I am estimating a time series model using OLS. The LHS variable has a downtrend across the period. There is certainly autocorrelation on both the LHS and RHS.
the regression is:
$us10yr = \alpha + \beta_1 {X} + e_t $
I have split the periods up and have found that the constant has significant variation across the sample. This is probably best seen from the below chart (which shows a rolling 4yr window).
As you can see from the 4yr rolling estimate: the constant moves a LOT, and typically in the direction of change in the LHS variable (lagging the changes a little).
I was worried about autocorrelation & some of the diagnostics — so I used HAC (Newey-West) standard errors.
data is here
I have three questions:
- What does the trending constant in the recursive estimation suggest?
- Does the use of HAC standard errors help?
- What estimators ought I to consider?