear Multivariate Models , 1998 .

[57]  M. Hashem Pesaran,et al.  Impulse response analysis in nonlinear multivariate models , 1996 .

[58]  Eduardo S. Schwartz,et al.  Arbitrage in Stock Index Futures , 1990 .

[59]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[60]  Clive W. J. Granger,et al.  Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models , 1989 .

[61]  T. Barna,et al.  Measuring Business Cycles. , 1946 .

[62]  Fabio Canova,et al.  Detrending and turning points , 1994 .

[63]  J. A. Lane,et al.  FORECASTING EXPONENTIAL AUTOREGRESSIVE MODELS OF ORDER 1 , 1989 .

[64]  Krishna Paudyal,et al.  THRESHOLD AUTOREGRESSIVE MODELING IN FINANCE: THE PRICE DIFFERENCES OF EQUIVALENT ASSETS , 1994 .

[65]  C. W. Coakley,et al.  A Bounded Influence, High Breakdown, Efficient Regression Estimator , 1993 .

[66]  H. Tong,et al.  On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations , 1985, Advances in Applied Probability.

[67]  Halbert White,et al.  Artificial neural networks: an econometric perspective ∗ , 1994 .

[68]  C. Granger.  Some properties of time series data and their use in econometric model specification , 1981 .

[69]  Francis X. Diebold,et al.  Have Postwar Economic Fluctuations Been Stabilized? , 2020, Business Cycles.

[70]  International Evidence on Friedman's Theory of the Business Cycle , 1993 .

[71]  Christopher F. Baum,et al.  Nonlinear adjustment to purchasing power parity in the post-Bretton Woods era , 2001 .

[72]  Daniel E. Sichel.  Inventories and the three phases of the business cycle , 1994 .

[73]  F. Peracchi,et al.  Robust M-Tests , 1991, Econometric Theory.

[74]  Philip Hans Franses,et al.  Nonlinear Time Series Models in Empirical Finance: Frontmatter , 2000 .

[75]  Michael P. Clements,et al.  A Monte Carlo Study of the Forecasting Performance of Empirical Setar Models , 1999 .

[76]  B. Dumas.  Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World , 1992 .

[77]  Timo Teräsvirta,et al.  Aspects of modelling nonlinear time series , 1986 .

[78]  Gary Koop,et al.  Parameter uncertainty and impulse response analysis , 1996 .

[79]  Peter F. Christoffersen.  Evaluating Interval Forecasts , 1998 .

[80]  Oscar H. Bustos,et al.  Robust Estimates for ARMA Models , 1986 .

[81]  D. Ruppert,et al.  Breakdown in Nonlinear Regression , 1992 .

[82]  P. Rothman,et al.  The Current Depth-of-Recession and Unemployment-Rate Forecasts , 1998 .

[83]  John. Pemberton.  EXACT LEAST SQUARES MULTI‐STEP PREDICTION FROM NONLINEAR AUTOREGRESSIVE MODELS , 1987 .

[84]  Clive W. J. Granger,et al.  Strategies for Modelling Nonlinear Time‐Series Relationships* , 1993 .

[85]  Shigeru Iwata,et al.  Asymmetric persistence in GDP? A deeper look at depth , 1997 .

[86]  Xuming He,et al.  Bounded Influence and High Breakdown Point Testing Procedures in Linear Models , 1994 .

[87]  R. Tsay.  Time Series Model Specification in the Presence of Outliers , 1986 .

[88]  E. Handschin,et al.  Bad data analysis for power system state estimation , 1975, IEEE Transactions on Power Apparatus and Systems.

[89]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[90]  Herman K. van Dijk,et al.  Classical and Bayesian aspects of robust unit root inference , 1995 .

[91]  M. Priestley.  STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS , 1980 .

[92]  Michael P. Clements,et al.  The Performance of Alternative Forecasting Methods for SETAR Models , 1997 .

[93]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[94]  Lon-Mu Liu,et al.  Joint Estimation of Model Parameters and Outlier Effects in Time Series , 1993 .

[95]  H. Müller,et al.  Local Polynomial Modeling and Its Applications , 1998 .

[96]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[97]  Rob J. Hyndman,et al.  Highest‐density forecast regions for nonlinear and non‐normal time series models , 1995 .

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

[99]  A. Stromberg.  Computation of high breakdown nonlinear regression parameters , 1993 .

[100]  Mark A. Wynne,et al.  Are Deep Recessions Followed by Strong Recoveries , 1992 .

[101]  Lawrence Fisher,et al.  Some New Stock-Market Indexes , 1966 .

