Evaluation and Comparison of Forecast Performances of Linear and Non-linear Methods for TEPIX Daily Returns

Forecasting economic and financial variables is of high significance to economic policymakers and investors; however, it is a difficult and complicated task due to the volatile and complex nature of such data. Numerous studies have been conducted concerning different methods of forecasting macroeconomic and financial variables so far. Although frequent and sophisticated methods have been applied to forecast such variables, the nature of data under consideration has not sufficiently been taken into consideration. In terms of complexity, type and nature of data might impact the accuracy of forecasting models. In other words, linear or non-linear behaviors of data can be effective in the selection of the forecasting model. Recent research indicates that a better understanding of the generating process of variable data (linear/ non-linear) leads to easier and more accurate forecasts. If, for instance, the variable follows a linear behavior, linear models, such as ARMA, will produce more acceptable accuracy. On the contrary, using more complex modeling methods such as ANN and ANFIS is more justifiable when the variable behavior is non-linear and chaotic. Using complex models for a variable with linear behavior might lead to excessive model dependency on unnecessary volatility and, in turn, reduced forecast accuracy. This paper focuses on the study of linearity, non-linearity, and/or chaotic nature of TEPIX from March 25th, 2009 to October 15th, 2011 (625 observations) using BDS test. This test was administered in three stages to determine linearity, non-linearity, or “chaotic-ness” of TEPIX: First, the test was administered on daily stock market index return; second, the test was applied to ARMA model residuals; and finally, the test was carried out for ANFIS, GARCH, and ANN residuals. The results suggest that TEPIX return variable follows a non-linear behavior. Therefore, it is expected that non-linear models are better capable of forecasting this variable. Then, different prediction techniques in ARMA linear model were compared with those of non-linear models including ANN, ANFIS, and GARCH. According to the evaluation criteria at hand (RMSE, MAE, U-Thiel, and MAPE), the accuracy of forecasts was compared. The results show that non-linear models enjoy better performance than ARMA model regarding all the criteria above. In addition, among non-linear models, ANFIS model displays the best performance in forecasting daily stock market index return. Taking the non-linear nature of data used into account, such results were predicable.