Wald Decomposition Theorem Any zero mean covariance stationary processxt can be represented in the form of xt = 1X j =0 dj t j + j ; where d0 = 1 ; 1X j =0 d 2 j < 1 The termt is white noise and represents the prediction error defined to bet = xt P[xt j xt 1;]...
Asymptotic Noramlity of Maximum Likelihood Estimator and the distribution of Lagrange Multiplier and Likelihood Ratio test statistic This article gives the proof of the asymptotic normality of maximum likelihood estimator and the distribution of LM and LR stat...
1 Introduction Fama[1970] says a market in which prices always ”fully reflect” available information is called ”efficient”, that is, successive price changes (or more usually, successive one-period returns) are independent. In other words, if the flow ...
Contract Theory 1 Adverse Selection Let us set up the problem as follows. The set of supplier’s type;Q = fq0;q1g, where 0< q0 < q1. Here supplier of typeq0 is superior, and supplier of typeq1 is inferior. And assume that the true type of supplier is only know...
Econometrics Theory 1 Linear Regression Model 1.1 Basics and estimation Let us conside a simple linear regression model below. yt= b1+ b2xt+ ut; for t= 1;;n This function is mapping fromxt toyt, that is,xt ! yt. Here we call each variables,yt as explained vari...