A Higher order Markov model for time series forecasting

The values of some time series in the real world usually change randomly but they may contain information from history. In these cases, today value can depend not only on yesterday value but also on further values in history. Hence, a forecast model which takes the information from two or three days ago to predict today value can give a more accurate prediction. This paper presents a novel higher Markov model for time series forecasting where the state space of the Markov chain was contructed from different levels of changes of the time series. Once the transition matrix has been calculated based on the fuzzy sets, the mean of the levels of changes along with transition probabilities allow caculating the data for forecast values. The experiment with different data shows a significantly improved accuracy compared to other previous models such as ARIMA, ANN, HMM-based models and combined HMM-Fuzzy models.