Maximum likelihood estimation of linear continuous time long memory processes with discrete time data
Henghsiu Tsai, Institute of Statistical Science, Academia Sinica, Taipei, Taiwan 115, Republic of China.
E‐mail: htsai@stat.sinica.edu.tw
Abstract
Summary. We develop a new class of time continuous autoregressive fractionally integrated moving average (CARFIMA) models which are useful for modelling regularly spaced and irregu‐larly spaced discrete time long memory data. We derive the autocovariance function of a stationary CARFIMA model and study maximum likelihood estimation of a regression model with CARFIMA errors, based on discrete time data and via the innovations algorithm. It is shown that the maximum likelihood estimator is asymptotically normal, and its finite sample properties are studied through simulation. The efficacy of the approach proposed is demonstrated with a data set from an environmental study.
Citing Literature
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- Natalia Żywucka, Mariusz Tarnopolski, Markus Böttcher, Łukasz Stawarz, Volodymyr Marchenko, Optical Variability Modeling of Newly Identified Blazar Candidates behind Magellanic Clouds, The Astrophysical Journal, 10.3847/1538-4357/ab5fe5, 888, 2, (107), (2020).
- Mariusz Tarnopolski, Natalia Żywucka, Volodymyr Marchenko, Javier Pascual-Granado, A Comprehensive Power Spectral Density Analysis of Astronomical Time Series. I. The Fermi-LAT Gamma-Ray Light Curves of Selected Blazars, The Astrophysical Journal Supplement Series, 10.3847/1538-4365/aba2c7, 250, 1, (1), (2020).
- Anne Philippe, Caroline Robet, Marie-Claude Viano, Random discretization of stationary continuous time processes, Metrika, 10.1007/s00184-020-00783-1, (2020).
- Andrew M. Stuhr, Eric D. Feigelson, Gabriel A. Caceres, Joel D. Hartman, Autoregressive Planet Search: Feasibility Study for Irregular Time Series, The Astronomical Journal, 10.3847/1538-3881/ab26b3, 158, 2, (59), (2019).
- Theodore Simos, Mike Tsionas, Bayesian inference of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme, Computational Statistics, 10.1007/s00180-018-0799-6, 33, 4, (1687-1713), (2018).
- Lin Sun, Lin Wang, Pei Fu, Maximum likelihood estimators of a long-memory process from discrete observations, Advances in Difference Equations, 10.1186/s13662-018-1611-1, 2018, 1, (2018).
- Eric D. Feigelson, G. Jogesh Babu, Gabriel A. Caceres, Autoregressive Times Series Methods for Time Domain Astronomy, Frontiers in Physics, 10.3389/fphy.2018.00080, 6, (2018).
- Fengwei Chen, Hugues Garnier, Marion Gilson, Juan C. Agüero, Tao Liu, Refined instrumental variable parameter estimation of continuous-time Box–Jenkins models from irregularly sampled data, IET Control Theory & Applications, 10.1049/iet-cta.2016.0506, 11, 2, (291-300), (2017).
- Hagai Kirshner, Michael Unser, John Paul Ward, On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data, IEEE Transactions on Signal Processing, 10.1109/TSP.2013.2296879, 62, 6, (1361-1376), (2014).
- Xiaojun Zhao, Pengjian Shang, Jingjing Huang, Continuous detrended cross-correlation analysis on generalized Weierstrass function, The European Physical Journal B, 10.1140/epjb/e2012-30244-6, 86, 2, (2013).
- Qi Sun, Weijun Xu, Weilin Xiao, An empirical estimation for mean-reverting coal prices with long memory, Economic Modelling, 10.1016/j.econmod.2013.04.015, 33, (174-181), (2013).
- Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik, Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik, Origins and Generation of Long Memory, Long-Memory Processes, 10.1007/978-3-642-35512-7, (43-106), (2013).
- Muneya Matsui, Narn-Rueih Shieh, On the exponential process associated with a CARMA-type process, Stochastics, 10.1080/17442508.2012.654791, 85, 5, (743-762), (2012).
- Weijun Xu, Qi Sun, Weilin Xiao, A new energy model to capture the behavior of energy price processes, Economic Modelling, 10.1016/j.econmod.2012.05.009, 29, 5, (1585-1591), (2012).
- Hagai Kirshner, Simona Maggio, Michael Unser, A Sampling Theory Approach for Continuous ARMA Identification, IEEE Transactions on Signal Processing, 10.1109/TSP.2011.2161983, 59, 10, (4620-4634), (2011).
- Du Xiuli, Wang Fengquan, Modal identification based on Gaussian continuous time autoregressive moving average model, Journal of Sound and Vibration, 10.1016/j.jsv.2010.04.018, 329, 20, (4294-4312), (2010).
- Tsung-Lin Cheng, An efficient algorithm for estimating a change-point, Statistics & Probability Letters, 10.1016/j.spl.2008.09.031, 79, 5, (559-565), (2009).
