This thesis contains new developments in various topics in time series analysis and forecasting. These topics include: model selec- tion, estimation, forecasting and diagnostic checking.;In the area of model selection, finite and large sample properties of the commonly used selection criteria, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), are discussed. In the finite case, the study is limited to the two sample problem. The exact probability of selection is obtained for finite samples. The risk of each criterion is evaluated in the two sample situation. Empirical evidence regarding these risks are given for autoregressive processes. The asymptotic distribution of the (\u27)h is given, where (\u27)h is the estimate of the number of extra parameters in the model selected by the AIC criterion. This derivation is based on large sample properties of the likelihood ratio test statistic. The asymptotic distribution of the AIC in PAR models is also discussed.;In estimation, an explicit expression for the efficiency of strongly consistent estimates for the ARMA(1,1) model is derived. Empirical efficiency and the empirical estimate are examined by simulation.;On the topic of forecasting, the asymptotic variance of the fore- cast error is derived for an autoregressive model of first order. In the derivation, the estimated parameter is not assumed to be independ- ent of the data. The variance of the one-step forecast error is also derived for the fractional noise model.;In the last topic, empirical results for portmanteau test statistics are studied. It is shown that the modified Portmanteau test of Ljung and Box (1980) outperforms the modified test of Li and McLeod (1981). In testing for whiteness, the modified Portmanteau test is shown to have lower power than the cumulative periodogram test against both fractional noise and standard ARMA alternatives
