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Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process

100%
Szczepocki P.
Statistics in Transition new series
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2020
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vol. 21
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issue 2
173-187
EN
Barndorff-Nielsen and Shephard (2001) proposed a class of stochastic volatility models in which the volatility follows the Ornstein-Uhlenbeck process driven by a positive Levy process without the Gaussian component. The parameter estimation of these models is challenging because the likelihood function is not available in a closed-form expression. A large number of estimation techniques have been proposed, mainly based on Bayesian inference. The main aim of the paper is to present an application of iterated filtering for parameter estimation of such models. Iterated filtering is a method for maximum likelihood inference based on a series of filtering operations, which provide a sequence of parameter estimates that converges to the maximum likelihood estimate. An application to S&P500 index data shows the model perform well and diagnostic plots for iterated filtering ensure convergence iterated filtering to maximum likelihood estimates. Empirical application is accompanied by a simulation study that confirms the validity of the approach in the case of Barndorff-Nielsen and Shephard's stochastic volatility models.
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Estimation of Yu and Meyer bivariate stochastic volatility model by iterated filtering

100%
Szczepocki P.
Przegląd Statystyczny
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2022
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vol. 69
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issue 4
1-19
EN
In financial applications, understanding the asset correlation structure is crucial to tasks such as asset pricing, portfolio optimisation, risk management, and asset allocation. Thus, modelling the volatilities and correlations of multivariate stock market returns is of great importance. This paper proposes the iterated filtering algorithm for estimating the bivariate stochastic volatility model of Yu and Meyer. The iterated filtering method is a frequentist-based approach that utilises particle filters and can be applied to estimating the parameters of non-linear or non-Gaussian state-space models. The paper presents an empirical example that demonstrates the way in which the proposed estimation method might be used to estimate the correlation between the returns of two assets: Standard and Poor's 500 index and the price of gold in US dollars. This is accompanied by a simulation study that proves the validity of the approach.
3
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Application of Iterated Filtering for Parametric Estimation of Instantaneous Variance in the Case of Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Processes

100%
Szczepocki P.
Przegląd Statystyczny
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2019
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vol. 66
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issue 1
51-68
EN
The article presents a method for parametric estimation of instantaneous variance in the case of non-Gaussian Ornstein-Uhlenbeck stochastic volatility process by means of the iterated filtering and realized variance estimator. The method is applied to realized variance of S&P500 index data. Empirical application is accompanied with simulation study to examine performance of the estimation technique.
4
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Estimation of the Cholesky Multivariate Stochastic Volatility Model Using Iterated Filtering

75%
Szczepocki P.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2023
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vol. 27
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issue 4
44-58
PL
Cel: Celem artykułu jest zaproponowanie nowej metody estymacji dla wielowymiarowego modelu stochastycznej zmienności z dekompozycją Choleskiego w oparciu o algorytm iterowanej filtracji (Ionides et al., 2006, 2015). Metodyka: Iterowana filtracja jest metodą należącą do klasycznego częstościowego wnioskowania, która poprzez wielokrotne powtórzenia procesu filtrowania zapewnia sekwencję aktualizowanych oszacowań parametrów zbieżnych do estymatora największej wiarygodności. Wyniki: Efektywność zaproponowanej metody estymacji została pokazana na przykładzie empirycznym, w którym wykorzystano wielowymiarowy model stochastyczny zmienności z dekompozycją Choleskiego w badaniu aktywów bezpiecznej przystani dla jednego indeksu rynkowego: Standard and Poor's 500 oraz trzech kandydatów na aktywa bezpiecznej przystani: złota, Bitcoina i Ethereum. Implikacje i rekomendacje: W dalszych badaniach metodę iterowanej filtracji można zastosować do bardziej zaawansowanych wielowymiarowych modeli zmienności stochastycznej, które uwzględniają np. efekt dźwigni (Ishihara et al., 2016) oraz rozkłady gruboogonowe (Ishihara i Omori, 2012). Oryginalność/Wartość: Głównym osiągnięciem artykułu jest propozycja nowej metody estymacji wielowymiarowego modelu stochastycznej zmienności z dekompozycją Choleskiego w oparciu o iterowany algorytm filtrowania. Jest to jedna z niewielu metod klasycznego częstościowego wnioskowania dla wielowymiarowych modeli stochastycznej zmienności.
EN
Aim: The paper aims to propose a new estimation method for the Cholesky Multivariate Stochastic Volatility Model based on the iterated filtering algorithm (Ionides et al., 2006, 2015). Methodology: The iterated filtering method is a frequentist-based technique that through multiple repetitions of the filtering process, provides a sequence of iteratively updated parameter estimates that converge towards the maximum likelihood estimate. Results: The effectiveness of the proposed estimation method was shown in an empirical example in which the Cholesky Multivariate Stochastic Volatility Model was used in a study on safe-haven assets of one market index: Standard and Poor’s 500 and three safe-haven candidates: gold, Bitcoin and Ethereum. Implications and recommendations: In further research, the iterating filtering method may be used for more advanced multivariate stochastic volatility models that take into account, for example, the leverage effect (as in Ishihara et al., 2016) and heavy-tailed errors (as in Ishihara and Omori, 2012). Originality/Value: The main contribution of the paper is the proposition of a new estimation method for the Cholesky Multivariate Stochastic Volatility Model based on iterated filtering algorithm This is one of the few frequentist-based statistical inference methods for multivariate stochastic volatility models.
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