If we had two random time series X[xt1, xt2, ...xtn], Y[yt1,yt2,...ytn],
first has influence (correlates) to another, but those are suppressed
with third one Z[zt1,zt2,...ztn].
What is the best suitable model for estimation?
Multivariate time series model- VAR (http://cran.r-project.org/web/packages/vars/vignettes/vars.pdf) is the one to captue the dynamics and correlations followed by Granger causality, Impulse Response Function and FEVD.
We recommend using cross-correlation and then use dynamic regression or cointegration models time-series, according to the nature of the series. for more information write to email [email protected]; [email protected]
Suggest to run as:
(1) Y = B0 + B1X + B2Z + B3XZ + e
... where B3XZ is the interaction between XZ and verify whether this interaction is significant by:
(2) T = (B1 - B2) / SQRT((C + D) / E)
(2.1) C = n1SE12
(2.2) D = n2SE22
(2.3) E = n1 + n2 - 2
If the test verifies as significant, use (1) above as the general model. If the test shows insignificant, then the model is reduce to a simple regression:
(3) Y = B0 + B1X1 + e
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