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I have historical revenue data available from 2015 to 2018 at the daily level. I am trying to predict future revenue numbers by week. Using Auto ARIMA for it as I am giving some predictor variables also. To train the model, data is provided from 2015-2017 and I am forecasting 2018. When I checked the variance between the weekly forecasted value and the actual, it's too high. So I tried to forecast by month and now the forecasted numbers are pretty close to the actuals. Now I am trying to split the monthly numbers by week. For which I am struggling to come up with a logic as the first and last week of a month will mostly not have all 7 days. One solution is to split by days and check in the history if the month is starting with weekday what is the revennue% and what is the revenue% when it's starting by the weekend. Then sum up the day data to week. Is there any other better way to do the same?

Thanks

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    $\begingroup$ Why do you say that the weekly forecast variance is too high? It is to be expected that at lower frequencies (monthly) the accuracy will be better than at higher frequencies. You are not necessarily going to get a better fc by starting with the monthly and then disaggregating it back to weekly; in fact, if there is weekly seasonality in the data for instance you would likely get worse results. $\endgroup$ – Chris Umphlett Feb 5 at 16:25
  • $\begingroup$ @ChrisUmphlett Yes, I agree the accuracy will be better when we do a monthly forecast as compare to weekly forecast. Yes the data has in week seasonality and for that reason, I am using msts() function from R but still, the accuracy is not as good as the monthly forecast. $\endgroup$ – Rohan Singh Dhaka Feb 6 at 6:41
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    $\begingroup$ When u say it’s not as accurate, have u compared it apples to apples? (Sum the weeks up to month level). For a simple (ie one function, not having to aggregate and disaggregate) check out the MAPA package (kourentzes.com/forecasting/2014/04/19/…). This will automatically combine forecasts where the day is rolled up to different frequencies. If u feel there’s some valuable information in the month and week you could use it to combine a 1 week and 4 week. $\endgroup$ – Chris Umphlett Feb 6 at 10:19
  • $\begingroup$ @ChrisUmphlett thanks. This is something new and interesting which I didn't know about. I went through it but I don't think so I will be able to use my predictor variables with MAPA package or not. $\endgroup$ – Rohan Singh Dhaka Feb 13 at 6:29
  • $\begingroup$ He has a MAPAx package to include predictors. $\endgroup$ – Chris Umphlett Feb 13 at 9:43
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If I understand you, you have daily data and you are making weekly forecasts and monthly forecasts and finding the monthly forecasts more accurate, so you believe that if you forecast by month and then try to disaggregate this into weekly values you'll have better results than if you forecast by week in the first place?

The monthly forecasts are better because they ignore weekly effects, smoothing/averaging things out. They have a lower variance because you're aggregating together more data and throwing away distinctions that are in the data. If you then try to pull weekly results back out, you've essentially taken a round-about way of smoothing your data and then doing weekly predictions.

As an example, if you're looking at business data and you don't appropriately model a holiday in a week, that will totally mess up that week's prediction. If you are modeling a month, the holiday's impact will be 1/4 or less (assuming four weeks in a month) than it is in a week.

Similarly, if the holiday doesn't always fall in the same week of the year, it may still fall in the same month, so it would not affect your monthly forecasts but it would add a lot of noise to weekly forecasts as it hops from week to week.

Last, you would also be using data from the future for your weekly forecast. Your weekly forecast in week 1 of a month will be based on data from all four weeks in the month, which you won't have in week 1 when you try to predict in the future.

Weekly forecasting is hard for a variety of reasons, which is why official government statistics are usually based on months or quarters. You may improve the results of a poorly-specified weekly model by disaggregating from a monthly model but that's only because you're smoothing over mistaken assumptions in the weekly model and you're pulling weekly data from future weeks to help you.

(I'm not even getting into the fact that there aren't a whole number of weeks in a year, so they'll never line up from year to year and seasonal effects will be wonky on a weekly scale. You really don't want to do weekly prediction if you can avoid it.)

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  • $\begingroup$ Thanks Wayne. Totally agree to your above mentioned points why weekly forecast is difficult.. Even I thought of the same and that's why I am trying to split monthly forecast to weeks. But I am not able to come up with a proper logic for it. Currently I am in process to come up with a predictor variable which will give me the holiday impact as well as it's lag and lead effect. I feel that this can boost my weekly forecast accuracy.. and if it doesn't work I will I will try to split monthly forecast to weeks. Any ideas for this? $\endgroup$ – Rohan Singh Dhaka Feb 7 at 19:34
  • $\begingroup$ @RohanSinghDhaka I think splitting monthly into weekly will never work. If you know enough to split the monthly forecast into weeks, you'd know enough to correctly predict the weeks directly. If you don't know enough to predict the weeks directly, how can you know how to slice up your monthly predictions and allocate the parts appropriately? $\endgroup$ – Wayne Feb 8 at 15:18

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