Long Memory in Nonlinear Processes
TL;DR: In this paper, the authors present several nonlinear long memory models, and discuss the properties of the models, as well as associated parametric andsemiparametric estimators, and the search for a realistic mechanism for generating long memory has led to the development of other nonlinear LMs.
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Abstract: It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing such behavior. A popular class of such models is the autoregressive fractionally integrated moving average (ARFIMA) which is a linear process. However, there is also a need for nonlinear long memory models. For example, series of returns on financial assets typically tend to show zero correlation, whereas their squares or absolute values exhibit long memory. Furthermore, the search for a realistic mechanism for generating long memory has led to the development of other nonlinear long memory models. In this chapter, we will present several nonlinear long memory models, and discuss the properties of the models, as well as associated parametric andsemiparametric estimators.
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References
Conditional heteroskedasticity in asset returns: a new approach
TL;DR: In this article, an exponential ARCH model is proposed to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987, which is an improvement over the widely-used GARCH model.
11.5K
A long memory property of stock market returns and a new model
TL;DR: In this paper, a Monte-Carlo analysis of stock market returns was conducted and it was found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return also has quite high autocorrelation for long lags.
3.9K
•Book
Modelling Extremal Events: for Insurance and Finance
Paul Embrechts,Thomas Mikosch,Claudia Klüppelberg +2 more
- 02 Jun 1997
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
3.8K
An introduction to long‐memory time series models and fractional differencing
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
3.8K