Ch. 9 Heteroscedasticity Regression disturbances whose variance are not constant across observations are heteroscedastic. In the heteroscedastic model we assume that

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. 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

where a subscribed element of a matrix is always read as arou, column. Here we confine the element to be real number a vector is a matrix with one row or one column. Therefore a row vector is Alxk and a column vector is AixI and commonly denoted as ak and ai,respec- tively. In the followings of this course, we follow conventional custom to say that a vector is a columnvector except for

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. 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. 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. 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

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