DescriptionMy thesis focuses on the order identification schemes of the widely-used time series model - Autoregressive Integrated Moving-Average (ARIMA) model and the applications of the order determination methods. The first part investigates the impact of dependent but uncorrelated innovations (errors) on the traditional autoregressive integrated moving average (ARIMA) model order determination schemes such as autocorrelation function (ACF), partial autocorrelation function (PACF), extended autocorrelation function (EACF) and unit-root test. We also propose a new order determination scheme to address those impacts and can be used to time series sequences with uncorrelated innovations. In the second part, a unified approach for the tentative specification of both the seasonal and nonseasonal orders of general multiplicative seasonal model is proposed. This new approach has the advantages of determining the seasonal and nonseasonal orders simultaneously and automatically. In the third part, a hierarchical model approach is presented for predicting the end-of-day stock trading volume (total daily volume). It effectively combines two sources of information: the trading volume already accumulated from the beginning of the trading day to the time of prediction, and the historical daily trading volume dynamics.