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I am using a distributed lag model to analyze a time series data. The duration of study period is 18 years, and the observation is yearly data. When including a 1-year lag effect, the first year of the lag variable becomes missing. Then, a 2-year lag effect makes the first two data of lag variable missing, and so on.

I am going to analyze five lag effects in my studies, but five lag variables caused 5 missing data. I assume the multiple imputation may help me overcome the loss of information in these lag variables, but the imputation result is not reasonable.

Is there any better idea to impute the missing data in lag variables?

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what in particular distributed lag scheme are you implementing (Almond or Koyck or some other)? I always thought that it is as it is, including lags means the loss of information, both by additional parameters to estimate and decrease in degrees of freedom. Well you may forecast backwards the values (by exponential smoothing or similar), but I personally would not be doing so. – Dmitrij Celov Apr 16 '11 at 17:10
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Why are you testing out various lag effects? Why aren't you trying to IDENTIFY the model using the Cross Correlation Function? The Box-Jenkins process is to Identify, Estimate and Forecast. – Tom Reilly May 27 '11 at 16:43

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You can't help but lose information when you use lags. I can't think of any way around this, except to use shorter lags.

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