| dc.contributor.author | Szczepocki, Piotr | |
| dc.date.accessioned | 2018-09-21T14:10:33Z | |
| dc.date.available | 2018-09-21T14:10:33Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0208-6018 | |
| dc.identifier.uri | http://hdl.handle.net/11089/25799 | |
| dc.description.abstract | Barndorff‑Nielsen and Shephard (2001) proposed a class of stochastic volatility models in which the volatility process is the Ornstein‑Uhlenbeck process driven by a Levy process without gaussian component. Parameter estimation of these models is difficult because the appropriate likelihood functions do not have a closed‑form expression. The article deals with application of the Kalman filter technique for parameter estimation of such models. The method is applied to EUR/PLN daily exchange rate data. Empirical application is accompanied with simulation study to examine statistical properties of the estimators. | en_GB |
| dc.description.abstract | O. E. Barndorff‑Nielsen i N. Shephard (2001) zaproponowali klasę modeli stochastycznej zmienności typu Ornsteina‑Uhlenbecka, opartych na procesie Lévy’ego bez składnika Gaussowskiego. Estymacja parametrów modeli tego typu jest trudna, ponieważ nie można wyznaczyć odpowiedniej funkcji wiarygodności w postaci jawnego wzoru. W artykule zaprezentowana zostanie propozycja zastosowania filtru Kalmana do wyznaczania estymatorów parametrów w przypadku złożenia kilku procesów zmienności. Podejście to zostanie wykorzystane do modelowania kursu EUR/PLN. Empiryczny przykład uzupełnia eksperyment symulacyjny mający na celu zbadanie własności tak otrzymanych estymatorów. | pl_PL |
| dc.language.iso | pl | pl_PL |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl_PL |
| dc.relation.ispartofseries | Acta Universitatis Lodziensis. Folia Oeconomica;337 | |
| dc.subject | stochastic volatility models | en_GB |
| dc.subject | Levy processes | en_GB |
| dc.subject | stochastyczne modele zmienności | pl_PL |
| dc.subject | proces Lévy’ego | pl_PL |
| dc.title | Zastosowanie filtru Kalmana do modeli stochastycznej zmienności typu Ornsteina‑Uhlenbecka | pl_PL |
| dc.title.alternative | Application of Kalman Filter to Stochastic Volatility Models of the Orstein‑Uhlenbeck Type | en_GB |
| dc.type | Article | pl_PL |
| dc.rights.holder | © Copyright by Authors, Łódź 2018; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2018 | pl_PL |
| dc.page.number | 183-201 | |
| dc.contributor.authorAffiliation | Uniwersytet Łódzki, Wydział Ekonomiczno‑Socjologiczny, Katedra Metod Statystycznych | |
| dc.identifier.eissn | 2353-7663 | |
| dc.references | Andrieu C., Doucet A., Holenstein R. (2010), Particle Markov Chain Monte Carlo Methods, „Journal of the Royal Statistical Society: Series B (Statistical Methodology)”, t. 72(3), s. 269–342. | pl_PL |
| dc.references | Barndorff‑Nielsen O.E., Shephard N. (2001), Non‑Gaussian Ornstein‑Uhlenbeck‑based models and some of their uses in financial economics, „Journal of the Royal Statistical Society: Series B (Statistical Methodology)”, t. 63, nr 2, s. 167–241. doi: 10.1111/1467–9868.00282. | pl_PL |
| dc.references | Barndorff‑Nielsen O.E., Stelzer R. (2013), The multivariate supOU stochastic volatility model, „Mathematical Finance”, t. 23(2), s. 275–296. | pl_PL |
| dc.references | Bertoin J. (1996), Lévy processes, t. 121, Cambridge Tracts in Mathematics, Cambridge University Press, London. | pl_PL |
| dc.references | Bibby B.M., Sørensen M. (1995), Martingale estimation functions for discretely observed diffusion processes, „Bernoulli”, t. 1, nr 1/2, s. 17–39, doi: 10.2307/3318679. | pl_PL |
| dc.references | Byrd R.H., Lu P., Nocedal J., Zhu C. (1995), A limited memory algorithm for bound constrained optimization, „SIAM J. Scientific Computing”, t. 16, nr 5, s. 1190–1208, doi: 10.1137/0916069. | pl_PL |
| dc.references | Cont R., Tankov P. (2004), Financial Modelling with jump processes, Chapman Hall/CRC, Boca Raton. | pl_PL |
