Singular-value Decomposition In Time Series Analysis

Time series are data generated by the dynamical systems, they always can be used to understand the underlying mechanisms. So far the time series analyses have made a rapid progress in many fields. This paper aims at applying SVD to investigate the fractal time series, so as to provide some basic theory for further study of the time series analysis.In this paper, we use SVD to investigate the series which have been preprocessed, because these processes are common in scientific research, such as adding a trend to the original series or making a transformation. Then we compare the singular values of the series before and after the preprocessed to find the character and regularity. There maybe some differences between theory and practice, we analyze two kinds of data, one are data generated by computer, the other are measurable system's output. With Multurelnformation method and Cao method ,we can get the delay time and embedding dimension for the phase space reconstruction. So we investigate how various preprocessing affect the singular values. At last we use SVD to analyze the intrinsic mode functions of the series to find their relationship with the original series.Based on the topics above,this paper consists of four parts as below:Charpter1: Introduction.Charpter2: Effect of filters on singular value of the time series.Charpter3: Effect of trends on singular value of the time series.Charpter4: Empirical mode decomposition and singular-value decomposition intime series.