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Multicollinearity in Time Series Data

To develop a forecasting model for time series data with many variables, principal component analysis is used to deal with the problem of multi collinearity, but before using MLR for forecasting is it necessary to take autocorrelation into account... and finally how to go about for forecasting?

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Comment by Arun on April 13, 2010 at 11:54am
Nidhi, I see that I've got a problem with the basics here. Let me restate what you've just said.

PCA is used for multicollinearity?! I think not! PCA is used to identify variables that seem to have similar information that can be loaded onto a factor!
Where's multicollinearity here?

Why would you use MLR for TimeSeries? MLR cannot handle Autocorrelation! You need to take care of autocorrelation before running a regression on it, and that an ARIMA can help with. Other wise, you need to pre-whiten the series and then feed it into the MLR. When I say pre-whiten, you may need to use differencing based on which time lag has effect on the x(t). This can be obtained from ACF, IACF & PACF plots from ARIMA.

Your forecasted model would look like
Y = a + b1X1+ b11X1(t-1)+...+b2X2+b21X2(t-1)+...+e
if Y is not autocorrelated.
If Y is also autocorrelated, then
add another set of variables a1Y(t-1)+a2Y(t-2) etc..

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