A comparative study of threshold autoregressive, smooth transition regression and markov switching autoregressive models on stock price behaviour

Abstract

This study compared the in-sample forecasting accuracy of three forecasting nonlinear models namely: the Smooth Transition Regression (STR) model, the Threshold Autoregressive (TAR) model and the Markov-switching Autoregressive (MS-AR) model. Data used was daily close stock prices of five banks in the South African banking sector and was obtained from the Johannesburg Stock Exchange (JSE). It covered the period from 2010 to 2012 with a total of 563 observations. Nonlinearity and nonstationarity tests used confirmed the validity of the assumptions of the study. The study used model selection criteria, SBC to select the optimal lag order and for the selection of appropriate models. The Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) served as the enor measures in evaluating the forecasting ability of the models. The MS-AR models proved to perform well with lower enor measures as compared to LSTR and TAR models in most cases. The decision by error measures were supported by Diebold and Mariano test. The findings of the study revealed that the three nonlinear models and forecasting techniques are good but there is room for further improvement. More specifically, in the case of TAR and MS-AR, where autoregressive specifications were used, study recommended that the moving average (MA) and/or autoregressive moving average (ARMA) be used and results compared with the current results.