Non-linear time series models in economics:Theory and an application to Turkey

Recently some non-linear time series models have been proposed to capture asymmetric behaviour of economic variables. Among these proposed models, ST(A)R (Smooth Transition (Auto)regressive) model characterized by regimeswitching behaviour is chosen to investigate and estimate possible non-linear dynamics of/between growth rate of industral production and consumer price indexes of Turkey. In the theoretical part of this study the main dynamics, different types of transition functions and modelling procedure of STAR models are examined within the limits of existing literature. After linearity and diagnostics tests specific to STAR models are considered in details, some extensions of univariate STAR model such as multivariate and multiple regime models are briefly introduced. The application part of this study is twofold. The first application of STAR model aims to find evidence of the non-linear asymmetric behavior of economic activity which is proxied by growth rate of quarterly industrial production index running from 1980:2 to 2006:3 in Turkey. STAR modelling procedure is employed to this data by beginning with testing STAR-type linearity. After rejecting the null hypothesis of linearity, an adequate logistic smooth transition autoregressive (LSTAR) model which passes all diagnostic tests is successfully estimated. Secondly the dynamic properties of the estimated model are investigated by numerically obtaining long-run solution based on extrapolation and calculating dominant roots of the model. The second application focuses on exploring the non-linear relationship between growth and inflation with smooth transition regression (STR) model using quarterly data from 1980:2 to 2006:3 in Turkey. A unidirectional causality from inflation to growth is detected by using non-linear Granger causality analysis. Firstly a STR model is estimated. Since the estimated STR model is not adequate, a multiple regime STR (MRSTR) model is estimated to capture non-linear effects of inflation on growth. In conclusion, the use of STAR and MRSTR model for the Turkish data under consideration is justified by estimation results. Keywords: Nonlinearity, STAR model, Turkish Economy, Growth, Inflation.