Monitoring process and assessing uncertainty for ANFIS time series forecasting

Although intelligent tools such as neural network, fuzzy logic and neuro-fuzzy methods have been applied in time series forecasting for some time, problems of monitoring forecasting processes and assessing uncertainty for the forecasts represent a major challenge that need to be fully investigated. In this research, we use statistical methods to analyze nonstationary time series forecasting where forecasts are accrued from a neuro-fuzzy ANFIS model. The main focus is to monitor the process and assess the uncertainty of the forecasts.; Single-step-ahead forecasts and multiple-step-ahead forecasts have been investigated by using three nonstationary time series data sets. It is shown that the tracking signals test provides an effective way to detect the nonrandom change in the forecasting process; while prediction intervals give good indication of the uncertainty and risk associated with the forecasts. The difficulty with building prediction intervals here lies in the derivation of the forecast error variance due to the underlying model structure. A bootstrapping technique has been used for forecast error variance estimation. Different numbers of bootstrapping replications B have been tested; the results showed that B = 20 is usually informative for neuro-fuzzy model forecasts resampling. Further, the tracking signal tests for the monitoring process and bootstrapping method for estimating forecast error variance could also be extended to other intelligent forecasting applications.; A comparison between the results from the ARIMA model and from the ANFIS forecast has also been provided. It is observed that, for single-step-ahead forecast, ARIMA model performs better, given the precondition that the model parameters were specified appropriately. ANFIS model in general performs well; and therefore it is better for multiple-step-ahead forecast since the current forecast does not depend on the previous forecasting values.