Journal ArticleDOI
Stationarity and Persistence in the GARCH(1,1) Model
TLDR
In this article, necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process were established, and it was shown that the IGARCH(1,1) process with no drift converges almost surely to zero.Abstract:
This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition of persistence. We also develop necessary and sufficient conditions for the finiteness of absolute moments of any (including fractional) order.read more
Citations
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Journal ArticleDOI
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.
Journal ArticleDOI
ARCH modeling in finance: A review of the theory and empirical evidence
TL;DR: An overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data can be found in this paper, where several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and pricing of derivative assets, are also discussed.
Journal ArticleDOI
Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances
TL;DR: In this paper, the authors study the properties of the quasi-maximum likelihood estimator and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood is maximized but the assumption of normality is violated.
Journal ArticleDOI
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.
Book
Quantitative Risk Management: Concepts, Techniques, and Tools
TL;DR: The most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management can be found in this paper, where the authors describe the latest advances in the field, including market, credit and operational risk modelling.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
TL;DR: In this article, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced, which are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances.
Journal ArticleDOI
Generalized autoregressive conditional heteroskedasticity
Tim Bollerslev,Tim Bollerslev +1 more
TL;DR: In this paper, a natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in 1982 to allow for past conditional variances in the current conditional variance equation is proposed.
BookDOI
Density estimation for statistics and data analysis
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.