3
$\begingroup$

I have 2 time series, $X$ and $Y$, and I'm trying to find the best lag range that correlates $X$ to $Y$ (find the amount(s) of lag of $X$ that best correlate to the target variable $Y$).

For instance, if the best lag range is between $t = 8$ and $t = 10$, then the final equation would be $Y_t = \alpha_1 X_{t-8} + \alpha_2 X_{t-9} + \alpha_3 X_{t-10} + \alpha_4$.

Since the value of $Y$ could depend not only on some specific lag of $X$, but rather on a range of lags, I can't just find the correlation coefficient between $Y$ and different time lags of $X$ individually, and can't just run a regression model for several lags of $X$ as independent variables, since there are huge colinearities between those lags (series $X$ is a slow-changing time series).

Is there a way to find what are the best lags of $X$ to be used to predict my variable $Y$?

$\endgroup$
1
  • $\begingroup$ Cross-correlograms $\endgroup$
    – Dayne
    Jan 16 at 18:00

1 Answer 1

0
$\begingroup$

This is commonly called cross-correlation, lagged regression, or distributed lag.

One commonly applied algorithm is ARMAX model.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.