Statistical inference for time-varying ARCH processes

By Rainer Dahlhaus, S. Rao. 2006

255 citations recorded by the source corpus.

In this paper the class of ARCH(oo) models is generalized to the nonstationary class of ARCH(oo) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation "locally stationary ARCH(oo) process." The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < oo) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/f12aa3c3c98eafd233350b346d061fad839052ae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Mixing properties of ARCH and time-varying ARCH processes (2011, methodology): “1(i)–(ii) guarantees that the ARCH process has a Volterra expansion as a solution (see [11], Section 5).”
Locally stationary long memory estimation (2009, methodology): “This approach was recently used for volatility estimation using time varying (short memory) non-linear processes, see [10,15].”
Nonparametric regression for locally stationary time series (2012, background): “Dahlhaus and Subba Rao [9] analyze a class of ARCH models with time-”
Stock Market Volatility and Macroeconomic Fundamentals (2013, background): “The fact that we have a time-varying long-run component that is nonstationary does not preclude us from doing proper maximum likelihood inference (see Dahlhaus & Rao, 2006, for more details).”
Conditional Correlation Models of Autoregressive Conditional Heteroscedasticity With Nonstationary GARCH Equations (2014, background): “Previously, Diebold (1986) and Lamoureux and Lastrapes (1990) also argued that spurious long memory may be detected from a time series with structural breaks.”
Locally Stationary Functional Time Series (2016, methodology): “It would therefore be of interest to develop an adaptive procedure as proposed in van Delft and Eichler (2015) to select the bandwidth parameters.”
ECONOMETRIC ANALYSIS OF VOLATILITY COMPONENT MODELS (2014, background): “, Dahlhaus and Rao (2006). The component model of Engle and Lee (1999) consists of two additive GARCH(1,1) components. One is identified as short-run (transitory) component, while the other is identified as long-run (trend) component. The component models that have been suggested recently are not of”
Detecting gradual changes in locally stationary processes (2013, background): “Analogous model formulations can be found for example in Subba Rao (2004) and Atak et al. (2011).”
A Component Model for Dynamic Correlations (2011, methodology): “The asymptotic properties of the two-step estimator are discussed in Engle and Sheppard (2001), Comte and Lieberman (2003), Ling and McAleer (2003) and McAleer, Chan, Hoti, and Lieberman (2006).”
On some nonstationary, nonlinear random processes and their stationary approximations (2006, methodology): “And the conditions stated here are slightly more general than the conditions given in Dahlhaus and Subba Rao (2006) .”