Multistep-ahead time series prediction

Multistep-ahead prediction is the task of predicting a sequence of values in a time series. A typical approach, known as multi-stage prediction, is to apply a predictive model step-by-step and use the predicted value of the current time step to determine its value in the next time step. This paper examines two alternative approaches known as independent value prediction and parameter prediction. The first approach builds a separate model for each prediction step using the values observed in the past. The second approach fits a parametric function to the time series and builds models to predict the parameters of the function. We perform a comparative study on the three approaches using multiple linear regression, recurrent neural networks, and a hybrid of hidden Markov model with multiple linear regression. The advantages and disadvantages of each approach are analyzed in terms of their error accumulation, smoothness of prediction, and learning difficulty.