Autocorrelation

 What is autocorrelation?

Autocorrelation is is likely to occur in a time series framework. The covariance and correlation between different DishTV disturbance are all zero.

Cov(ut,us)=0 for all t is not equal s

ut and us are independently distributed term serial independence.if this exemptions is no longer true then the disturbances are not pairwise independent but are there wise autocorrelated in this situation,:

Cov(ut,us) not equal 0 for some t is not equal s.which means that an error occurred at period t may be correlated with one at period s.

when data are arranged in chronological order the error in one period may affect the error in the other time periods.it is highly likely that there will be inter correlation among the successive observations especially when the interval is short such as daily weekly or monthly frequency compared to a cross-sectional data set.

What are main causes of autocorrelation?

One factor that can cause auto correlation is omitted variables.

Second cause autocorrelation can occur because of missing furcation of the model.

Third factor is systematic errors in measurement.

Consequence of autocorrelation for the OLS estimators.

Yt=B1+B2X2t+B3X3t+........BkXkt+ut.

If the error term ut in this equation is known to to exhibit serial correlation then consequence for OLS estimator can be

B's are Steel unbiased and consistent. The OLS estimators will be inefficient and therefore no longer BLUE.the estimated variance of the regression coefficient will be best and inconsistent and therefore hypothesis testing is no longer valid. In most of the case R square will be overestimated and the statistics will tend to be higher.

Detecting autocorrelation

There is one simple way to detect autocorrelation to exam in whether the residential plots against time and the scatter plot of of ut against ut -1 exhibit pattern similar.

The Durbin-Watson test

The Breusch-Godfrey LM test for serial correlation

Durbin's h test.