Removing leading zeros from time series Currently, I am working with a lot of time series data. A lot of my time series data have a lot of leading zeros. For example, 
ts = [0, 0, 0, 0, 0, 0, 256, 129, 345, ...]

All, of the time series I am investigating are on a monthly cadence. My overall goal is to get the best forecast after fitting with Prohet, ARIMA, etc.
My first thought with these time series that have many zeros, was to remove them and then fit a model. However, this does not always yield the best results in terms of RMSE or MAPE. So my questions are:


*

*Is it customary to remove leading zeros from a time series?

*Are there any types of analysis or tests that can determine when to remove leading zeros from a time series?


I have done some searching online but there is not a lot of information on this topic that I could find on my own. Any comments or resources would be greatly appreciated. 
 A: *

*No, this is not customary.
Your time series may be an intermittent-time-series: demand is often zero and sometimes nonzero. In this case, leading zeros would just represent bona fide zero demand. Removing them would bias your forecast upward.
Conversely, your leading zeros might result from padding a series with zeros, and represent an artifact of data munging. In this case, you should of course remove them.
You need to understand where your data comes from and what has been done with it in order to know what to do with it.

*If your series starts with a "long" string of zeros and there are "few" zeros after, then you probably have the second one of the two cases above, and you could remove the zeros with a certain level of confidence. Appropriate values for "long" and "few" will depend on your time series, especially on its time granularity and what it actually represents. You should also remove the zeros if they are physically impossible or at least highly implausible, e.g., if they represent humidity measures taken someplace wet.
Bottom line: subject matter expertise is pretty much indispensable here.

Incidentally, you write that "this does not always yield the best results in terms of RMSE or MAPE". Be aware that the RMSE and the MAPE are usually minimized by different point forecasts. See Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)?. I have an upcoming invited commentary on the M4 forecasting competition, which should soon appear in the International Journal of Forecasting and which discusses this further. If you are interested, I can send you the manuscript.
A: My approach ( given that it is not intermittent demand data ) is to reverse forecast. Take your time series and arrange it from last to first (without tailing zeroes) and model it to obtain predicted values for the unrecorded past.
See https://stats.stackexchange.com/search?q=user%3A3382+reverse+forecasting . Additionally some researches use the term backcasting to fill in /estimate values that went unrecorded. Also see hindcast What is the proper name for a backward forecast?
