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Empirical Finance
Lecture 4: When OLS is no longer valid: examples of alternative estimators used in empirical finance.
Module Leader: Dr Stuart Fraser
stuart.fraser@wbs.ac.uk
代写留学生论文Room D1.18 (Social Studies)Warwick Business School 2
Introduction
Last time…
Estimating and testing CAPM and 3-factor model.
Need to carry out misspecification testing (test assumptions of the CLRM).
Today…
Consequences of heteroscedasticityand autocorrelation for OLS estimators.
Look at a solution widely used in empirical finance: Newey-West HAC var-covmatrix.
Consequences of endogenous regressors(correlated with the error term).
https://www.51lunwen.org/StudentPapers.htmlAlternative estimators used in empirical finance when regressorsare endogenous: IV/GMMWarwick Business School 3
Consequences of heteroscedasticityand autocorrelation
In the presence of heteroscedasticityor autocorrelation OLS point estimators remain unbiased and consistent (see e.g., Gujarati Chps11+12; Brooks Chp4)
However the standard formula for the variance-covariance matrix…
…is no longer correct.
Therefore whilst OLS pointestimators are unbiased(and consistent) inferencesbased on the above formula (t-, F-tests and confidence intervals) are invalid.
()()12ˆvar−′=XXσβ
An estimator is consistent if its sampling distribution ‘collapses’on the true
parameter value as T→∞Warwick Business School 4
Consequences of heteroscedasticityand autocorrelation
Under het. and/or auto. the correct formula for is: Therefore if a consistentestimator of can be found then we can…Use OLS point estimators (which are unbiased and consistent)Combined with a consistent estimator of…yielding an estimator which is consistent andgives valid inferences. Principle underlying the use of OLS point estimateswith inferences based on a Newey-West HAC var-covmatrix.()βˆ var()()()()εεβ′=Ω′Ω′′=−−EXXXXXX11ˆvar()βˆ var()βˆ varΩis the variance-covariance matrix of the error terms. If the errors are homoscedasticand uncorrelated then this matrix is diagonalIn that case1Appendix see 2Iσ=Ω()()12ˆvar−′=XXσβWarwick Business School 6
Application of Newey-West HAC variance-covariance matrix
So to re-cap:
OLS point estimates with inferences based on Newey-West HAC standard errors (rather than OLS standard errors) is one solution to the problem of het. and/or auto.
However this estimator is not BLUE –there is an estimator with a smaller variance (more efficient): Generalized Least Squares (GLS).
Nonetheless Newey-West HAC var-covmatrices are widely used in empirical finance.
A common instance in which they are used is where the holding period for returns is greater than the sampling frequency of the data.
⇒Overlapping data problem(see VerbeekChp4.11.3 for an illustration of this problem in the FX market and see below).Warwick Business School 7
Overlapping data problem
Suppose we have a sample of daily datafor returns but our model is for m-period holding returns(m > one day)Even if the one-period returns are independent the m-period returns for different periods consist of ‘overlapping’one-period returns ⇒the m-period returns are correlated: Any static model involving the m period returns will therefore have an autocorrelated[MA(m-1)] error term ⇒OLS inferences are invalid.Use of NeweyWest standard errors is an appropriate remedy in this case.()()()mtttmtmtttttmttmtrrrpppppppp本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。