Interpreting Seasonality Component Exponential Smoothing Models

Question

I am building an exponential smoothing model that has seasonality in it, I would like to analyze the data with the seasonal factor removed so I can tell if a performance one month was due to seasonal factors or if it was just an over/under performing month. I wanted to see if the approach I am taking makes sense or if I am widely off base.

For an example I looked at the Air Passengers data. When using the ETS function it produces a MAM model and so then I look at the seasonal component.

library(datasets)
library(forecast)
fit <- ets(AirPassengers)
season <- fit$states[,"s1"]

I am going to use a bit of rounding for simplicity sake but let's say that for 1960 the first part of season is as follows:

Jan - 0.90
Feb - 0.89
Mar - 1.01
Apr - 0.99
....

Am I correct in interpreting this as January will be 10% lower due to seasonality factors, February 11% lower, March 1% higher, and April 1% lower?

If this is incorrect, is there a way to interpret the seasonality component in a similar way so that it can be "factored" out of other analysis?

Answer 1

Am I correct in interpreting this as January will be 10% lower due to seasonality factors, February 11% lower, March 1% higher, and April 1% lower?

Yes. Given that your seasonality is multiplicative (the final "M" in the (M, Ad, M) model), this is exactly the correct interpretation. (If your seasonality were additive, you would need to interpret it as an additive offset.)