Top

Published in:

2024 | OriginalPaper | Chapter

Periodic Trawl Processes: Simulation, Statistical Inference and Applications in Energy Markets

Author : Almut E. D. Veraart

Published in: Quantitative Energy Finance

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both short- and long-memory settings. We derive some of the key probabilistic properties of periodic trawl processes and present relevant examples. Moreover, we show how such processes can be simulated and establish the asymptotic theory for their sample mean and sample autocovariances. Consequently, we prove the asymptotic normality of a (generalised) method-of-moments estimator for the model parameters. We illustrate the new model and estimation methodology in an application to electricity prices.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Hawkes Processes in Energy Markets: Modelling, Estimation and Derivatives Pricing

next chapter Fuelling the Energy Transition: The Effect of German Wind and PV Electricity Infeed on TTF Gas Prices

Available only for authorised users

Alomari, H.M., Ayache, A., Fradon, M., Olenko, A.: Estimation of cyclic long-memory parameters. Scand. J. Stat. 47(1), 104–133 (2020). https://doi.org/10.1111/sjos.12404MathSciNetCrossRef

Andel, J.: Long memory time series models. Kybernetika 22, 105–123 (1986)MathSciNet

Arteche, J.: Semiparametric robust tests on seasonal or cyclical long memory time series. J. Time Ser. Anal. 23(3), 251–285 (2002). https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9892.00264MathSciNetCrossRef

Arteche, J., Robinson, P.M.: Semiparametric inference in seasonal and cyclical long memory processes. J. Time Ser. Anal. 21(1), 1–25 (2000). https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9892.00170MathSciNetCrossRef

Ayache, A., Fradon, M., Nanayakkara, R., Olenko, A.: Asymptotic normality of simultaneous estimators of cyclic long-memory processes. Electron. J. Stat. 16(1), 84–115 (2022). https://doi.org/10.1214/21-ejs1953MathSciNetCrossRef

Bacro, J., Gaetan, C., Opitz, T., Toulemonde, G.: Hierarchical space-time modeling of asymptotically independent exceedances with an application to precipitation data. J. Am. Stat. Assoc. 115(530), 555–569 (2020). https://doi.org/10.1080/01621459.2019.1617152MathSciNetCrossRef

Barndorff-Nielsen, O.E.: Stationary infinitely divisible processes. Braz. J. Probab. Stat. 25(3), 294–322 (2011). https://doi.org/10.1214/11-BJPS140MathSciNetCrossRef

Barndorff-Nielsen, O.E., Benth, F.E., Veraart, A.E.D.: Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19(3), 803–845 (2013). http://www.jstor.org/stable/23525714MathSciNetCrossRef

Barndorff-Nielsen, O.E., Lunde, A., Shephard, N., Veraart, A.E.D.: Integer-valued trawl processes: a class of stationary infinitely divisible processes. Scand. J. Stat. 41(3), 693–724 (2014)MathSciNetCrossRef

10.

Barndorff-Nielsen, O.E., Benth, F.E., Veraart, A.E.D.: Ambit Stochastics, vol. 88. Probability Theory and Stochastic Modelling. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94129-5

11.

Bennedsen, M., Lunde, A., Shephard, N., Veraart, A.E.D.: Inference and forecasting for continuous-time integer-valued trawl processes. J. Econom. 236(2), 105476 (2023). https://www.sciencedirect.com/science/article/pii/S0304407623001926MathSciNetCrossRef

12.

Bennett, W.R.: Statistics of regenerative digital transmission. Bell Syst. Tech. J. 37, 1501–1542 (1958). https://doi.org/10.1002/j.1538-7305.1958.tb01560.xMathSciNetCrossRef

13.

Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer Series in Statistics. Springer, New York (1987). https://doi.org/10.1007/978-1-4899-0004-3

14.

Cohen, S., Lindner, A.: A central limit theorem for the sample autocorrelations of a Lévy driven continuous time moving average process. J. Stat. Plan. Inference 143(8), 1295–1306 (2013). https://www.sciencedirect.com/science/article/pii/S0378375813000670CrossRef

15.

Courgeau, V., Veraart, A.E.: Asymptotic theory for the inference of the latent trawl model for extreme values. Scand. J. Stat. 49(4), 1448–1495 (2022). https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12563MathSciNetCrossRef

16.

Curato, I.V., Stelzer, R.: Weak dependence and GMM estimation of supOU and mixed moving average processes. Electron. J. Stat. 13(1), 310–360 (2019). https://doi.org/10.1214/18-EJS1523MathSciNetCrossRef

17.

Das, S., Genton, M.G.: Cyclostationary processes with evolving periods and amplitudes. IEEE Trans. Signal Process. 69, 1579–1590 (2021)MathSciNetCrossRef

18.

Doukhan, P., Jakubowski, A., Lopes, S., Surgailis, D.: Discrete-time trawl processes Stoch. Process. Appl. 129(4), 1326–1348 (2019). https://www.sciencedirect.com/science/article/pii/S0304414918301571MathSciNetCrossRef

19.

