A simple nonlinear time series model with misleading linear properties. (English) Zbl 0918.90044

Summary: This paper gives an example of a first-order nonlinear autoregressive time series model with short memory such that autocorrelations estimated from data generated by the model point at a long-memory model.


91B84 Economic time series analysis
Full Text: DOI


[1] Beran, J.A., 1994. Statistics For Long Memory Processes, Chapman and Hall, New York. · Zbl 0869.60045
[2] Davydov, J.A., On the strong mixing property for farkov chains with a countable number of states, Dok. akad. nank. SSSR, 187, 825-827, (1969) · Zbl 0191.47402
[3] Geweke, J.; Porter-Hudak, S., The estimation and application of long memory time series models, Journal of time series analysis, 4, 2211-2238, (1983)
[4] Granger, C.W.J.; Joyeux, R., An introduction to long memory time series models and fractional differencing, Journal of time series analysis, 1, 15-39, (1980) · Zbl 0503.62079
[5] Granger, C.W.J.; Ding, Z., Varieties of long memory models, Journal of econometrics, 73, 61-78, (1996) · Zbl 0854.62100
[6] Lasota, A.; Mackey, M.C., Stochastic perturbation of dynamical systems: the weak convergence of measures, Journal of mathematical analysis and applications, 135, 232-248, (1989) · Zbl 0668.93081
[7] Rydén, T., Teräsvirta, T., Åsbrik, S., 1998. Stylized facts of daily returns series and the hidden Markov model, Journal of Applied Economics, in press.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.