Top-Down Hierarchical Forecasting
1. Top-Down Hierarchical Forecasting
Bottom-up forecasting is typically preferred, but you don't always have the time to forecast every element of a bottom layer in a hierarchy.2. Top-down Forecasting
Top-down forecasting is when you forecast the top level of a hierarchy and then reconcile your forecasts down the hierarchy.3. Top-down Reconciliation
How do you reconcile down a hierarchy? There are two common techniques - average of historical proportions and proportion of historical averages. One thing I want to mention was that typically when we do top-down forecasting our reconciled lower level forecasts aren't as accurate compared to us forecasting them directly. This shouldn't be too surprising since you aren't using all the information available to you. However, people don't do top-down forecasting for the accuracy, but for the convenience.4. Forecast Regional Total Sales
Before reconciling down a hierarchy, we need to build a forecast for the whole mountain region. We actually did this back in Chapter 1, but we can repeat it here. First, we need to sum up the sales from all of the products in the region. Next, we are going to forecast the regional sales with time series. It isn't as easy to use regression because we have many products rolled into one sales number per time period, so which price would we use? We have our time series model built here with the auto dot arima function.5. Forecast Regional Total Sales
After building the time series model we need to forecast the sales values. We are going to convert this forecast object into an xts object as we always have in this course. Now let's see how accurate we were. Looks like our MAPE is about 2 percentage points higher than when we built the bottom-up forecast for the region. Again, this isn't surprising since we aren't using all of the available information because we aren't forecasting each product in the region. Remember, we are doing this top-down forecast because we don't have the time to forecast all of the products below this level individually.6. Average of Historical Proportions
The easiest way to explain the difference between the two common top-down reconciliation techniques is through an example. Let's look at the first 5 weeks of sales for the high value product. Now let's look at the first 5 weeks of total sales for the mountain region.7. Average of Historical Proportions
What if we took the ratio (or proportion) of these two vectors element by element? We can see the historical proportion of total product sales that the high value product sales were for each week.8. Average of Historical Proportions
By taking the average (or mean) of the vector of historical proportions we can calculate an average historical proportion for the high value product in the mountain region. We can do the same thing for the low value product too.9. Average of Historical Proportions
To get the forecast for each product, we now multiply these proportions by our total regional forecast. Now we can see how accurate our individual product forecasts are. Not surprisingly these aren't as good as forecasting them individually.10. Proportion of Historical Averages
For the proportion of historical averages you just switch the order in which you do things. First, you take the average sales of a product and the average total sales of the region.11. Proportion of Historical Averages
Next, you take the ratio of these two averages for each product. You multiply these values by the total regional forecast just as before to get the product forecasts. From our MAPE's we can see that we improved one, but not another compared to the previous technique. Which technique should we use? Which product do you care about predicting more accurately?12. Let's practice!
Now it's your turn to try top-down forecasting!Create Your Free Account
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