Doukhan, P., Roueff, F., Rynkiewicz, J.: Spectral estimation for non-linear long range dependent discrete time trawl processes. Electron. J. Stat. 14(2), 3157–3191 (2020). https://doi.org/10.1214/20-EJS1742MathSciNetCrossRef

20.

Espejo, R.M., Leonenko, N.N., Olenko, A., Ruiz-Medina, M.D.: On a class of minimum contrast estimators for Gegenbauer random fields. TEST 24, 657–680 (2015). https://doi.org/10.1007/s11749-015-0428-4MathSciNetCrossRef

21.

Fasen, V.: Extremes of regularly varying Lévy-driven mixed moving average processes. Adv. Appl. Probab. 37(4), 993–1014 (2005)MathSciNetCrossRef

22.

Ferrara, L., Guégan, D.: Comparison of parameter estimation methods in cyclical long memory time series. In: Junis, C., Moody, J., Timmermann, A. (eds.) Development in Forecast Combination and Portfolio Choice. Wiley, New York (2001)

23.

Fuchs, F., Stelzer, R.: Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM: Probab. Stat. 17, 455–471 (2013)MathSciNetCrossRef

24.

Gardner, W.A., Napolitano, A., Paura, L.: Cyclostationarity: half a century of research. Signal Process. 86(4), 639–697 (2006). https://www.sciencedirect.com/science/article/pii/S0165168405002409CrossRef

25.

Genton, M.G., Hall, P.: Statistical inference for evolving periodic functions. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 69(4), 643–657 (2007). https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9868.2007.00604.x

26.

Geweke, J., Porter-Hudak, S.: The estimation and application of long memory time series models. J. Time Ser. Anal. 4(4), 221–238 (1983). https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9892.1983.tb00371.xMathSciNetCrossRef

27.

Giraitis, L., Hidalgo, J., Robinson, P.M.: Gaussian estimation of parametric spectral density with unknown pole. Ann. Stat. 29(4), 987–1023 (2001). http://www.jstor.org/stable/2674066MathSciNetCrossRef

28.

Gladyšev, E.G.: Periodically correlated random sequences. Dokl. Akad. Nauk SSSR 137, 1026–1029 (1961)MathSciNet

29.

Grahovac, D., Leonenko, N.N., Taqqu, M.S.: Intermittency of trawl processes. Stat. Probab. Lett. 137, 235–242 (2018). https://www.sciencedirect.com/science/article/pii/S0167715218300415MathSciNetCrossRef

30.

Gray, H.L., Zhang, N.-F., Woodward, W.A.: On generalized fractional processes. J. Time Ser. Anal. 10(3), 233–257 (1989). https://doi.org/10.1111/j.1467-9892.1989.tb00026.xMathSciNetCrossRef

31.

Hall, P., Reimann, J., Rice, J.: Nonparametric estimation of a periodic function. Biometrika 87(3), 545–557 (2000). http://www.jstor.org/stable/2673629MathSciNetCrossRef

32.

Hidalgo, J.: Semiparametric estimation for stationary processes whose spectra have an unknown pole. Ann. Stat. 33(4), 1843–1889 (2005). https://doi.org/10.1214/009053605000000318MathSciNetCrossRef

33.

Hidalgo, J., Soulier, P.: Estimation of the location and exponent of the spectral singularity of a long memory process. J. Time Ser. Anal. 25(1), 55–81 (2004). https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9892.2004.00337.xMathSciNetCrossRef

34.

Hosking, J.R.M.: Fractional differencing. Biometrika 68(1), 165–176 (1981). http://www.jstor.org/stable/2335817MathSciNetCrossRef

35.

Hurd, H.L.: An investigation of periodically correlated stochastic processes. PhD thesis, Duke University, Department of Electrical Engineering (1969)

36.

Hurd, H.L., Miamee, A.: Periodically Correlated Random Sequences: Spectral Theory and Practice. Wiley Series in Probability and Statistics. Wiley-Interscience [John Wiley & Sons], Hoboken (2007). https://doi.org/10.1002/9780470182833

37.

Leonte, D., Veraart, A.E.D.: Simulation methods and error analysis for trawl processes and ambit fields. Math. Comput. Simul. 215, 518–542 (2024). https://doi.org/10.1016/j.matcom.2023.07.018MathSciNetCrossRef

38.

Maddanu, F.: A harmonically weighted filter for cyclical long memory processes. AStA Adv. Stat. Anal. 106, 49–78 (2022). https://doi.org/10.1007/s10182-021-00394-9MathSciNetCrossRef

39.

Mátyás, L. (ed.): Generalized Method of Moments Estimation. Cambridge University Press, Cambridge (1999). https://doi.org/10.1017/CBO9780511625848

40.

Noven, R.C.: Statistical models for spatio-temporal extrema and dependencies. PhD thesis, Imperial College London (2016). http://hdl.handle.net/10044/1/48048

41.

Noven, R., Veraart, A., Gandy, A.: A latent trawl process model for extreme values. J. Energy Mark. 11(3), 1–24 (2018). https://doi.org/10.21314/JEM.2018.179CrossRef

42.

