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Note on AR(1)-characterisation of stationary processes and model fitting
Volume 6, Issue 2 (2019), pp. 195–207
Marko Voutilainen   Lauri Viitasaari   Pauliina Ilmonen  

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https://doi.org/10.15559/19-VMSTA132
Pub. online: 8 March 2019      Type: Research Article      Open accessOpen Access

Received
5 October 2018
Revised
13 February 2019
Accepted
13 February 2019
Published
8 March 2019

Abstract

It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.

References

[1] 
Bahamonde, M., Torres, S., Tudor, C.A.: ARCH model with fractional Brownian motion. Stat. Probab. Lett. 134, 70–78 (2018). MR3758583. https://doi.org/10.1016/j.spl.2017.10.003
[2] 
Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer (2013). MR2839251
[3] 
Cheridito, P., Kawaguchi, H., Maejima, M.: Fractional Ornstein-Uhlenbeck processes. Electron. J. Probab. 8, 3–14 (2003). MR1961165. https://doi.org/10.1214/EJP.v8-125
[4] 
Hamilton, J.D.: Time Series Analysis vol. 2. Princeton University Press (1994). MR1278033
[5] 
Ilmonen, P., Torres, S., Tudor, C., Viitasaari, L., Voutilainen, M.: On generalized ARCH model with stationary liquidity. arXiv preprint arXiv:1806.08608 (2018)
[6] 
Kubilius, K., Mishura, Y., Ralchenko, K.: Parameter Estimation in Fractional Diffusion Models. Springer (2018). MR3752152. https://doi.org/10.1007/978-3-319-71030-3
[7] 
Viitasaari, L.: Representation of stationary and stationary increment processes via Langevin equation and self-similar processes. Stat. Probab. Lett. 115, 45–53 (2016). MR3498367. https://doi.org/10.1016/j.spl.2016.03.020
[8] 
Voutilainen, M., Viitasaari, L., Ilmonen, P.: On model fitting and estimation of strictly stationary processes. Mod. Stoch.: Theory Appl. 4(4), 381–406 (2017). MR3739015. https://doi.org/10.15559/17-vmsta91

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Keywords
AR(1)-characterisation stationary processes covariance functions

MSC2010
60G10 62M10

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