Statistical Analysis Of Discrete-valued Time Series

In this thesis, we study the discrete-valued time series using categorical ARM A models. After defining the Pegram’s operator*, we calculate the auto-odds-ratio func-tion θ(h) of DAR(p) and DARMA(p,q) for the stationary binary processes as well as the general processes.We use the Yule-Walker equation approach and MLE to estimate the coefficients φj, then we give the Fisher information for φ. We also propose the new model selection criterion named HTIC for the discrete-valued time series, which is better than AIC and BIC. We extend the use of HTIC for DAR(p) to DARMA(p,q). Moreover, we investigate the goodness-of-fit test.Finally, we show the data analysis for the matches of the Real Madrid. We apply the AIC, BIC and HTIC criterions to get the DAR(2) model after analyzing the ACF and PACF of the data. The computation results indicate that this model fits very well.