Pakkanen, M.S., Passeggeri, R., Sauri, O., Veraart, A.E.D.: Limit theorems for trawl processes. Electron. J. Probab. 26, 1–36 (2021). https://doi.org/10.1214/21-EJP652MathSciNetCrossRef

43.

Paulauskas, V.: A note on linear processes with tapered innovations. Lith. Math. J. 60, 64–79 (2020). https://doi.org/10.1007/s10986-019-09445-wMathSciNetCrossRef

44.

Pedersen, J.: The Lévy-Itô decomposition of an independently scattered random measure. MaPhySto Research Report 2003-2 (2003). https://www.maphysto.dk/publications/MPS-RR/2003/2.pdf

45.

Quinn, B.G., Thomson, P.J.: Estimating the frequency of a periodic function. Biometrika 78(1), 65–74 (1991). http://www.jstor.org/stable/2336896MathSciNetCrossRef

46.

Rajput, B.S., Rosiński, J.: Spectral representations of infinitely divisible processes. Probab. Theory Relat. Fields 82(3), 451–487 (1989)MathSciNetCrossRef

47.

Sato, K.: Lévy Processes and Infinitely Divisible Distributions, vol. 68. Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1999). Translated from the 1990 Japanese original, Revised by the author

48.

Shephard, N., Yang, J.J.: , Likelihood inference for exponential-trawl processes, In: Podolskij, M., Stelzer, R., Thorbjørnsen, S., Veraart, A.E.D. (eds.) The Fascination of Probability, Statistics and Their Applications: In Honour of Ole E. Barndorff-Nielsen, pp. 251–281. Springer International Publishing, Cham (2016). https://doi.org/10.1007/978-3-319-25826-3_12CrossRef

49.

Shephard, N., Yang, J.J.: Continuous time analysis of fleeting discrete price moves. J. Am. Stat. Assoc. 112(519), 1090–1106 (2017). https://doi.org/10.1080/01621459.2016.1192544MathSciNetCrossRef

50.

Surgailis, D., Rosinski, J., Mandrekar, V., Cambanis, S.: Stable mixed moving averages. Probab. Theory Relat. Fields 97, 543–558 (1993). https://doi.org/10.1007/BF01192963MathSciNetCrossRef

51.

Talarczyk, A., Treszczotko, L.: Limit theorems for integrated trawl processes with symmetric Lévy bases. Electron. J. Probab. 25, 1–24 (2020). https://doi.org/10.1214/20-EJP509CrossRef

52.

Veraart, A.E.D.: Modeling, simulation and inference for multivariate time series of counts using trawl processes. J. Multivar. Anal. 169, 110–129 (2019). https://doi.org/10.1016/j.jmva.2018.08.012MathSciNetCrossRef

53.

Veraart, A.E.D.: ambit: Simulation and Estimation of Ambit Processes. R package version 0.1.2 (2022). https://cran.r-project.org/web/packages/ambit/index.html

54.

Veraart, A.E.D.: PeriodicTrawl-Energy. R code, release v1.0.0 (2023). https://doi.org/10.5281/zenodo.7706091

55.

Veraart, A.E.D., Veraart, L.A.M.: Modelling electricity day-ahead prices by multivariate Lévy semistationary processes. In: Benth, F.E., Kholodnyi, V.A., Laurence, P. (eds.) Quantitative Energy Finance: Modeling, Pricing, and Hedging in Energy and Commodity Markets, pp. 157–188. Springer, New York (2014). https://doi.org/10.1007/978-1-4614-7248-3_6CrossRef

56.

Wolpert, R.L., Brown, L.D.: Stationary infinitely-divisible Markov processes with non-negative integer values. Working paper, April 2011 (2011). https://faculty.wharton.upenn.edu/wp-content/uploads/2011/09/2011d-Stationary-Infinitely-Divisible-Markov-Processes-with-Non-negative-Integer-Values.pdf

57.

Wolpert, R.L., Taqqu, M.S.: Fractional Ornstein–Uhlenbeck Lévy processes and the Telecom process: upstairs and downstairs. Signal Process. 85, 1523–1545 (2005). https://doi.org/10.1016/j.sigpro.2004.09.016CrossRef

58.

Woodward, W.A., Cheng, Q.C., Gray, H.L.: A k-factor GARMA long-memory model. J. Time Ser. Anal. 19(4), 485–504 (1998). https://doi.org/10.1111/j.1467-9892.1998.00105.xMathSciNetCrossRef

59.

Yajima, Y.: Semiparametric estimation of the frequency of unbounded spectral densities. J. Stat. Stud. 26, 143–155 (2007). http://www.jstor.org/stable/27639901MathSciNet

Title: Periodic Trawl Processes: Simulation, Statistical Inference and Applications in Energy Markets
Author: Almut E. D. Veraart
Publisher: Springer Nature Switzerland
Book: Quantitative Energy Finance
Print ISBN: 978-3-031-50596-6

Electronic ISBN: 978-3-031-50597-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50597-3_3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"