I have a dataset which shows the expense of users in a specific expense category daily, along the time. I am building a time series in order to predict whether this person will buy this some product on this category in the next days. I defined the time series and all the components: trend (using moving average with m= 7 days), season, noise. Now I am trying to figure out and interpret the auto-correlation chart because i want identify the terms to implement SARIMA for forecasting. My dilemma is: The person doesn't buy everyday on that category, then I don't know if should I fill the dates that don't have any purchase observation using some imputation techniques such as interpolation or don't because I think doesn't make any sense fill some number in a day that didn't occur the event. Thank you in advance! ;)
You are correct to question if we should impute or not. We should not "fill" a time-series where the gaps or dips are real observations rather than failures or corrupted data. The days that there was no purchasing reflect the true underlying purchasing pattern. Most buyers do not go out and buy things every day; imputing these variable would create an artificial pattern.
There are certain methodologies to deal with zero-inflated time-series or intermittent time-series; in R the packages
tsintermittent can be your first choice tools respectively. Notice that in such analyses using additional explanatory variables (regressors) might be helpful to explain the intermittent patterns in our data. Similarly if there are not many zeros maybe a negative binomial model for count time series like the ones in
tscount may offer an attractive alternative.