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I am trying to forecast the demand of a product for the next 36 months, based on its sales history. The demand plot is shown below.

I honestly don't know what to do with it. I tried linear and non-linear regression analysis but even with the best fitting curve (an exponential curve), the MSE, MAD and MAPE are too high and the residual plots suggest correlation.

Any guidance would be much appreciated. Thanks in advance!

enter image description here

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    $\begingroup$ Have you tried a time series model, given that you have time series data? Also 36 months seems way too much. $\endgroup$ – user2974951 Feb 14 at 12:46
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The first thing to look at is what happened in months 10 and 11: where did the large increases come from? Has the product reached a plateau? If so, essentially forecast a flat line on the level of sales in months 11-17. Or is another increase of a similar magnitude likely? Or was this a one-time push that saturated the market, so that future sales will drop down to the level in months 1-9?

Forecasting 36 months based on 18 months history is very hard.

with the best fitting curve (an exponential curve)

In-sample fit is not a good proxy for out-of-sample predictive accuracy. Fitting an exponential curve to 18 months of history and extrapolating 36 months out invites disaster. You should not be expending more than two parameters on only 18 observations.

the MSE, MAD and MAPE are too high

What is "too high"? Your series may simply be hard to forecast. How to know that your machine learning problem is hopeless?

and the residual plots suggest correlation.

Given the upward trend, this does not surprise me. The important thing is to understand where that trend came from, and whether the driver is likely to continue.

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  • $\begingroup$ Hi! Thank you for replying. This is the sales history for a sofa cover that's sold through Amazon Spain, so I honestly don't know what the cause of the increase could be. Months 11 and 12 are also August and September, so there are no special dates that could blow up sales like that. I am aware of the risk of extrapolating, however I've been tasked with forecasting the demand until Dec 2021 with no additional information. Regarding "Too high", MAPE is 30% and MAD is 200 units. $\endgroup$ – Luisa Feb 14 at 13:10
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    $\begingroup$ Then I would go with the average of months 11-17. There is nothing you can seriously do better than that. $\endgroup$ – Stephan Kolassa Feb 14 at 13:14

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