Ch. 22 Unit root in Vector Time series 1 Multivariate Wiener Processes and multivari- ate FCLT Section 2.1 of Chapter 21 described univariate standard Brownian motion W(r) as a scalar continuous-time process(W: rE0, 1-R). The variable W(r) has a N(O, r)distribution across realization, and for any given realization, w(r) is continuous function of the date r with independent increments. If a set of k such independent processes, denoted

Ch. 24 Johansen's mle for Cointegration We have so far considered only single-equation estimation and testing for cointe- gration. While the estimation of single equation is convenient and often consis- tent, for some purpose only estimation of a system provides sufficient information This is true, for example, when we consider the estimation of multiple cointe- grating vectors, and inference about the number of such vectors. This chapter examines methods of finding the cointegrating rank and derive the asymptotic

一、多重共线性 对于模型 在求最小二乘估计时,要求XX的逆存在。当XX的逆不 存在时,即,x之间存在高相关的情况,我们称之为多重 共线性

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. 3 Estimation 1 The Nature of statistical Inference It is argued that it is important to develop a mathematical model purporting to provide a generalized description of the data generating process. A prob bility model in the form of the parametric family of the density functions p=f(:0),0E e and its various ramifications formulated in last chapter

Ch. 5 Hypothesis Testing The current framework of hypothesis testing is largely due to the work of Neyman and Pearson in the late 1920s, early 30s, complementing Fisher's work on estimation. As in estimation, we begin by postulating a statistical model but instead of seeking an estimator of 6 in e we consider the question whether

Chapter 5 Large sample properties of the LSE 5.1 Stochastic convergence Suppose that Xn} is a sequence of random varia bles with a corresponding sequence of distribution functions{Fn} If Fn(x)(x) at every continuity point x of F, Fn is said to converge weakly to F, written FnF. In this case,{xn} is said to converge in distribution to where

Chapter 3 Least Squares Methods for Estimating B Methods for estimat ing B Least squares estimation Maximum like lihood estimation Met hod of moments est imation Least a bsolute deviat ion est imation 3.1 Least squares estimation The criterion of the least squares estimation is

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

Ch. 7 Violations of the ideal conditions 1 ST pecification 1.1 Selection of variables Consider a initial model. which we assume that Y=x1/1+E, It is not unusual to begin with some formulation and then contemplate adding more variable(regressors) to the model