| dc.references | Gander M.P.S., Stephens D.A. (2007a), Stochastic volatility modelling in continuous time with general marginal distributions: Inference, prediction and model selection, „Journal of Statistical Planning and Inference”, t. 137, nr 10, s. 3068–3081, doi: 10.1016/j.jspi.2006.07.015. | pl_PL |
| dc.references | Gander M.P.S., Stephens D.A. (2007b), Simulation and inference for stochastic volatility models driven by levy processes, „Biometrika”, t. 94, nr 3, s. 627–646, doi: 10.1093/biomet/asm048. | pl_PL |
| dc.references | Gourieroux C., Monfort A., Renault E. (1993), Indirect inference, „Journal of Applied Econometrics”, t. 8, nr 1, s. S85–S118, doi: 10.1002/jae.3950080507. | pl_PL |
| dc.references | Grewal M., Andrews A. (2010), Applications of Kalman filtering in aerospace 1960 to the present, „Historical perspectives. IEEE Control Systems Magazine”, t. 30, nr 3, s. 69–78, doi: 10.1109/mcs.2010.936465. | pl_PL |
| dc.references | Griffin J.E., Steel M.F.J. (2006), Inference with non‑gaussian Ornstein‑Uhlenbeck processes for stochastic volatility, „Journal of Econometrics”, t. 134, nr 2, s. 605–644, doi: 10.1016/j.jeconom.2005.07.007. | pl_PL |
| dc.references | Griffin J.E., Steel M.F.J. (2010), Bayesian inference with stochastic volatility models using continuous superpositions of non‑gaussian Ornstein‑Uhlenbeck processes, „Computational Statistics Data Analysis”, t. 54, nr 11, s. 2594–2608, doi: 10.1016/j.csda.2009.06.008. | pl_PL |
| dc.references | Hamilton J.D. (1994), State‑space models, [w:] R.F. Engle, Handbook of econometrics, t. 4, North Holland, Amsterdam. | pl_PL |
| dc.references | Hubalek F., Posedel P. (2011), Joint analysis and estimation of stock prices and trading volume in Barndorff‑Nielsen and Shephard stochastic volatility models, „Quantitative Finance”, t. 11(6), s. 917–932. | pl_PL |
| dc.references | Kliber P. (2013), Zastosowanie procesów dyfuzji ze skokami do modelowania polskiego rynku finansowego, Wydawnictwo Uniwersytetu Ekonomicznego w Poznaniu, Poznań. | pl_PL |
| dc.references | Nicolato E., Venardos E. (2003), Option pricing in stochastic volatility models of the Ornstein‑Uhlenbeck type, „Mathematical Finance”, t. 13, nr 4, s. 445–466, doi: 10.1111/1467–9965.t01–1–00023. | pl_PL |
| dc.references | Parkinson M. (1980), The extreme value method for estimating the variance of the rate of return, „Journal of Business”, t. 53, nr 1, s. 61–65. | pl_PL |
| dc.references | Pigorsch C., Stelzer R. (2009), A multivariate Ornstein‑Uhlenbeck type stochastic volatility model, https://mediatum.ub.tum.de/doc/1079183/file.pdf [dostęp: 28.01.2018]. | pl_PL |
| dc.references | Pitt M.K., Shephard N. (1999), Filtering via simulation: Auxiliary particle filters, „Journal of the American Statistical Association”, t. 94, nr 446, s. 590–599, doi: 10.2307/2670179. | pl_PL |
| dc.references | Roberts G.O., Papaspiliopoulos O., Dellaportas P. (2004), Bayesian inference for non‑gaussian Ornstein‑Uhlenbeck stochastic volatility processes, „Journal of the Royal Statistical Society: Series B (Statistical Methodology)”, t. 66, nr 2, s. 369–393, doi: 10.1111/j.1369–7412.2004.05139.x. | pl_PL |
| dc.references | Stelzer R., Tosstorff T., Wittlinger M. (2015), Moment based estimation of supOU processes and a related stochastic volatility model, „Statistics Risk Modeling”, t. 32(1), s. 1–24. | pl_PL |
| dc.references | Taufer E., Leonenko N. (2009), Simulation of Levy‑driven Ornstein‑Uhlenbeck processes with given marginal distribution, „Computational Statistics Data Analysis”, t. 53(6), s. 2427–2437. | pl_PL |
| dc.references | Taufer E., Leonenko N., Bee M. (2011), Characteristic function estimation of Ornstein‑Uhlenbeck‑based stochastic volatility models, „Computational Statistics Data Analysis”, t. 55(8), s. 2525–2539. | pl_PL |
| dc.contributor.authorEmail | szczepocki@op.pl | |
| dc.identifier.doi | 10.18778/0208-6018.337.12 | |
| dc.relation.volume | 4 | pl_PL |
| dc.subject.jel | C58 | |
