# Possible issues using moving average as an input for exponential smoothing?

I'm currently working with an ERP system that applies Exponential Smoothing to what it defines as "demand," which is itself a simple 90-day moving average of sales. I initially didn't trust it whatsoever since I found I had much better results doing exponential smoothing with optimization of hyperparameters, but I'm now being asked to rely on the ERP system's baked in forecasting instead of providing my own external forecasts. Alarms are going off in my head here. I'd like to understand what kind of issues I might face going forward, and how to compensate for them. Currently I'm still going to keep running my own forecasts on the side to keep it honest.

Edit: To clarify. Here is what's happening at each stage with the ERP:

Given:
Time series of sales per day $$t$$ with $$n$$ consecutive measurements, one for each day. Zeroes included. First measurement is labelled $$t_0$$ and is always nonzero, last measurement is labelled $$t_{n-1}$$ and is present day.

1. Find your "demand" sequence $$d$$ such that
$$d_i=\frac{1}{90}\sum_{k=i-89}^{i}{t_k} \mid i\ge 89$$
2. Apply backcasted Exponential Smoothing (Single, Double, or Triple) to $$d$$ to find initial values for level and trend $$\ell_0$$ and $$b_0$$ using default hyperparameters for $$\alpha=.15$$, $$\beta=.15$$, $$\gamma=.5$$.

3. (SPECULATIVE since documentation is fuzzy here) Optimize with initial values of $$\ell_0$$ and $$b_0$$ to find values for $$\alpha$$, $$\beta$$, and $$\gamma$$.

4. Solve for $$d_{n-89}$$

My concern with this lies with the fact that the sequence, $$d$$, is a moving average. Rather than just applying Exponential Smoothing directly with sales (which is what I do), it is first averaging the series and THEN feeding it to the Exponential Smoothing model. I'm not sure what ramifications this might have and was looking for guidance as to what unusual behavior I can expect, if any, by this method.

• Your words somewhat confuse me. Perhaps you could provide data and the results at each stage in order to clarify your problem/worry. Commented Dec 30, 2019 at 20:38
• @IrishStat I have updated this a little more. Please let me know if you need even more clarification, I'll get to it as soon as I can Commented Dec 30, 2019 at 21:54

As you presented you are first applying filter1 ( equal weights ) ( 90 day average ) and then you are applying filter2 to analyze/convert/smooth those results.

This is akin to creating a cumulative series from a random series and then finding that the best filter to forecast this new series is to difference it.

Two rongs don't make a rite ( so to speak !) . The results will be unpredictable and probably useless.

You injected "silly" and are using "silly" to extract a resultant/composite of silliness ...where silly in my opinion is ANY assumed filter .

By computing an average , albeit a 60 period average , one unknowingly injects autocorrelation into the derived series only to possibly pull it out (detect it) in the second phase. This injection is the basis of Slutsky's theorem .

I'm chiming in here because I can't find more current discussions on the topic of using moving average data as an INPUT to exponential smoothing. The OP is concerned about this -- my situation is the opposite in that I would feel more confident. Why? We have seasonality across the 12 months but our sales have some random factors which include how many Wednesdays are in a month and random purchasing behavior from customers. Month to month our sales can vary greatly but the long term trend is usually very apparent. I don't want to straight-line the forecast because it does have seasonality, but the month-to-month swings predicted by a triple exponential smoothing calculation relying on 12 month seasonality is just too large -- people will expect that a forecast of 300 in July and 100 in August really means we expect to sell three times the amount in July vs. August, but that's just what happened last year -- the forecast is really selling about 200 each month because the monthly variation is truly "noise."

I was hoping to find some slick formulas to use excel's FORECAST.ETS function but smoothing the data to a 3 month moving average first (all within one formula -- I can do the moving averages directly but it makes the table huge and unwieldy). Unfortatenly nothing is coming up.

But specifically to the OP I think I understand the reason for doing the smoothing on rolling average data -- it's because reducing the granularity of the data just creates noise (perhaps).

• If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. - From Review Commented Feb 23, 2022 at 5:24