How and if to scale an ARIMA model based on relevant information

Question

Suppose I am using an ARIMA model to predict monthly sales in my business.

Now my data has some seasonality month on month and overall a trend upwards.

I use some mathematical tools to make the data stationary and happily apply my model.

Now for the question:

For the last 4 years my sales look like this:

Year 1: $1,000,000

Year 2: $1,500,000

Year 3: $2,250,000

Year 4: $3,375,000

My ARIMA model might well predict based on previous values a growth of 50% again in Year 5 as we have seen this trend historically.

Now for some reason (maybe a new shop opened next door, maybe new regulations, maybe something completely different like a recession, whatever!) I know that it would be very unlikely to be seeing this kind of growth next year.

Maybe I expect to see a 10% or 20% growth rather than 50%.

My question is:

Should I take the ARIMA predicted values and scale then down by some factor like take 20% off all predictions for instance?

Or should I look into using a new type of model completely?

Or some other thing I should consider doing?

Any suggestions are great.

Thanks.

Answer 1

If you have a reason that you expect your trend to change, try adding that as a variable in your analysis. Not every reason for an expected decline is easily quantified, but you may be surprised at what you can add to your equation. Consider using regression or another model to try and understand the fluctuations in the underlying trend in your data.

This page has some great information on isolating the trend from the seasonality so you can work with them separately, and on recomposing:

https://anomaly.io/seasonal-trend-decomposition-in-r/

For your example of a shop opening up across the street, you likely won't want to put a single "is there a shop across the street? yes/no" variable because you have no historical data with a "yes" value to work with. You could, however, come up with a count of similar shops within the radius of 5, 10, 25 miles that were open during the time you are using to model.

You can also add economic data as new predictor variables. Unemployment rate, for example, could be used as a measure in your model creation. Deflation or disinflation might also be examined.

What you do in practice regarding setting a goal for yourself or an employee doesn't necessarily have to follow your model, but if you want to report a model for the future, discounting the prediction by an arbitrarily decided upon amount would be tough to defend to a client/co-worker.