Autoregressive moving-average model: Difference between revisions

Revision as of 14:29, 6 January 2025

Revision as of 18:47, 14 April 2025

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In order for the model to remain [[Stationary process|stationary]], the roots of its [[Autoregressive model#Characteristic polynomial|characteristic polynomial]] must lie outside the unit circle. For example, processes in the AR(1) model with <math>|\varphi_1| \ge 1</math> are not stationary because the root of <math>1 - \varphi_1B = 0</math> lies within the unit circle.<ref>{{Cite book |last1=Box |first1=George E. P. |url=https://www.worldcat.org/oclc/28888762 |title=Time series analysis : forecasting and control |last2=Jenkins |first2=Gwilym M. |last3=Reinsel |first3=Gregory C. |date=1994 |publisher=Prentice Hall |isbn=0-13-060774-6 |edition=3rd |___location=Englewood Cliffs, N.J. |pages=54–55 |language=en |oclc=28888762}}</ref>

The [[augmented Dickey–Fuller test]] can assesses the stability of IMFan [[intrinsic mode function]] and trend components. For stationary time series, the ARMA modelmodels iscan be used, while for non-stationary series, LSTM[[Long short-term memory]] models arecan be used to derive abstract features. The final value is obtained by reconstructing the predicted outcomes of each time series.{{Citation needed|date=April 2025}}

=== Moving average model ===

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== References ==

{{Reflist}}

== Further reading ==

* {{cite book |last=Mills |first=Terence C. |title=Time Series Techniques for Economists |publisher=Cambridge University Press |year=1990 |isbn=0521343399 |url-access=registration |url=https://archive.org/details/timeseriestechni0000mill }}