Self-similar Based Time Series Analysis and Prediction
Ruoqiu Wang · TSpace (University of Toronto) · 2014
Fractals have been observed in many natural phenomena, and self-similarity is the most important statistical property of fractals. In the literature, the concepts of self-similarity and long-range-dependence (LRD), the increment process of a self-similar signal when the Hurst parameter is between 0.5 and 1, are often confused. On the other hand, the forecasting of many real-life signals exhibiting these properties is useful yet remains challenging. The objective of this thesis is to provide the readers with a clear and detailed explanation of the relevant concepts, and then to compare forecasting models (including FARIMA, HAR-RV, wavelet-based and average-VAR) for self-similar and LRD signals via real-life data (arterial blood pressure signals and volatility indexes). Numerical studies show that the four models perform similarly, while the FARIMA model is not recommended due to its time-consuming computation; and the performance of detecting large decrease is more accurate than that of detecting large increase.