Why should we remove seasonality from a time series? While working with time series, we sometimes detect and remove seasonality using spectral analysis. I am a real beginner in time series, and I am confused why one would want to remove seasonality from the original time series? Doesn't removing seasonality distort the original data?
What benefits do we get by constructing a time series by removing the seasonality?
 A: *

*Burman, J. Peter (1980), “Seasonal Adjustment by Signal Extraction,” Journal of the Royal Statistical Society, Series A, 143, p.321


The reasons according to Burman:

The most common is to provide an estimate of the current trend so
  that judgemental short-term forecasts can be made. Alternatively, it
  may be applied to a large number of series which enter an economic
  model, as it has been found impracticable to use unadjusted data with
  seasonal dummies in all but the smallest models: this is often called
  the historical mode of seasonal adjustment



*

*Shiskin, Julius (1957), “Electronic Computers and Business Indicators", Journal of Business, 30, 219-267.



A principal purpose of studying economic indicators is to determine
  the stage of the business cycle at which the economy stands. Such
  knowledge helps in forecasting subsequent cyclical movements and
  provides a factual basis for taking steps to moderate the amplitude
  and scope of the business cycle. . . . In using indicators, however,
  analysts are perennially troubled by the difficulty of separating
  cyclical from other types of fluctuations, particularly seasonal
  fluctuations.

If you want my 2 kopeks, then I'd summarize it like this:


*

*Convenience: If you deal with multiple economic series, each of them will have its own seasonality. It becomes impractical to deal with seasonality of each series in multivariate models. So, it's easier to de-seasonalize all economic series before adding them to multivariate models, or analyzing them together.

*Trend extraction: many economic series are inherently seasonal, e.g. house prices are higher in summer. Hence, when house price index suddenly goes down, it is not always because it signals something important in economy, but it could simply be the seasonal drop, which has no significant information. Hence, we want to deseasonalize the series to understand where we are.

A: When looking at relationships between two variables which are time series, seasonality will reduce the degrees of freedom because the data will not be independent. This "serial" correlation will result in spurious correlations.  Thus the seasonality is removed with the goal of increasing the degrees of freedom.
