Spectral Analysis Of Mixture Time Series Model

The major work of this paper focus on MAR model and generalized two classes of models:(HMTD), (MAR-ARCH), which are derived of recursive formula of autocovariance function and "three-stage algorithm" of computationing spectral density, thus we solve spectral analysis problem of these serval classes of models.In chapter 1, firstly, we infer recursive formula of autocovariance function and three-stage algorithm of computationing spectral density for the MAR models, then discuss the specific formula of spectral density on some usual circumstances and on regular conditions of autocovariance function for the model; secondly, we raise two problems that the relationship between autocovariance function and corresponding eigenequational roots; between stationarity and absolutely summable property of autocovariance function. we achive regular results to the first problem; finally, we list the first-order and the second-order stationarity conditions for autoregressive order p is 1 and 2.In chapter 2, firstely, similarly to the MAR model, we infer recursive formula of autocovariance function for the HMTD model, and discuss the specific formula of spectral density on some usual circumstances and on regular conditions of autocovariance function for the model; secondly, we list the first-order and the second -order stationarity conditions for autoregressive order p is 1 and 2; finally, we prove them.In chapter 3, firstely, similarly to the MAR model, we infer recursive formula of autocovariance function for the MAR-ARCH model, and discuss the specific formula of spectral density on some usual circumstances and on regular conditions of autocovariance function for the model; secondly, we list the first-order and the second -order stationarity conditions for autoregressive order p is 0 and 1. (stationarity conditions have been achived by Chun Shan Wong).