# Ecture Notes in Financial Econometrics (Msc Course)

**Topics:**Normal distribution, Variance, Probability density function

**Pages:**225 (52269 words)

**Published:**January 23, 2013

Paul Söderlind1 1 January 2013

of St. Gallen. Address: s/bf-HSG, Rosenbergstrasse 52, CH-9000 St. Gallen, Switzerland. E-mail: Paul.Soderlind@unisg.ch. Document name: FinEcmtAll.TeX

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Contents

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Review of Statistics 1.1 Random Variables and Distributions . . . . . . . . . . . . . . 1.2 Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Distributions Commonly Used in Tests . . . . . . . . . . . . . 1.4 Normal Distribution of the Sample Mean as an Approximation

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5 5 11 14 17 19 22 22 44 51 54 57 63 66 66 67 72 74 77 81

A Statistical Tables 2 Least Squares Estimation 2.1 Least Squares . . . . 2.2 Hypothesis Testing . 2.3 Heteroskedasticity . . 2.4 Autocorrelation . . .

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A A Primer in Matrix Algebra A Statistical Tables 3 Index Models 3.1 The Inputs to a MV Analysis . 3.2 Single-Index Models . . . . . 3.3 Estimating Beta . . . . . . . . 3.4 Multi-Index Models . . . . . . 3.5 Principal Component Analysis 3.6 Estimating Expected Returns .

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Testing CAPM and Multifactor Models 4.1 Market Model . . . . . . . . . . . . . . . . . . 4.2 Calendar Time and Cross Sectional Regression 4.3 Several Factors . . . . . . . . . . . . . . . . . 4.4 Fama-MacBeth . . . . . . . . . . . . . . . . .

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83 83 94 96 97 101 104 104 105 106 106 115 116 117 119 121 132 132 136 144 147 149 161 168 168 174 175 175

A Statistical Tables 5 Time Series Analysis 5.1 Descriptive Statistics . . . 5.2 Stationarity . . . . . . . . 5.3 White Noise . . . . . . . . 5.4 Autoregression (AR) . . . 5.5 Moving Average (MA) . . 5.6 ARMA(p,q) . . . . . . . . 5.7 VAR(p) . . . . . . . . . . 5.8 Impulse Response Function 5.9 Non-stationary Processes .

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Predicting Asset Returns 6.1 Asset Prices, Random Walks, and the Efﬁcient Market Hypothesis 6.2 Autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Other Predictors and Methods . . . . . . . . . . . . . . . . . . . 6.4 Spurious Regressions and In-Sample Overﬁt . . . . . . . . . . . 6.5 Out-of-Sample Forecasting Performance . . . . . . . . . . . . . . 6.6 Security Analysts . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum Likelihood Estimation 7.1 Maximum Likelihood . . . . . 7.2 Key Properties of MLE . . . . 7.3 Three Test Principles . . . . . 7.4 QMLE . . . . . . . . . . . .

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ARCH and GARCH 177 8.1 Heteroskedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

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