# Calculating “deseasonalised sales y” when forecasting 2004Q1-2004Q2

I'm currently having difficulty calculating values for the deseasonalised sales column. How do you go about doing it for 2004Q1-2004Q2?

Btw in case you are wondering:

$$2004Q1$$

$$First MA = {\frac{20+12+9+7}{4}} = 12$$ $$Centered MA = {\frac{11.5+12}{2}} = 11.750$$ $${\frac{Sales}{CMA}} = {\frac{12}{11.750}} = 1.02$$

$$2004Q2$$

$$First MA = {\frac{12+9+7+25}{4}} = 13.75$$ $$Centered MA = {\frac{12+13.25}{2}} = 12.625$$ $${\frac{Sales}{CMA}} = {\frac{9}{12.625}} = 0.71$$

This is the pattern being followed throughout.

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Deseasonalizing the data means dividing the sales by a constant, where that constant is defined for a particular time of year. In the context of time series, this can be based on previous performance and some sort of percentage of total sales in a previous year. Here it seems that each quarter has its own constant that persists over the years: divide observed sales 2001q1 by its related deseasonalized sales to get ~1.14. You get about the same value for 2002q1 and 2003q1. So it stands that you would get the same with a hypothetical value for deseasonalized sales of 2004q1, for a value of $12/x=1.14\to x=12/1.14$. The solution is analogous for 2004q2.