Signal identification and forecasting in nonstationary time series data.

摘要

Traditional time series analysis focuses on finding the optimal model to fit the data in a learning period and using this model to make predictions in a future period. However, many practical applications, such as earthquake time series or epileptic brain electroencephalogram (EEG) time series, may only contain a few meaningful, or predictable patterns, which can be used for meaningful forecasting such as the occurrences of some specific events following similar patterns. In these cases, the traditional time series model such as the autoregressive (AR) model usually gives poor predictions since the model is constructed to fit the entire learning period, while the pattern useful for prediction may occur during only a small portion of the period.; The purpose of this research is to provide a statistical algorithm to identify the most predictable pattern in a given time series and to apply this pattern to make predictions.; In this dissertation, we propose the Pattern Match Signal Identification (PMSI) algorithm to identify the most predictable pattern in a given time series. In this algorithm, the concept of the pattern match is used instead of the generally used value match criterion. The most predictable pattern is then identified by the significance of a test statistic. The feasibility of this algorithm is proved analytically and is confirmed by simulation studies. An epileptic brain EEG time series and the well known Wolf's monthly sunspot time series are used as applications of this algorithm.; A forecasting method based on the identified pattern by the PMSI algorithm is introduced. Multivariate regression models are applied to subsequences in the learning period with the most predictable patterns, and these regression equations are used to make predictions in a future period. The performance of this method is compared with the one by the autoregressive (AR ) models. The two applications (EEG and sunspot time series) show that the proposed forecasting method gives significantly better predictions than AR models, especially for more step ahead predictions.