# Constant changes in time series model

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:

1. What does the trending constant in the recursive estimation suggest?
2. Does the use of HAC standard errors help?
3. What estimators ought I to consider?
• What is the model? (Time series is a type of data, not a type of model.) Without knowing the model, it is difficult to suggests estimators. Aug 28, 2019 at 11:03
• It is a model that contains monthly observations of bond yields (which have been trending down for the best part of a decade) on the LHS and some potential explanatory variables on the RHS. Estimated using OLS. No lags. Aug 28, 2019 at 11:39

A model with no lags or differences and no arima structure is often a NO-NO when you have time series data due to untreated auto-correlation . Time series analysis model identification enables more powerful model structure to be used. See https://autobox.com/pdfs/regvsbox-old.pdf for a good introduction. Perhaps you could explicitly present not only your model BUT the actual data in a csv format to facilitate further discussion .

EDITED AFTER RECEIPT OF YOUR DATA 246 MONTHLY VALUES (US10yr) starting 2005/1 WITH 3 POSSIBLE PREDICTORS:

What does the trending constant in the recursive estimation suggest?

My ans to question 1

1 in a univariate setting a shifting of the mean

2) in a causal setting ..not much can be said

I took your 246 values and found that a useful model required Weighted Estimation as the error variance was markedly lower in the most recent data. The model is here with a supporting scatter plot of Y and your 3rd candidate predictor.

The Actual/Fit and Forecast is here

If you can predict X3 that will aid your prediction of Y

• Note that OLS is an estimation technique while model structure considers the definition of the model itself, thus it is questionable if they can be contrasted. Aug 28, 2019 at 12:44
• since the OP said no lags and no reference to identifiable deterministic structure I to I inferred ( perhaps incorrectly) that his model specification might be suspect. Aug 28, 2019 at 12:55
• I am not questioning the structure you inferred but rather the comparison of a model with an estimation technique. I find it helpful to keep the distinction clear. Aug 28, 2019 at 13:21
• @IrishStat added a chart and some data. thanks for your help. Sep 2, 2019 at 13:44
• Two questions: how does one decide when it is time to switch to weighted GLS? Also there’s the remaining question about HAC standard errors? Sep 2, 2019 at 23:19