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Some Non-linear AR-type Models for Non-Gaussian Time Series

In: Non-Gaussian Autoregressive-Type Time Series

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  • N. Balakrishna

    (Cochin University of Science and Technology, Department of Statistics)

Abstract

: The sequences of non-negative rvs find applications in many areas of the real world. For example, sequence of times to events in survival analysis, the inter-arrival times of events in renewal processes, modelling of volatility in finance, modelling of wind velocity, rainfall in meteorologic studies, modelling of run-off data in hydro-logical studies etc. The variables in these examples are serially dependent in time and exhibit a tendency to follow long-tailed marginal distributions such as Weibull, extreme-value type, Pareto etc. But processes with these marginal distributions cannot be generated with linear constant (or random) coefficient models described in earlier chapters. In view of the practical applications of time series with stationary marginal distribution over the positive support, several non-linear models were introduced during the last four decades. This chapter discusses some of such non-linear time series models generating stationary Markov sequences and possesses some of the characteristics of linear time series. The models with minification and product structures are explored here.

Suggested Citation

  • N. Balakrishna, 2021. "Some Non-linear AR-type Models for Non-Gaussian Time Series," Springer Books, in: Non-Gaussian Autoregressive-Type Time Series, chapter 0, pages 127-154, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-8162-2_5
    DOI: 10.1007/978-981-16-8162-2_5
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