What is Autocorrelation?
Covariant between ui and uj is not zero - a shock that occurred in time t is correlated to shock that occured in time t-1. Correlation between error terms
What type of data is common for autocorrelation?
Time series
How do you visually detect autocorrelation?
Any obvious trend or pattern
What are the name of two formal tests of autocorrelation?
Durbin-Watson and Breusch-Godfrey tests
What are the consequences of autocorrelation?
OLS estimators are no longer BLUE as they are not efficient and in most cases the standard errors are underestimated and therefore unreliable, even in large samples
DW test statistic equation
(Et - et-1)^2 / et^2
If d > upper bound
No correlation
If d < lower bound
Positive correlation exists - reject the null
If d is between upper and lower bounds
Inconclusive
Null hypothesis for Durbin-Watson test
Residuals are uncorrelated
What is the solution of autocorrelation?
The First Difference Transformation model
How does First Difference Transformation model work?
If autocorrelation is of the 1st order than take first difference of dependent variable and all regressors.
Ut - put-1 = vt
Consequences of multicollinearity?
- OLS estimators still BLUE but 1st regression coefficients have large standard errors and therefore small t ratios.
- high R^2 but few sig coefficients
- Can misleadingly conclude that true value of coefficients is zero
- Regression coefficients May be sensitive to small changes in data, especially if sample is small
How to detect multicollinearity?
- High R^2 but few sig t values
- High pair-wise correlation between regressors and explanatory variable
- High partial correlation between coefficients
- Auxiliary regression producers sig F stat
- High VIF and low TF
Assumptions of the DW
- Regression model must include OG model
- Variables are fixed in repeated sampling
- Ut follows first order autoregressive scheme
- Error terms follow normal distribution
- Regressors do not include lagged values of dependent variables
What is the BG test?
A more general test of AC that allows for higher order AC. Also allows for lagged dependent variable
Procedure to run BG
- Run OLS and obtain residuals
- Regress et on regressors and the p autoregressive terms
- Obtain R^2
Alternative Hypothesis for DW
Autocorrelation exists
