I am doing a monthly rainfall forecasting model. I have monthly data from 1998 to 2012. I found in previous research that they have used partial autocorrelations and stepwise regression as an input variable selection method so they can be used as inputs for the neural network.
My questions is:
What is the procedure I must follow to choose the "lag length"? The previous researchers used lag24 and lag25 without justification or citation.The autocorrelation of one of the studies applied (lag length = 25) to the autocorrelation and the the plot showed that lag 24 is the highest and lag1, lag4, lag11, lag12 showed values above the confidence level (95%). So according to these values they have selected all 24 lags (lag1, lag2, lag3, ..., lag23, lag24) as the most significant lags and applied them to the stepwise regression to find the most significant variables among the 24.
My question here is:
If we used autocorrelation and the results showed that only five lags are above the confidence level, why do we need to apply them again to stepwise regression? Why not only apply the lags above the confidence level to the stepwise regression or just proceed to the neural network and skip the stepwise regression?
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$\begingroup$ Whats your time variable look like? Days, hours, weeks? If it is hourly data - 24 lags sounds good´? $\endgroup$– ThorstCommented Oct 2, 2015 at 11:35
2 Answers
Question 1: Rob J Hyndman has a nice blog post on lag length selection for Ljung-Box test, which is very similar in nature to examining the ACF and PACF plots. He says
...we recommended using $h=10$ for non-seasonal data and $h=2m$ for seasonal data, where $m$ is the period of seasonality. These suggestions were based on power considerations. We want to ensure that h is large enough to capture any meaningful and troublesome correlations. For seasonal data, it is common to have correlations at multiples of the seasonal lag remaining in the residuals, so we wanted to include at least two seasonal lags.
Thus using lag $h=24$ is in line with the suggestion for monthly data where $m=12$.
Question 2: I share your confusion. Perhaps the authors checked the ACF and PACF plots just as an extra diagnostic and expected that a stepwise regression would pick up those lags by its algorithm. One thing to remember, though, is that a couple or more regressors may be individually insignificant but jointly significant, which would not be easy to detect from ACF and PACF plots only. I guess stepwise regression takes care of that, at least partly.
The coefficients in a lagged regression model (ADL/PDL) are the conditional impacts of each lag thus if anything you should be using the Partial ACF to "preliminarily identify appropriate lag structure" not the ACF which only measures the unconditional impact. Having said that both the ACF and the PACF implicitly assume no Pulses, no Level/Step Shifts, no Seasonal Pulses and no time trends ( series of the form 1,2,3,...t and/or 0,0,0,0,1,2,3,4 ...) and of course no parameter changes over time and a constant error variance.
