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Empirical Financial Economics

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Empirical Financial Economics 2. The Efficient Markets Hypothesis - Generalized Method of Moments Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June 19 ... – PowerPoint PPT presentation

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Title: Empirical Financial Economics


1
Empirical Financial Economics
  • 2. The Efficient Markets Hypothesis - Generalized
    Method of Moments

Stephen Brown NYU Stern School of Business UNSW
PhD Seminar, June 19-21 2006
2
Random Walk Hypothesis
  • Random Walk hypothesis a special case of EMH
  • Overidentification of model
  • Provides a test of model (variance ratio
    criterion)
  • Allows for estimation of parameters (GMM
    paradigm)

3
Variance ratio tests
using sample quantities
The variance ratio is
asymptotically Normal
4
Overlapping observations
Non-overlapping observations
ln(pt)
t
tT
Overlapping observations
ln(pt)
unbiassed estimators
Variance ratio is asymptotically Normal
5
Random walk model and GMM
aggregate into moment conditions
and express as three observations of a nonlinear
regression model
6
Generalized method of moment estimators
  • Choose to minimize . is
    referred to as the optimal weighting matrix,
    equal to the inverse covariance matrix of
  • Estimators are asymptotically Normal and
    efficient
  • Minimand is distributed as Chi-square with d.f.
    number of overidentifying information
  • Methods of obtaining
  • 1. Set (Ordinary Least Squares).
    Estimate model. Set (Generalized
    Least Squares). Reestimate .
  • 2. Use analytic methods to infer

7
GMM and the Efficient Market Hypothesis
1 asset and 1 instrument
1 equation and k unknowns
m assets and 1 instrument
m equations and gtk unknowns
m assets and n instrument
mxn equations and gtk unknowns
8
Autocovariances and cross autocovariances
xt
yt
t
tk
t-k
9
Cross autocovariances are not symmetrical!
Autocovariances are given by
Cross autocovariances are given by
10
Cross autocovariances and the weighting function
11
Assuming stationarity
12
Apply this to cross covariances
13
A simple expression for the inverse weighting
matrix
14
Some applications of GMM
  • Fixed income securities
  • Construct moments of returns based on
    distribution of it?
  • Estimate ? by comparing to sample moments
  • Derivative securities
  • Construct moments of returns by simulating PDE
    given ?
  • Estimate ? by comparing to sample moments
  • Asset pricing with time-varying risk premia
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