A Two-Factor Autoregressive Moving Average Model Based on Fuzzy Fluctuation Logical Relationships

Many of the existing autoregressive moving average (ARMA) forecast models are based on one main factor. In this paper, we proposed a new two-factor first-order ARMA forecast model based on fuzzy fluctuation logical relationships of both a main factor and a secondary factor of a historical training time series. Firstly, we generated a fluctuation time series (FTS) for two factors by calculating the difference of each data point with its previous day, then finding the absolute means of the two FTSs. We then constructed a fuzzy fluctuation time series (FFTS) according to the defined linguistic sets. The next step was establishing fuzzy fluctuation logical relation groups (FFLRGs) for a two-factor first-order autoregressive (AR(1)) model and forecasting the training data with the AR(1) model. Then we built FFLRGs for a two-factor first-order autoregressive moving average (ARMA(1,m)) model. Lastly, we forecasted test data with the ARMA(1,m) model. To illustrate the performance of our model, we used real Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Dow Jones datasets as a secondary factor to forecast TAIEX. The experiment results indicate that the proposed two-factor fluctuation ARMA method outperformed the one-factor method based on real historic data. The secondary factor may have some effects on the main factor and thereby impact the forecasting results. Using fuzzified fluctuations rather than fuzzified real data could avoid the influence of extreme values in historic data, which performs negatively while forecasting. To verify the accuracy and effectiveness of the model, we also employed our method to forecast the Shanghai Stock Exchange Composite Index (SHSECI) from 2001 to 2015 and the international gold price from 2000 to 2010.