AUTOCORRELATION.

1. Autocorrelation refers to error term one observation related to or affected by the error term of another observation in other words it correlated to it. There is no similar number of features between autocorrelation and heteroscedasticity. It occurs in data when the error term of a regression forecasting model is correlated.

2. Consequences of autocorrelation.

v The estimates of the regression coefficients no longer have a minimum variable property and may be inefficient.

v The variance of the square error terms may be greatly underestimated by the mean sequence error value.

v The true standard deviation of the estimated regression coefficient is seriously underestimated.

v The confidence intervals and test using T and E distributed are no longer strictly applicable.

v Ordinary least square (OLS) estimators are still unbiased and linear. This is because both unbiased and consistency do not depend on the assumption six which in this case is violated.

v As ∑e² is affected then R² is also affected.

v The ordinary square estimators will be inefficient and therefore no longer BLUE.

 

3 The ways of detection of autocorrelation.

v Graphical Method: There are various ways of examining the residuals. The time sequence plot can be produced. Alternatively, we can plot the standardized residuals against time. The standardized residuals are simply the residuals divided by the standard error of the regression. If the actual and standard plot shows a pattern, then the errors may not be random. We can also plot the error term with its first lag. A positive autocorrelation is identified by a clustering of residuals with the same sign. A negative autocorrelation is identified by fast changes in the signs of consecutive residuals.

v The Runs Test- Consider a list of estimated error term, the errors term can be positive or negative. In the following sequence, there are three runs.(─ ─ ─ ─ ─ ─ ) ( + + + + + + + + + + + + + )  (─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─  ) A run is defined as uninterrupted sequence of one symbol or attribute, such as + or -. The length of the run is defined as the number of element in it. The above sequence as three runs, the first run is 6 minuses, the second one has 13 pluses and the last one has 11 minuses

v Use the Durbin-Watson statistic to test for the presence of autocorrelation. The test is based on an assumption that errors are generated by a first-order autoregressive process. If there are missing observations, these are omitted from the calculations, and only the no missing observations are used. To get a conclusion from the test, you will need to compare the displayed statistic with lower and upper bounds in the table.  If D > upper bound, no correlation exists; if D < lower bound, positive correlation exists; if D is in between the two bounds, the test is inconclusive.

4. Remedies of autocorrelation

1. To find out if the autocorrelation is pure and not the result of mis- specification of the model. Sometimes we observe patterns in residual because the model is mis- specified, that is to say it has excluded some important variables or because it is functional form is incorrect.
2. Transformation of the origin model
   If it is pure autocorrelation, one can use appropriate transformation of origin model so that in the transformed model we do not have the problem of pure autocorrelation. As in the case of heterogeneity, we will have to use some type of generalized Least – square (GLS) method.
3. Newey – west method.

In large samples we can use the newey- west method to data standard error of ordinal least square (OLS) estimator that are corrected for autocorrelation. This method is actually an extension of White’s heteroscadicity consistent standard error method.

4. Ordinary Least Square OLS)

In some situation we can use the ordinary least square method