Advanced Econometrics Takeshi Amemiya

Time Series Analysis

Because there are many books concerned solely with time series analysis, this chapter is brief; only the most essential topics are considered. The reader who wishes to study this topic further should consult Doob (1953) for a rigorous probabilistic foundation of time series analysis; Anderson (1971) or Fuller (1976) for estimation and large sample theory; Nerlove, Grether, and Car­valho (1979) and Harvey (1981 a, b), for practical aspects of fitting time series by autoregressive and moving-average models; Whittle (1983) for the theory of prediction; Granger and Newbold (1977) for the more practical aspects of prediction; and Brillinger (1975) for the estimation of the spectral density.

In Section 5.1 we shall define stationary time series and the autocovariance function and spectral density of stationary time series. In Section 5.2 autore­gressive models will be defined and their estimation problems discussed. In Section 5.3 autoregressive models with moving-average residuals will be de­fined. In Section 5.4 we shall discuss the asymptotic properties of the LS and ML estimators in the autoregressive model, and in Section 5.5 we shall discuss prediction briefly. Finally, in Section 5.6 we shall discuss distributed-lag models.