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Random Walk Tests and Variance Ratios

Fin250f: Lecture 4.1 Fall 2005 Reading: Taylor, chapter 5.1-5.6. Random Walk Tests and Variance Ratios. Outline. Variance ratios Autocorrelation sampling theory. Types of Random Walks. e(t) IID: No volatility persistence e(t): expectation zero, zero correlation No linear predictors

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Random Walk Tests and Variance Ratios

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  1. Fin250f: Lecture 4.1 Fall 2005 Reading: Taylor, chapter 5.1-5.6 Random Walk Tests and Variance Ratios

  2. Outline • Variance ratios • Autocorrelation sampling theory

  3. Types of Random Walks • e(t) IID: • No volatility persistence • e(t): expectation zero, zero correlation • No linear predictors • Might be nonlinear predictors • Allows for volatility prediction

  4. Random Walks and Market Efficiency • Classic implications • Price forecasting hopeless • Technical analysis useless • Modern thoughts/reminders • Dynamic strategies that • Increase expected returns • Increase risk • Still consistent with market efficiency

  5. Variance Ratio Tests

  6. Variance Ratio Tests

  7. Variance Ratios: Random Walk Test • Test: VR(N)=1 • Two problems • Distribution of VR? • Which N?

  8. Distribution of VR(N): Asymptotic

  9. Matlab Examples • vratio • vratiotest • nmcvratio • bsvratio

  10. Longer Time Horizons • Weekly • Lo and Mackinlay(1988) • Strong rejections on weekly equal weighted index (not value weighted) • Few rejections for individual stocks • Stale prices and nontrading?

  11. Longer Time Horizons • Monthly • Poterba and Summers(1988) • Weak positive correlations (not sig) • Annual • Weak negative long range correlations (not sig)

  12. Autocorrelations • For r(t) IID • Autocorrelations are asymptotically distributed N(0, 1/n) • n=sample size • 95% confidence bands • +-1.96/sqrt(n) • pacf.m

  13. Autocorrelations: Small sample issues

  14. Autocorrelations: Variance

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