ANAREG WEEK 14AUTOCORRELATION IN TIME SRIES DATAProblems of autocorrelationFirst-order autoregressive error modelDurbin-Watson test for autocorrelationRemedial measures for autocorrelation

PROBLEMS OF AUTOCORRELATIONWhen there is an autocorrelation:1. The estimated regression coefficient are still

unbiased, but they no longer have the minimum variance property and may be quite inefficient.

2. MSE may seriously underestimate the variance of the error terms.

3. S(bk) calculated according to ordinary least squares procedures may seriously under-estimate the true standard deviation of the estimated regression coefficient.

4. The confidence intervals and tests using the t and F distributions, discussed earlier, are no longer strictly applicable.

FIRST-ORDER AUTOREGRESSIVE ERROR MODELSuppose in multiple linear regression model with the random error terms following a first-order autoregressive process is given by:

Where ρ is a parameter such that | ρ| < 1ui are independent N(0,σ2)It can be shown that the mean and variance of εi for the first-order autoregressive error models are as follows:

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DURBIN-WATSON TESTS FOR AUTOCORRELATIONHypotheses statements:

Ho : ρ = 0

Ha : ρ ǂ 0

The test statistics D is calculated by:Where n is the number of cases. The decision rule:

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REMEDIAL MEASURES FOR AUTOCORRELATIONTwo principal remedial measures when autocorrelated error terms exist are:1.To add one or more independent variables to the regression model, or2.To use transformed variables

There are three methods on transformed variables:Cochrane-Orcutt procedureHildreth-Lu procedureFirst-difference procedure

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REMEDIAL MEASURES FOR AUTOCORRELATION (2)Cochrane-Orcutt Procedure1. Estimation of ρ, by calculating:2. Fitting of transformed model Yt’3. Test for need to iterate by using the Durbin-

Watson test

First-Difference procedure:1. Transformed2. Regress Yt’ on Xt’ 3. Use Durbin-Watson test to examine whether

the first-diffrence procedure has removed the autocorrelations

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