I would like to disaggregate monthly forecasts of sales into daily data. I have historical data about daily sales over the past two years (which mainly depends on deterministic effects like day-of-the-week, holiday, end-of-month effect,..).
Which technique can I use to predict future daily sales starting from available monthly forecasts according to the historical distribution of sales by day and ensuring that the daily forecasts sum up to the monthly forecasts?
Ideally, you want to forecast at the level you need forecasts for. One alternative is using Temporal Hierarchical forecasting via: http://robjhyndman.com/papers/temporalhierarchies.pdf - (implented in the R thief package). This uses multiple aggregation levels (daily, weekly, biweekly, etc.), forecasts out each and reconciles the forecasts. Alternatively, you could try multiple seasonal TBATS or double seasonal Holt-Winters.
Lastly, you could also try moving averages of the Day of Week pattern, index day of month, or seasonal index day of month (i.e. Jan. 2016 index 1 received 2% of total monthly volume, index day 2 received 1.4%, etc.). With all of these methods, it would be wise to use test sets to see which have the best predictive accuracy so you can select the one that is best for your data.
