Ch. 19 Models of Nonstationary Time Series In time series analysis we do not confine ourselves to the analysis of stationary time series. In fact, most of the time series we encounter are nonstationary. How to deal with the nonstationary data and use what we have learned from stationary model are the main subjects of this chapter 1 Integrated Process

Ch. 18 Vector Time series 1 Introduction In dealing with economic variables often the value of one variables is not only related to its predecessors in time but, in addition, it depends on past values of other variables. This naturally extends the concept of univariate stochastic process to vector time series analysis. This chapter describes the dynamic in

Ch. 17 Maximum likelihood estimation e identica ation process having led to a tentative formulation for the model, we then need to obtain efficient estimates of the parameters. After the parameters have been estimated, the fitted model will be subjected to diagnostic checks This chapter contains a general account of likelihood method for estimation of the parameters in the stochastic model

Ch. 16 Stochastic Model Building Unlike linear regression model which usually has an economic theoretic model built somewhere in economic literature, the time series analysis of a stochastic process needs the ability to relating a stationary ARMA model to real data. It is usually best achieved by a three-stage

Ch. 15 Forecasting Having considered in Chapter 14 some of the properties of ARMA models, we now show how they may be used to forecast future values of an observed time series. For the present we proceed as if the model were known ecactly Forecasting is an important concept for the studies of time series analysis. In the scope of regression model we usually

Ch. 14 Stationary ARMA Process a general linear stochastic model is described that suppose a time series to be generated by a linear aggregation of random shock. For practical representation it is desirable to employ models that use parameters parsimoniously. Parsimony may often be achieved by representation of the linear process in terms of a small number of autoregressive and moving

Ch. 13 Difference Equations 1 First-Order Difference Equations Suppose we are given a dynamic equation relating the value y takes on at date t to another variables Wt and to the value y took in the previous period: where o is a constant. Equation(1)is a linear first-order difference equation a difference equation is an expression relating a variable yt to its previous values

Ch. 12 Stochastic Process 1 Introduction a particularly important aspect of real observable phenomena, which the random variables concept cannot accommodate, is their time dimension; the concept of random variable is essential static. A number of economic phenomena for which we need to formulate probability models come in the form of dynamic processes

Ch. 11 Panel Data model Data sets that combine time series and cross sections are common in econo- metrics. For example, the published statistics of the OECD contain numerous series of economic aggregate observed yearly for many countries. The PSID is a studies of roughly 6000 families and 15000 individuals who has been interviews periodically from 1968 to the present

Ch. 10 Autocorrelated Disturbances In a time-series setting, a common problem is autocorrelation, or serial corre- lation of the disturbance across periods. See the plot of the residuals at Figure