# How to deal with timeseries regressors of different lengths in Dynamic Regression Model

I plan to build a dynamic regression model with weekly sales data over a three year period (Jan 2014-Dec 2016). The three series are sales, price and advertising spend. I have complete data for all three series. However, the weekly media spend data does not start until week 26 of the first year (no media exist prior to the 26th week). My assumption is that I want to just place zeros in the first 25 weeks and build my model with the full three years of data. Alternatively, I can start all of the data at week 26 of 2014. Are there problems with either approach? Which approach is better? Thank you

## 1 Answer

No, you can't plug zero instead of the missing observation. There are many ways to deal with missing data, especially if it's missing at random (MAR). You could impute the missing values, or simply skip them if using MLE techniques. For instance, arima package in R would handle missing data coded with NAs properly, since it uses MLE.

• Absolutely in agreement ! – IrishStat Aug 30 '17 at 16:58
• Thanks for the quick response the problem is not that the data is missing it is that it does not exist prior to the 26th week. There was no media spend prior to this week. That is what I am struggling with should it be considered missing when it simply did not exist. – yanga Aug 30 '17 at 17:28
• If I understand you right then it is not the case of missing data. It's that you did not spend money on ads. In this case you plug zeros. Don't call it "non existent" because it's confusing. The data exists. You know there was no spending so the correct value is zero – Aksakal Aug 30 '17 at 17:34
• Fair point. I should say have said media was first introduced in week 26. – yanga Aug 30 '17 at 17:41