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Model Estimation 277 Another generalization involves the case when regressors are determin- istic but we relax the assumption th ...

278 The Basics of financial economeTrics It can be demonstrated that the estimator of the regression coefficients becomes bX=()V ...

Model Estimation 279 distributions of the data. If we do not know the distribution, we cannot compute the likelihood function. M ...

280 The Basics of financial economeTrics principle is applied to determine the parameters of a distribution. We will again use o ...

Model Estimation 281 of logL with respect to the mean μ and variance σ^2 or using commercial software. We obtain the following e ...

282 The Basics of financial economeTrics The first term is a constant, the second and the third terms are negative; therefore, m ...

Model Estimation 283 A normal distribution has the following multivariate probability distri- bution function: () () Σ= ()() πΣ ...

284 The Basics of financial economeTrics the variables z are independent from the errors ε and are correlated with x. The variab ...

Model Estimation 285 If we have to estimate k parameters, we can compute the first k empiri- cal moments and equate them to the ...

286 The Basics of financial economeTrics method of moments (GMM).^7 GMM does not assume complete knowledge of the distribution b ...

Model Estimation 287 values for Y for some of the observations are different. If we repeat the same calculations as above, we fi ...

288 The Basics of financial economeTrics Now, given that a normal distribution has only two parameters, there is no way we can f ...

Model Estimation 289 the data and the parameters. These conditions typically take the form of equations where the expectation of ...

290 The Basics of financial economeTrics ■ (^) The weighted least squares (WLS) estimator, used when residuals have different va ...

291 CHAPTER 14 Model Selection A fter reading this chapter you will understand: ■ (^) The notion of machine learning. ■ (^) The ...

292 The Basics of financial economeTrics distinguished economists and physicists, the seminar introduced the idea that economic ...

Model Selection 293 of any financial system and economy change too much over time to confirm that laws in financial economics ar ...

294 The Basics of financial economeTrics The machine learning approach to financial modeling is in principle a consequence of th ...

Model Selection 295 Learning theory constrains the dimensionality of models to make them adapt to the sample size and structure. ...

296 The Basics of financial economeTrics Data Snooping One of the most serious mistakes that a financial econometrician seeking ...