what is seasonal adjustment? I've always been curious about that. How do you get t0 454000 from 463500? Is there a formula saying that since a X people generally want to be employed in the summer, compared to Y in the other months, then we need to multiply the actual jobless rate by Y/X to compare? Something like that?
With respect to a hypothetical time series the underlying seasonality is either additive or multiplicative. Like sales increase by 40% in November is multiplicative or an extra 50 units are sold in December is additive.
You have to employ a seasonal smoothing parameter δ.
Additive model:
Forecast = St + It-p
Multiplicative model:
Forecast = St*It-p
St stands for the (simple) exponentially smoothed value of the series at time t, and It-p stands for the smoothed seasonal factor at time t minus p (the length of the season). This is to control for seasonality whether it be multiplicative or additive.
S if one was to generate an forecast you can enhance it by adding or multiplying the simple smoothed value by the predicted seasonal component. This seasonal component is derived analogous to the St value from simple exponential smoothing as:
Additive model:
It = It-p + δ*(1-α)*et
Multiplicative model:
It = It-p + δ*(1-α)*et/St
Here is a good example of seasonality in a time series for unemployment.
http://www.google.com/publicdata?ds=usunemployment&met=unemployment_rate&idim=county:CN060190&dl=en&hl=en&q=fresno+county+unemployment+rate