Autocorrelation: Serial Correlation Problem. Clrm Assumption Includes Non-Autocorrelation of Errors. Ut and Us Are Not Correlated

Autocorrelation: Serial Correlation Problem. CLRM assumption includes non-autocorrelation of errors. Ut and Us are not correlated

Ñ"Ð" (Ut Us) = 0

In real life this assumption is not valid. The errors are serially correlated

Reason: 1) Business cycle- inertia most macroeconomic data

2) Cob-Web phenomenon: positive error to negative error etc.

3) Other data manipulation and misspecification: esp. missing variables.

Consequences:

1. Can still estimate OLS Parameters

2. OLS estimators are linear and unbiased

3. But OLS estimators are not the Best. LUE but not BLUE(best linear unbiased estimator)

4. Standard errors are high and biased

5. R2 is overestimated or inflated

6. t test, f tests are not reliable

7. The forecasts are unreliable

Diagnostic: time series data usually suffer from Auto correlation

Graphical Check (Step 1) Run OLS, find yÐŽ¦s and then errors et = ut

Step 2) Then plot the errors

Durbin-Watson Test (DW)

Treatment (if positive or Negative Correlation)

Increase data sample, taking log or other transformations, generalized least squares (GLS)m Prais ÐŽV Wislen, Cochrave ÐŽV Orcult, Hildreth Lu, Durban two step.

Heteroscedasticity

Define: aka unequal variance. The variance of ui is no longer constant but varies from observation to observation. Occurs a lot in cross-sectional data. This is because we generally deal with members of a pop. at a given point in time. Also these members may be of different sizes, small, med, large, which results in a scale effect.

The variance of error changes across an observation. Especially in cross-section data. Scale effect ÐŽV changers according to individual. Ie. Bill Gates Money Loss.

Cosequences: Like Auto correlation

Under the assumptions of the CLRM, OLS estimators are the best Linear