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Hi,

I am using EViews 9 and am trying to identify a model for OLS analysis, my sample size is quite small (52), and I am using time series data for my dependent variable

The Adjusted R^2 of my model is ~0.9, but I am using a lagged independent variable so I did the Breusch-Godfrey LM Test, the prob(Chi-Square) was 0.00 and the output shows resid(-1) to have a prob of 0.00, and resid(-2) to be 0.56 so there is first-order autocorrelation, but not of a higher order

I adjusted my model to do OLS using HAC (Newey-West) covariance, but the new Durbin-Watson statistic is still 0.67, and the Breusch-Godfrey LM Test still shows resid(-1) to have a prob of 0.00

Is there something I'm missing here, shouldn't using HAC covariance fix the issue of auto-correlation?

No. HAC fixes standard errors for autocorrelation if the regression is otherwise okay. It does not remove the serial correlation. When there is a lagged dependent variable and serial correlation, the regression can be way off and HAC doesn't change that.

Try

I tried you suggestion but the Durbin-Watson is still ~0.5

For my original equation the adjusted R^2 was 0.91, and the prob of the f-statistic of the Ramsay RESET test was 0.00, which means we fail to reject the null that the equation is correctly specified. Doesn't this mean that the regression is otherwise okay?

Also, when you say "HAC fixes standard errors for autocorrelation if the regression is otherwise okay", does this mean the Durbin-Watson statistic wonn't change, but it's alright to use the output of the OLS regression ?

I tried you suggestion but the Durbin-Watson is still ~0.5

For my original equation the adjusted R^2 was 0.91, and the prob of the f-statistic of the Ramsay RESET test was 0.00, which means we fail to reject the null that the equation is correctly specified. Doesn't this mean that the regression is otherwise okay?

Nope. A regression with a lagged dependent variable and serial correlation is biased and inconsistent. Sometimes in a very big way.

When I remove the lag, I still get a ~0.5 DW stat.

I've tried variations of the variables, but when I get a ~2 DW stat, the independent variables all become insignificant at the 5% and 10% level,

Is there anything I can do to fix this, or is my model just not suitable

Hold on a second. I may have misread your original post. Is the lagged variable a lagged dependent or a lagged independent?

It's a lagged independent variable,

My dependent is time series data, it's an index that takes a value between 0-100

I probably misled you. Having a lagged independent variable on the right is in general perfectly okay. HAC will correct the standard errors, but doesn't change the regression coefficients.

You might want to try putting in several lags of the independent variable and see what that does. Alternatively, include a lagged dependent variable AND correct for serial correlation. For example

ls y c x(-1) x(-2) x(-3)
ls y c x(-1) y(-1) ar(1)

So just to clarify, when you have a lagged independent variable, and the Breusch-Godfrey test indicates first order autocorrelation, using HAC standard errors will correct the standard errors for the autocorrelation, but the results of the Breusch-Godfrey test will still show first order autocorrelation?

So just to clarify, when you have a lagged independent variable, and the Breusch-Godfrey test indicates first order autocorrelation, using HAC standard errors will correct the standard errors for the autocorrelation, but the results of the Breusch-Godfrey test will still show first order autocorrelation?

Exactly right.

Many thanks, is this also the same for the White test for heteroscedasticity?

Yes, where you would use White standard errors to correct the standard errors.

Yes, where you would use White standard errors to correct the standard errors.

Don't HAC (Newey West) standard errors correct for Heteroscedasticity and Auto Correlation?

Yes, they do. I thought you were asking about heteroskedasticity only.

One warning, both White and HAC are large sample corrections. Doing it with 52 observations may be questionable.

many thanks