[102]  S. M. Carroll,et al.  Construction of neural nets using the radon transform , 1989, International 1989 Joint Conference on Neural Networks.

[103]  Eric Ghysels,et al.  Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? , 1996 .

[104]  Mark A. Wynne,et al.  Are deep recessions followed by strong recoveries? Results for the G-7 countries , 1996 .

[105]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[106]  Eric Ghysels,et al.  Changes in Seasonal Patters: Are They Cyclical , 1994 .

[107]  Steven Thorley,et al.  Asymmetric business cycle turning points , 1993 .

[108]  Bryan W. Brown,et al.  Predictors in Dynamic Nonlinear Models: Large-Sample Behavior , 1989, Econometric Theory.

[109]  D. G. Simpson,et al.  On One-Step GM Estimates and Stability of Inferences in Linear Regression , 1992 .

[110]  W. Brock,et al.  Is the business cycle characterized by deterministic chaos , 1988 .

[111]  T. Breurch,et al.  A simple test for heteroscedasticity and random coefficient variation (econometrica vol 47 , 1979 .

[112]  L. Denby,et al.  Robust Estimation of the First-Order Autoregressive Parameter , 1979 .

[113]  J. MacKinnon,et al.  Heteroskedasticity-Robust Tests in Regression Directions , 1985 .

[114]  M. Watson,et al.  Business Cycle Durations and Postwar Stabilization of the U.S. Economy , 1992 .

[115]  A. Mullineux,et al.  NONLINEAR BUSINESS CYCLE MODELLING , 1993 .

[116]  Philip Rothman,et al.  Forecasting Asymmetric Unemployment Rates , 1998 .

[117]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[118]  V. Yohai,et al.  Influence Functionals for Time Series , 1986 .

[119]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[120]  Siu Hung Cheung,et al.  On robust estimation of threshold autoregressions , 1994 .

[121]  Norman R. Swanson,et al.  Further developments in the study of cointegrated variables , 2010 .

[122]  N. Swanson.  Finite sample properties of a simple LM test for neglected nonlinearity in error‐correcting regression equations , 1999 .

[123]  Philip Rothman,et al.  Time Irreversibility and Business Cycle Asymmetry , 1996 .

[124]  Salih N. Neftçi.  Statistical Analysis of Shapes in Macroeconomic Time Series: Is There a Business Cycle? , 1993 .

[125]  G. Pfann,et al.  Non-linear error correction, asymmetric adjustment and cointegration , 1998 .

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

[127]  Nathan S. Balke,et al.  Nonlinear dynamics and covered interest rate parity , 1998 .

[128]  D. Tjøstheim.  SOME DOUBLY STOCHASTIC TIME SERIES MODELS , 1986 .

[129]  R. Maronna.  Robust $M$-Estimators of Multivariate Location and Scatter , 1976 .

[130]  Jeffrey M. Wooldridge,et al.  On the application of robust, regression- based diagnostics to models of conditional means and conditional variances , 1991 .

[131]  Kenneth M. Emery,et al.  Forecasting turning points : Is a two-state characterization of the business cycle appropriate? , 1992 .

[132]  S. Johansen.  Likelihood-Based Inference in Cointegrated Vector Autoregressive Models , 1996 .

[133]  J. Stock,et al.  Evidence on Structural Instability in Macroeconomic Time Series Relations , 1994 .

[134]  Martin Sola,et al.  Stylized facts and regime changes: Are prices procyclical? , 1995 .

[135]  R. Eisinga,et al.  Timing of Vote Decision in First and Second Order Dutch Elections 1978–1995: Evidence from Artificial Neural Networks , 1998, Political Analysis.

[136]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[137]  Farshid Vahid,et al.  Testing multiple equation systems for common nonlinear components , 1998 .

[138]  L. Summers,et al.  Hysteresis in Unemployment , 1986 .

[139]  Timo Teräsvirta,et al.  Modelling Economic Relationships with Smooth Transition Regressions , 1996 .

[140]  Michael P. Clements,et al.  FORECASTING ECONOMIC TIME SERIES , 2000, Econometric Theory.

[141]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[142]  Gary Koop,et al.  Do recessions permanently change output , 1993 .

[143]  Stephen Gordon,et al.  Stochastic Trends, Deterministic Trends and Business Cycle Turning Points , 1997 .

[144]  Ruey S. Tsay,et al.  Testing and Modeling Threshold Autoregressive Processes , 1989 .

[145]  Michael P. Clements,et al.  A Comparison of the Forecast Performance of Markov�?Switching and Threshold Autoregressive Models of Us Gnp , 1998 .

[146]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .