Time series Count-data forecasting in R I have sales data shows the number of units sold (so it is a count data). 
I am evaluating the following models:


*

*the lightgbm

*Count Time Series Following Generalised Linear Models (R tscount library)

*arima (R forecast library)

*Multiple Aggregation Prediction Algorithm (MAPA  R library)
What would be the advantages and pitfalls of these models?
I would appreciate if you give me a piece of brief information on it.
This is only one of the TS. the data is a collection of 5000 ts.
 A: your data suggests not on;y a mean shift but a change in variance AND an anomaly at the last point. What you need to do is to identify a SARIMA model https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf and include any and all latent deterministic structure .
Consider http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html and any and all posts in SE dealing with INTERVENTION DETECTION https://stats.stackexchange.com/search?q=user%3A3382+INTERVENTION+DETECTION.
In my opinion none of the approaches you mentioned are sophisticated enough or general enough to deal with your kind of data in a comprehensive manner.
If you wish post the data fro your example and I will be of more help. Other readers might also be able to help. 
Stay way clear of auto.arima as it assumes no deterministic structure is present i.e. no level/step shifts , no local time trends using deterministic structure , no pulses AND assumes that all error variance treatments can be dealt with using power transforms ( logs et al ). It will inadvertently suggest a differencing operator to deal with the deterministic level shift. It will incorrectly suggest logarithms since the error variance is higher at the higher level When (and why) should you take the log of a distribution (of numbers)? whereas a Weighted Least Squares approach is more correct when the error variance changes at discrete points in time as in this case.
