Common Features in Vector Nonlinear Time Series Models

Common Features in Vector Nonlinear

Time Series Models

av

Dao Li

Akademisk avhandling

Avhandling för filosofie doktorsexamen i statistik, som kommer att försvaras offentligt Tisdag den 1 Oktober 2013 kl. 13.15,

HSL3, Långhuset, Örebro universitet Opponent: Professor Thomas Holgersson

Högskolan i Jönköping Jönköping, Sweden

Örebro universitet Handelshögskolan

Abstract

Dao Li (2013): Common Features in Vector Nonlinear Time Series Models. Örebro Studies in Statistics 6.

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting non-linear common features. The aim of this thesis is to develop new econo-metric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A defini-tion of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with com-mon features is set up for testing for comcom-mon features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointe-gration, is examined. The ST cointegration nests the previously devel-oped linear and threshold cointegration. An F-type test for examining the ST cointegration is derived when stationary transition variables are im-posed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for com-mon nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper con-siders forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail, and thereafter illustrated within two corre-sponding macroeconomic data sets.

Keywords: Nonliearity, Time Series, Econometrics, Smooth transition,

Common features, Cointegration, Forecasting, Residual-based, PPP. Dao Li, Department of Statistics, Örebro University School of Business Örebro University, SE-701 82 Örebro, Sweden, daoli2013@gmail.com