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ARCH Models as Diffusion Approximations
Journal of Econometrics, 1990Abstract This paper investigates the convergence of stochastic difference equations (e.g. ARCH) to stochastic differential equations as the length of the discrete time intervals between observations goes to zero. These results are applied to the GARCH(l,1) model of Bollerslev (1986) and to the AR(l) Exponential ARCH model of Nelson ...
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Robust modelling of ARCH models
Journal of Forecasting, 2001The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption.
Jiancheng Jiang +2 more
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ON STATIONARITY IN THE ARCH(∞) MODEL
Econometric Theory, 2002We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of ...
Vytautas Kazakevičius, Remigijus Leipus
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Journal of Statistical Planning and Inference, 2004
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Horváth, Lajos, Liese, Friedrich
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Horváth, Lajos, Liese, Friedrich
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On the estimation of β-ARCH models
Statistics & Probability Letters, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ARCH Models and an Application on Exchange Rate Volatility: ARCH and GARCH Models
2021The financial liberalization that began in the last quarter of the twentieth century caused sudden movements in the currencies and financial assets of the countries. These sudden movements are called volatility. Sudden price changes in financial assets made it difficult to predict the future and increased the risks of financial assets.
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Journal of Business & Economic Statistics, 1991
Abstract This article introduces a semiparametric autoregressive conditional hetero scedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a ...
Robert F Engle, Gloria Gonzalez-Rivera
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Abstract This article introduces a semiparametric autoregressive conditional hetero scedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a ...
Robert F Engle, Gloria Gonzalez-Rivera
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Modelling of an arch dam by polynomial interpolation
Mathematics and Computers in Simulation, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. H. Delgado, L. Márquez
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Bayesian analysis of the unobserved ARCH model
Statistics and Computing, 2005The Unobserved ARCH model is a good description of the phenomenon of changing volatility that is commonly appeared in the financial time series. We study this model adopting Bayesian inference via Markov Chain Monte Carlo (MCMC). In order to provide an easy to implement MCMC algorithm we adopt some suitable non-linear transformations of the parameter ...
Giakoumatos, Stefanos G. +5 more
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1998
Since the introduction of autoregressive conditional heteroskedastic models (ARCH) by Engle (1982), an enormous boom has evolved in both theory and applications. It became obvious that a powerful model class was developed that copes with the most important feature of financial time series, namely conditional heteroskedasticity.
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Since the introduction of autoregressive conditional heteroskedastic models (ARCH) by Engle (1982), an enormous boom has evolved in both theory and applications. It became obvious that a powerful model class was developed that copes with the most important feature of financial time series, namely conditional heteroskedasticity.
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