When a time series has "lots" of zeroes , one can approach it with tools that are referred to as Intermittent Demand Models also know as Sparse Data Models essentially dealing with two random variables ...the rate between demands and the interval between demands . With only 3 non-zeroes little can be done BUT if you have a more populated series there is hope.
Google "croston's method intermittent demand forecasting" to learn more
I and others have previously commented on these models https://stats.stackexchange.com/search?q=user%3A3382+croston