Introductory Econometrics
A brief overview of the classical linear regression model
What is a regression model?
Regression versus correlation
Simple regression
Some further terminology
Simple linear regression in EViews -- estimation of an optimal hedge ratio
The assumptions underlying the classical linear regression model
Properties of the OLS estimator
Precision and standard errors
An introduction to statistical inference
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27
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2.6
2.7
2.8
2.9
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Contents
2.10 A special type of hypothesis test: the t-ratio
2.11 An example of the use of a simple t-test to test a theory in finance: can US mutual funds beat the market?
2.12 Can UK unit trust managers beat the market?
2.13 The overreaction hypothesis and the UK stock market
2.14 The exact significance level
2.15 Hypothesis testing in EViews -- example 1: hedging revisited
2.16 Estimation and hypothesis testing in EViews -- example 2: the CAPM
Appendix: Mathematical derivations of CLRM results
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69
71
74
75
77
81
3 Further development and analysis of the classical linear regression model
3.1 Generalising the simple model to multiple linear regression
3.2 The constant term
3.3 How are the parameters (the elements of the β vector) calculated in the generalised case?
3.4 Testing multiple hypotheses: the F -test
3.5 Sample EViews output for multiple hypothesis tests
3.6 Multiple regression in EViews using an APT-style model
3.7 Data mining and the true size of the test
3.8 Goodness of fit statistics
3.9 Hedonic pricing models
3.10 Tests of non-nested hypotheses
Appendix 3.1: Mathematical derivations of CLRM results
Appendix 3.2: A brief introduction to factor models and principal components analysis
120
4 Classical linear regression model assumptions and diagnostic tests
4.1 Introduction
4.2 Statistical distributions for diagnostic tests
4.3 Assumption 1: E (u t ) = 0
4.4 Assumption 2: var(u t ) = σ 2 < ∞
4.5 Assumption 3: cov(u i
What is a regression model?
Regression versus correlation
Simple regression
Some further terminology
Simple linear regression in EViews -- estimation of an optimal hedge ratio
The assumptions underlying the classical linear regression model
Properties of the OLS estimator
Precision and standard errors
An introduction to statistical inference
27
27
28
28
37
2.6
2.7
2.8
2.9
v
40
43
44
46
51
vi
Contents
2.10 A special type of hypothesis test: the t-ratio
2.11 An example of the use of a simple t-test to test a theory in finance: can US mutual funds beat the market?
2.12 Can UK unit trust managers beat the market?
2.13 The overreaction hypothesis and the UK stock market
2.14 The exact significance level
2.15 Hypothesis testing in EViews -- example 1: hedging revisited
2.16 Estimation and hypothesis testing in EViews -- example 2: the CAPM
Appendix: Mathematical derivations of CLRM results
65
67
69
71
74
75
77
81
3 Further development and analysis of the classical linear regression model
3.1 Generalising the simple model to multiple linear regression
3.2 The constant term
3.3 How are the parameters (the elements of the β vector) calculated in the generalised case?
3.4 Testing multiple hypotheses: the F -test
3.5 Sample EViews output for multiple hypothesis tests
3.6 Multiple regression in EViews using an APT-style model
3.7 Data mining and the true size of the test
3.8 Goodness of fit statistics
3.9 Hedonic pricing models
3.10 Tests of non-nested hypotheses
Appendix 3.1: Mathematical derivations of CLRM results
Appendix 3.2: A brief introduction to factor models and principal components analysis
120
4 Classical linear regression model assumptions and diagnostic tests
4.1 Introduction
4.2 Statistical distributions for diagnostic tests
4.3 Assumption 1: E (u t ) = 0
4.4 Assumption 2: var(u t ) = σ 2 < ∞
4.5 Assumption 3: cov(u i
References: given as ‘Brooks (1999) demonstrated that . . . ’ or ‘A number of authors have concluded that Harvey, A.C. (1993) Time Series Models, second edition, Harvester Wheatsheaf, Hemel Hempstead, England Published articles Hinich, M.J. (1982) Testing for Gaussianity and Linearity of a Stationary Time Series, Journal of Time Series Analysis 3(3), 169--176 in the context of GARCH modelling (see Bauwens and Lubrano, 1998, or Vrontos et al., 2000 and the references therein for some examples), asset allocation (see, for example, Handa and Tiwari, 2006), portfolio performance