1

Often in my work I need to remove seasonality from a time series to see underlying trends/cycles. Usually the seasonality is removed using UCM, estimated by some method. However, we often also fit SARMA to the series for forecasting purpose.

For interest I would like to know how to extract seasonal component series after fitting a SARMA model, i.e., convert the fitted model to UCM form?

Dayne
  • 2,113
  • 1
  • 7
  • 24
  • please provide one example of your data ,,,and precisely specify the UCM form/model and the SARMA form//model that you are typically experiencing – IrishStat Dec 19 '19 at 14:59
  • I am looking for a general approach to convert seasonal ARMA to UCM to extract seasonal component. Not specific to a particular SARMA model. – Dayne Dec 19 '19 at 15:02
  • In order to understand/develop a general approach ..it generally makes sense to start with a particular example . Conversion of a SARIMA model to a PDL/ADL model is something that I have championed/programmed to help understand/explain the nature of the relationship in regression terms where Y is an explicit function of the past of Y , the past of the error term and the past of latent deterministic structure that may have been empirically identified.. – IrishStat Dec 19 '19 at 15:11
  • Ok great. So let's assume that model is (1,0,0)(1,0,0). You can simulate such a series with some random initial value. Now based on UCM approach we assume out series, say $Y_t$ can be written as $y_t=TC_t+S_t+e_t$. Here $TC_t$ is the trend-cycle component and $S_t$ is the seasonal component. My interest is to find/estimate (at least) S_t from the (1,0,0)(1,0,0) model. – Dayne Dec 19 '19 at 15:41

1 Answers1

-3

I took your suggested model (1,0,0)(1,0,0)12 enter image description here into a genenter image description here eral purpose time series simulator and obtained the following realization enter image description here .

Since there is no deterministic seasonal component ( i.e. your arima model is purely memory based) there is no TREND/CYCLIC representation possible.

IrishStat
  • 27,906
  • 5
  • 29
  • 55