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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.
2
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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.
3
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On upper gain bound for trading strategy based on cointegration

100%
Łochowski R.
Metody Ilościowe w Badaniach Ekonomicznych
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2010
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vol. 11
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issue 1
110-117
EN
A long-run trading strategy based on cointegration relationship between prices of two commodities is considered. A linear combination of the prices is assumed to be a stationary AR(1) process. In some range of parameters, AR(1) process is obtained by discrete sampling of Ornstein-Uhlenbeck process. This allows to calculate approximate number of transactions in long run trade horizon and obtain approximate upper bound for possible gain.
4
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ON AN UPPER GAIN BOUND FOR STRATEGIES WITH CONSTANT AND PROPORTIONAL NUMBER OF ASSETS TRADED

63%
Łochowski R.
Metody Ilościowe w Badaniach Ekonomicznych
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2013
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vol. 14
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issue 2
29-38
EN
We introduce general formulas for the upper bound of gain obtained from any finite-time trading strategy in discrete and continuous time models. We consider strategies with constant number of assets traded and strategies with proportional number of assets traded. Unfortunately, the estimates obtained in the discrete case become trivial in the continuous case, hence we introduce transaction costs. This leads to the interesting estimates in terms of the so called truncated variation of the price series. We apply the obtained estimates in specific cases of financial time series.
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