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
Keywords
Autoregressive process; spectral analysis; time series.
Paper coordinates
C. Vamoş, Ş.M. Şoltuz, M. Crăciun, Order 1 autoregressive process of finite length. Rev. Anal. Numér. Théor. Approx., 36 (2007) 2, 199-214.
References
see the expanding block below.
About this paper
Journal
Rev. Anal. Numér. Théor. Approx.
Publisher Name
Editura Academiei Romane
Paper on journal website
Print ISSN
?
Online ISSN
?
[1] Blender, R., Renormalization group analysis of autoregressive processes and fractional noise, Phys. Rev. E, 64, 067101 (2001).
[2] Brockwell, P.J. and Davis, R., Time Series: Theory and Methods, Springer-Verlag, New York, 1991.
[3] Brockwell, P.J. and Davis, R., Introduction to Time Series and Forecasting, Springer-Verlag, New York, 1996.
[4] Box, G. E. P. and Jenkins, G. M. Time Series Analysis: Forcasting and Control, 2nd ed., Holden-Day, San Francisco, 1976.
[5] Gao, J., Hu, J., Tung, W., Cao, Y., Sarshar, N. and Roychowdhury, V.P., Assessment of long-range correlation in time series: How to avoid pitfalls, Phys. Rev. E, 73, 016117 (2006).
[6] Guzman-Vargas, L. and Angulo-Brown, F., Simple model of the aging effect in heart interbeat time series, Phys. Rev. E, 67, 052901 (2003).
[7] Hallerberg, S., Altmann, E. G., Holstein, D. and Kantz, H., Precursors of extreme increments, Phys. Rev. E, 75, 016706 (2007).
[8] Hamilton, J.D., Time Series Analysis, Princeton University Press, 1994.
[9] Kaulakys, B., Autoregressive model of 1/f noise, Physics Letters A, 257, 37 (1999).
[10] Kiraly, A. and Janosi, I. M. , Stochastic modeling of daily temperature fluctuations, Phys. Rev. E, 65, 051102 (2002).
[11] Kugiumtzis, D., Statically transformed autoregressive process and surrogate data test for nonlinearity, Phys. Rev. E, 66, 025201 (2002).
[12] Liley, D. T., Cadusch, P. J., Gray, M. and Nathan, P. J., Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity, Phys. Rev. E, 68, 051906 (2003).
[13] Maraun, D., Rust, H.W. and Timmer, J., Tempting long-memory on the interpretation of DFA results, Nonlinear Processes in Geophysics, 11, 495-503 (2004).
[14] Morariu, V.V. and Coza, A. , Nonlinear properties of the atomic vibrations in protein backbones, Physica A, 320, 449 (2003).
[15] Palus, M. and Novotna, D., Sunspot Cycle: A Driven Nonlinear Oscillator? Phys. Rev. Lett., 83, 3406 (1999).
[16] Stoica, P. and Moses, R. L., Introduction to Spectral Analysis, Prentice-Hall, New Jersey, 1997.
[17] Timmer, J., Schwarz, U., Voss, H.U., Wardinski, I., Belloni, T., Hasinger, G., van der Klis, M and Kurths, J., Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1, Phys. Rev. E, 61, 1342 (2000).
[18] Vamos, C., Automatic algorithm for monotone trend removal, Phys. Rev. E, 75, 036705 (2007).
soon