# How to choose between additive and multiplicative decomposition in time series

I have a time series which is the number of weekly flu cases from 2010 to early 2018 in one county. I want to remove seasonality from my data so I can have a clearer data to infer the relationship with environmental factor PM2.5. I know if the amplitude over time is constant I can use additive model to extract seasonality and if it changes (decrease or increase over time) I use multiplicative model.

My problem is in my time series the amplitude does not increase or decrease monotonically and it kind of fluctuate. I searched a lot and went through couple of books but not sure what to use here.

Can you please help me what time of decomposition I can use to remove the seasonality from the data?

Also if I use additive model, when I subtract the seasonal component from the flu cases, I get a lot of negative values which do not make sense in terms of count. Is there any thing I can do about it?

• Show us the ACF and PACF plots. – user2974951 Jan 18 at 8:59
• The very high and single significant PACF lag is telling you to try an AR(1) model or alternatively a first order difference. Also try using stl to decompose the series (I'm assuming you are using R). – user2974951 Jan 18 at 15:25