I've developed an Arima model based on weekly data (52 weeks). I've been asked to apply the same after rolling up weekly data into months (12 data points) to determine monthly forecast. I am not convinced with this because when we work with weekly data we identify trend, seasonality etc. based on weekly numbers and we can not apply this model to monthly rolled up data. Client asking me to provide arithmetic behind this if this is not valid. Any help/suggestions regarding this will be highly appreciated.
I may not be understanding your clients question or yours, but perhaps you can offer a different response?
Calculate the monthly forecast by summing the forecasted weeks, accounting for overlaps in some manner. Your errors/confidence intervals won't be correct, but there isn't a statistical reason to not re-allocate your weekly estimates back to monthly estimates for planning purposes..
I would hesitate to roll up your weekly data into monthly to do forecasts as well, as that is essentially developing a different model from scratch. But, if its extra billable hours and its what the client wants, and you're getting paid....
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