Autocorrelation

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Autocorrelation

• Violation of assumption of Cov (uiuj/XiXj)0
• Autocorrelation may be defined as correlation
  between members of series of observation ordered
  in time (time series data) or space (cross
  section data)
• Lag 1 or more
• Positive and negative
• Consequence OLS estimates are best and unbiased,
  however not efficient. Inference making is
  affected

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Reasons for autocorrelation

• Inertia inbuilt momentum, nonstationarity
• Specification bias
• excluded variable
• Wrong functional form
• Lags
• Data manipulation
• Variance of OLS Estimator in the presence of
  autocorrelation (AR1) is still not efficient

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Detecting autocorrelation

• Graphical method residuals against time,
• residuals against lag of residuals
• Runs or Geary test non-parametric test
• Signs of the residuals are ordered in time
• Clustering of and are called runs ( R )
• No. of times there is runs are ( N1 )
• No. of times there is - runs are ( N2 )
• N is total no. of observations (N1 N2)
• If R lies outside the limits, autocorrelation
  exists.

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Durbin Watson d test

• Most popular autocorr. test
• As thumb rule, if d is clos to 2, no
  autocorrelation. If d is close o 4, negative
  autocorrelation. If d is close to 0, positive
  autocorrelation
• Assumptions
• Regression model includes constant
• No lagged dependent variables on RHS
• explanatory variables are fixed
• Detects first order autocorr only
• Error term is normally distributed
• No missing data

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DW decision rules
AutoCorr
- AutoCorr
No decision
No decision
NO Autocorrelation
0 dL dU
2 4-dU 4-dL
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Breusch-Godfrey test

• Lagged regressands, Higher order autocorrelation,
  higher order Y lags
• If estimated value is higher than critical
  chi-sq, reject the null hypothesis of no
  autocorrelation

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Remedial measures

• GLS when p is known( Cochrane-Orcutt two-step
  procedure)
• Prais-Winsten transformation
• When p is unknown (FGLS)
• Use DW test to estimate p and transform as above
• First difference method
• Newey West SE correction method (HAC) large
  sample test