Gaussian Semiparametric Estimation in Long Memory in Stochastic Volatility and Signal Plus Noise Models

By Josu Arteche. 2004

92 citations recorded by the source corpus.

This paper considers the persistence found in the volatility of many financial time series by means of a local Long Memory in Stochastic Volatility model and analyzes the performance of the Gaussian semiparametric or local Whittle estimator of the memory parameter in a long memory signal plus noise model which includes the Long Memory in Stochastic Volatility as a particular case. It is proved that this estimate preserves the consistency and asymptotic normality encountered in observable long memory series and under milder conditions it is more efficient than the estimator based on a log-periodogram regression. Although the asymptotic properties do not depend on the signal-to-noise ratio the finite sample performance relies upon this magnitude and an appropriate choice of the bandwidth is important to minimize the influence of the added noise. I analyze the effect of the bandwidth via Monte Carlo. An application to a Spanish stock index is finally included.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/de99ab10165f55be0442054f0afd5791c55c678c

How researchers see this paper

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In Economics and Econometrics

1. Jie Hou
2. Pierre Perron
3. Yang K. Lu
4. Per Frederiksen
5. Violetta Dalla
6. J. Hidalgo
7. Frank Nielsen
8. Esther Ruiz

In Finance

1. Jie Hou
2. Pierre Perron
3. Per Frederiksen
4. Violetta Dalla
5. J. Hidalgo
6. Frank Nielsen
7. Esther Ruiz
8. Carmen Broto

Citations in the corpus

• Estimation methods for stochastic volatility models: a survey (2004, background): “Alternatively, Arteche (2004) proposes a local Whittle estimator of the long-memory parameter that relaxes this assumption.”
• Modeling and forecasting stock return volatility using a random level shift model (2010, background): “, Arteche (2004) and Deo and Hurvich (2001). More recently, attempts have been made to distinguish between stationary noise plus level shift and long-memory models; see, in particular, Granger and Hyung (2004). They documented the fact that, when breaks determined via some pre tests are accounted fo”
• Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations (2014, methodology): “The theory of parametric estimators was developed by Fox and Taqqu (1986) and Dahlhaus (1989), among others. Semiparametric estimators of the memory parameter have become popular since they do not require knowing the speci…c form of the short memory structure. They are based on the periodograms of t”
• Consistent estimation of the memory parameter for nonlinear time series (2006, methodology): “In case of a linear process (nt), consistency and asymptotic distribution of the local Whittle estimator âlog were analysed in Hurvich et al. (2005) and Arteche (2004).”
• Local Polynomial Whittle Estimation of Perturbed Fractional Processes (2008, methodology): “(1998), Deo & Hurvich (2001), and Arteche (2004), among others, in the LMSV model. To accommodate the leverage effect, we could allow contemporaneous correlation, while the return process remains a martingale difference sequence by replacing yt with yt−1 in (3). An additional assumption of distribut”