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Factor Analysis and Principal Components Analysis 257 we can represent the variance of the ith data time series Xi as a weighted ...

258 The Basics of financial economeTrics From equation (12.12): XP 11 =+CV 11 PC 21 VP 28 ++ CV 18 and XP 81 =+CV 81 PC 28 VP 2 ...

Factor Analysis and Principal Components Analysis 259 For example, if we estimate a linear regression using MATLAB’s regress fun ...

260 The Basics of financial economeTrics FIGUre 12.2 Approximation to the True Data Obtained with Four Principal Components Note ...

Factor Analysis and Principal Components Analysis 261 matrix. PCA per se does not assume any probabilistic model for the data. F ...

262 The Basics of financial economeTrics If we look at the fundamental relationship ΣΨ=+BB' , it is easy to see that there is no ...

Factor Analysis and Principal Components Analysis 263 finite number of eigenvalues grows without bounds, all other eigenvalues a ...

264 The Basics of financial economeTrics To summarize, both factor models and principal components analysis try to find a parsim ...

265 ChAPter 13 Model estimation a fter reading this chapter you will understand: ■ (^) The concept of estimation and estimators. ...

266 The Basics of financial economeTrics Testing is complementary to estimation. Critical parameters are often tested before the ...

Model Estimation 267 comparing empirical estimators with test statistics or critical values com- puted from the sampling distrib ...

268 The Basics of financial economeTrics method is an approach to estimation that is essentially based on changing the observed ...

Model Estimation 269 table 13.1 Sample Data for Illustration Observation Y X 1 0.8 0.7 2 1.8 1.3 3 1.1 2.9 4 1.7 4.2 5 1.6 5.5 6 ...

270 The Basics of financial economeTrics points on the line. In this case, the sum for a generic a and b can be writ- ten as: () ...

Model Estimation 271 function. With the function polyfit (X,Y,1) we obtain the following solution: a = 0.1317, b = 0.8065. Figur ...

272 The Basics of financial economeTrics instead of y = a + bx. We therefore compute the sum S as follows: ()() ()() ()() ()() ( ...

Model Estimation 273 In order to decide what approximation is the best, we could use AIC or BIC criteria as discussed in Appendi ...

274 The Basics of financial economeTrics method applied to simple or multiple regressions under standard assump- tions is the OL ...

Model Estimation 275 We have also seen that the estimated regression parameters can be repre- sented in terms of the sample data ...

276 The Basics of financial economeTrics model is the expression shown in equation (3.1) in Chapter 3 reproduced here as equatio ...