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. 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. 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

Single equation regression models: -The dependent variable, Y, is expressed as a linear function of one or more explanatory variables, the Xs. Assumption the cause-and-effect relationship, if any, between Y and the Xs is unidirectional: explanatory variables are the cause; the dependent variable is the effect

14.1 Restricted Least Squares (RLS) 1. OLS and RLS ()Unrestricted least squares(ULS) When using the ordinary least square method(OLS) to estimate the parameters, we do not put any prior constraint() or restriction(s) on the parameters. So we can estimate the parameters without any restrictions. This is ULS

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

12.1 The Nature of Autocorrelation 1. Definition (1) CLRM assumption: No autocorrelation exist in dishurbances ui; E(iμi)=0 Autocorrelation means: E(μiμ)≠0 (2) Autocorrelation is usually associated with time series data, but it can also occur in cross-sectional data, which is called spatial correlation

一、狭义的工具变量法（IV） 二、间接最小二乘法(ILS) 三、二阶段最小二乘法(2SLS) 四、三种方法的等价性证明 五、简单宏观经济模型实例演示 六、主分量法的应用 七、其它有限信息估计方法简介 八、k级估计式

One of the CLRM assumptions is: there is no perfect multicollinearity-no exact linear relationships among explanatory variables, Xs, in a multiple regression. In practice, one rarely encounters perfect multicollinearity, but cases of near or very high multicollinearity where explanatory variables are approximately linearly related frequently arise in many applications