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. 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. 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. 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

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. 21 Univariate Unit Root process 1 Introduction Consider OLS estimation of a AR(1)process, Yt= pYt-1+ut where ut w ii d (0, 0), and Yo=0. The OLS estimator of p is given by and we also have

Ch. 23 Cointegration 1 Introduction An important property of (1) variables is that there can be linear combinations of theses variables that are I(O). If this is so then these variables are said to be cointegrated. Suppose that we consider two variables Yt and Xt that are I(1) (For example, Yt= Yt-1+ St and Xt= Xi-1+nt.)Then, Yt and Xt are said to be cointegrated if there exists a B such

Ch. 2 Probability Theory 1 Descriptive Study of Data 1.1 Histograms and Their Numerical Characteristics By descriptive study of data we refer to the summarization and exposition(tab- ulation, grouping, graphical representation) of observed data as well as the derivation of numerical characteristics such as measures of location, dispersion and shape

Ch. 4 Asymptotic Theory From the discussion of last Chapter it is obvious that determining the dis- tribution of h(X1, X2, . . Xr) is by no means a trival exercise. It turns out that more often than not we cannot determine the distribution exactly. Because of the importance of the problem, however, we are forced to develop approximations the subject of this Chapter

Ch. 6 The Linear model under ideal conditions The(multiple) linear model is used to study the relationship between a dependent variable(Y) and several independent variables(X1, X2, ,Xk). That is ∫(X1,X2,…,Xk)+ E assume linear function 1X1+B2X2+…+6kXk+E xB+ where Y is the dependent or explained