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
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.