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Modern Stochastics: Theory and Applications


On model fitting and estimation of strictly stationary processes
Volume 4, Issue 4 (2017), pp. 381–406
Pub. online: 22 December 2017      Type: Research Article      Open accessOpen Access
Received
13 September 2017
Revised
22 November 2017
Accepted
25 November 2017
Published
22 December 2017

Abstract

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are considered, modeling is traditionally based on fitting an autoregressive moving average (ARMA) process. However, we challenge this conventional approach. Instead of fitting an ARMA model, we apply an AR(1) characterization in modeling any strictly stationary processes. Moreover, we derive consistent and asymptotically normal estimators of the corresponding model parameter.

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Copyright
© 2017 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
AR(1) representation asymptotic normality consistency estimation strictly stationary processes

MSC2010
60G10 62M09 62M10 60G18

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