Order 1 autoregressive process of finite length

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Abstract

The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in time series theory one analyzes only stochastic processes of infinite length which need no such initial conditions and their properties are less difficult to be determined. In this paper we compare the properties of the order 1 autoregressive processes of finite and infinite length and we prove that the time series length has an important influence mainly if the serial correlation is significant. These different properties can manifest themselves as transient effects produced when a time series is numerically generated. We show that for an order 1 autoregressive process the transient behavior can be avoided if the first term is a Gaussian random variable with standard deviation equal to that of the theoretical infinite process and not to that of the white noise innovation.

Authors

C. Vamos
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

S. M. Soltuz
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

M. Craciun
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Keywords

Autoregressive process; spectral analysis; time series.

References

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About this paper

Cite this paper as:

C. Vamoş, Ş.M. Şoltuz, M. Crăciun, Order 1 autoregressive process of finite length, Rev. Anal. Numér. Théor. Approx., 36 (2007) no. 2, pp. 201-216

Print ISSN

1222-9024

Online ISSN

2457-8126

Google Scholar Profile

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