# 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. – Richard Hardy Aug 28 '19 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. – ricardo Aug 28 '19 at 11:39

## 1 Answer

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. – Richard Hardy Aug 28 '19 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. – IrishStat Aug 28 '19 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. – Richard Hardy Aug 28 '19 at 13:21
• @IrishStat added a chart and some data. thanks for your help. – ricardo Sep 2 '19 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? – ricardo Sep 2 '19 at 23:19