The paper provides general matrix formulas for minimum mean squared error signal extraction, for a finitely sampled time series whose signal and noise components are nonstationary ARIMA processes. These formulas are quite practical; as well as being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters. We also extend these formulas to estimates of future values of the unobserved signal, and show how this result combines signal extraction and forecasting.

Others in Series

Working Paper

Issues in Identifying Easter Effects in Economic Time Series

2006

This paper shows that analysis of X-11 extreme values and regARIMA outliers can contribute to better Easter effect decisions.

Working Paper

Issues in Modeling & Adjusting Effects in Economic Time Series

2007

The effectiveness of alternate models for estimating trading day and moving holiday effects in economic time series are examined.

Working Paper

Update on the Development of X-13ARIMA-SEATS

2009

This paper provides an update to Monsell (2007) to give details of new features found in the current prototype of X-13ARIMA-SEATS.

View All

Related Information

Time Series and Seasonal Adjustment Working Papers

Page Last Revised - October 8, 2021

Some content on this site is available in several different electronic formats. Some of the files may require a plug-in or additional software to view.

Is this page helpful?
Thumbs Up Image

Yes

NO THANKS

255 characters maximum

255 characters maximum reached

Thank you for your feedback.
Comments or suggestions?

Top