ABSTRACT
Usually, a histogram of a time series provides us with useful information for data analysis. It shows a certain shape implying the stationarity with its stationary density distribution function. In the late 1970s, many stationary nonlinear time series models were introduced for the analysis of non-Gaussian time series, but it is not known how the parameters of these nonlinear time series models affect the shape of the non-Gaussian density distribution of the process. The ExpAR model
x e x wt x
( )φ φ γ (8.1)
is one of a few exceptional examples whose parameters clearly explain what kind of shape the histogram of the generated time series is going to be.
