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An innovation approach to non-Gaussian time series analysis

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tohru Ozaki  and
Mitsunori Iino
Tohru Ozaki*
Affiliation:
Institute of Statistical Mathematics, Tokyo
Mitsunori Iino*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
1Postal address: Institute of Statistical Mathematics, 4-6-7 Minami-Azabu Minato-Ku, Tokyo 106-8569, Japan. Email: ozaki@ism.ac.jp
2Email: iino@ypri.co.jp
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Abstract

The paper shows that the use of both types of random noise, white noise and Poisson noise, can be justified when using an innovations approach. The historical background for this is sketched, and then several methods of whitening dependent time series are outlined, including a mixture of Gaussian white noise and a compound Poisson process: this appears as a natural extension of the Gaussian white noise model for the prediction errors of a non-Gaussian time series. A statistical method for the identification of non-linear time series models with noise made up of a mixture of Gaussian white noise and a compound Poisson noise is presented. The method is applied to financial time series data (dollar-yen exchange rate data), and illustrated via six models.

Keywords

Innovationsnon-linear modelingnon-Gaussian time series analysisdiffusion processpoint processwhite noisePoisson noiseLévy processexchange rate data

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G35: Signal detection and filtering
Type
Time series analysis
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 78 - 92
Copyright
Copyright © Applied Probability Trust 2001 

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