Highly Robust Estimation of the Autocovariance Function
Abstract
In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the influence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They confirm the robustness properties of the new estimator. An S‐Plus function for the highly robust autocovariance estimator is made available on the Web at http://www‐math.mit.edu/~yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank.
Citing Literature
Number of times cited according to CrossRef: 56
- S.A. David, J.A.T. Machado, C.M.C. Inácio, C.A. Valentim, A combined measure to differentiate EEG signals using fractal dimension and MFDFA-Hurst, Communications in Nonlinear Science and Numerical Simulation, 10.1016/j.cnsns.2020.105170, (105170), (2020).
- Valdério Anselmo Reisen, Céline Lévy-Leduc, Higor Henrique Aranda Cotta, Pascal Bondon, Marton Ispany, Paulo Roberto Prezotti Filho, An Overview of Robust Spectral Estimators, Cyclostationarity: Theory and Methods – IV, 10.1007/978-3-030-22529-2_12, (204-224), (2020).
- Carina Gerstenberger, Robust discrimination between long‐range dependence and a change in mean, Journal of Time Series Analysis, 10.1111/jtsa.12554, 0, 0, (2020).
- Marcio Valk, Gabriela Bettella Cybis, U -Statistical Inference for Hierarchical Clustering , Journal of Computational and Graphical Statistics, 10.1080/10618600.2020.1796398, (1-11), (2020).
- Valdério Anselmo Reisen, Adriano Marcio Sgrancio, Céline Lévy-Leduc, Pascal Bondon, Edson Zambon Monte, Higor Henrique Aranda Cotta, Flávio Augusto Ziegelmann, Robust factor modelling for high-dimensional time series: An application to air pollution data, Applied Mathematics and Computation, 10.1016/j.amc.2018.09.062, 346, (842-852), (2019).
- Yuichi Goto, Masanobu Taniguchi, Robustness of Zero Crossing Estimator, Journal of Time Series Analysis, 10.1111/jtsa.12463, 40, 5, (815-830), (2019).
- Carlos Trucíos, Luiz K. Hotta, Pedro L. Valls Pereira, On the robustness of the principal volatility components, Journal of Empirical Finance, 10.1016/j.jempfin.2019.03.006, (2019).
- Carlos César Trucíos Maza, João Henrique Gonçalves Mazzeu, Luiz Koodi Hotta, Pedro L. Valls Pereira, Marc Hallin, Robustness and the General Dynamic Factor Model With Infinite-Dimensional Space: Identification, Estimation, and Forecasting, SSRN Electronic Journal, 10.2139/ssrn.3509166, (2019).
- Carlo Corrêa Solci, Valdério Anselmo Reisen, Alessandro José Queiroz Sarnaglia, Pascal Bondon, Empirical study of robust estimation methods for PAR models with application to the air quality area, Communications in Statistics - Theory and Methods, 10.1080/03610926.2018.1533970, (1-17), (2019).
- Andres Algaba, Kris Boudt, Steven Vanduffel, The variance implied conditional correlation, The European Journal of Finance, 10.1080/1351847X.2019.1615524, (1-23), (2019).
- Valdério Anselmo Reisen, Edson Zambon Monte, Glaura da Conceição Franco, Adriano Marcio Sgrancio, Fábio Alexander Fajardo Molinares, Pascal Bondon, Flávio Augusto Ziegelmann, Bovas Abraham, Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations, Mathematics and Computers in Simulation, 10.1016/j.matcom.2017.10.004, 146, (27-43), (2018).
- Andres Algaba, Kris Boudt, Steven Vanduffel, The Variance Implied Hedge Ratio, SSRN Electronic Journal, 10.2139/ssrn.3125020, (2018).
- Carlos CCsar Truccos Maza, Luiz Koodi Hotta, Pedro L. Valls Pereira, On the Robustness of the Principal Volatility Components, SSRN Electronic Journal, 10.2139/ssrn.3143870, (2018).
- References, Robust Statistics, undefined, (407-422), (2018).
- F. A. Fajardo, V. A. Reisen, C. Lévy-Leduc, M. S. Taqqu, M -periodogram for the analysis of long-range-dependent time series , Statistics, 10.1080/02331888.2018.1427751, 52, 3, (665-683), (2018).
- Wanbo Lu, Rui Ke, Some closed form robust moment‐based estimators for the MEM(1,1), Applied Stochastic Models in Business and Industry, 10.1002/asmb.2259, 33, 6, (559-574), (2017).
- V.A. Reisen, C. Lévy-Leduc, M.S. Taqqu, An -estimator for the long-memory parameter , Journal of Statistical Planning and Inference, 10.1016/j.jspi.2017.02.008, 187, (44-55), (2017).
- Timothy J. Vogelsang, Jingjing Yang, Exactly/Nearly Unbiased Estimation of Autocovariances of a Univariate Time Series With Unknown Mean, Journal of Time Series Analysis, 10.1111/jtsa.12184, 37, 6, (723-740), (2016).
- Erdi Dasdemir, Christian Weiß, Murat Caner Testik, Sven Knoth, Evaluation of Phase I analysis scenarios on Phase II performance of control charts for autocorrelated observations, Quality Engineering, 10.1080/08982112.2015.1104540, 28, 3, (293-304), (2016).
- Christopher C. Chang, Dimitris N. Politis, Robust Autocorrelation Estimation, Journal of Computational and Graphical Statistics, 10.1080/10618600.2014.969431, 25, 1, (144-166), (2016).
- Qi Li, Heng Lian, Fukang Zhu, Robust closed-form estimators for the integer-valued GARCH (1,1) model, Computational Statistics & Data Analysis, 10.1016/j.csda.2016.03.006, 101, (209-225), (2016).
- M. Angeles Carnero, Ana Pérez, Esther Ruiz, Identification of asymmetric conditional heteroscedasticity in the presence of outliers, SERIEs, 10.1007/s13209-015-0131-4, 7, 1, (179-201), (2015).
- Eugen Ursu, Jean-Christophe Pereau, Application of periodic autoregressive process to the modeling of the Garonne river flows, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-015-1193-3, 30, 7, (1785-1795), (2015).
- Alexander Dürre, Roland Fried, Tobias Liboschik, Robust estimation of (partial) autocorrelation, WIREs Computational Statistics , 10.1002/wics.1351, 7, 3, (205-222), (2015).
- Gabriel Rodríguez, A Comparative Note about Estimation of the Fractional Parameter under Additive Outliers, Communications in Statistics - Simulation and Computation, 10.1080/03610918.2014.892322, 45, 1, (207-221), (2014).
- Stefan Aelst, Outliers, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Mia Hubert, Peter J. Rousseeuw, Stefan Aelst, Robustness in the Linear Regression M+N105odel, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Eugen Ursu, Jean-Christophe Pereau, Robust modelling of periodic vector autoregressive time series, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2014.07.005, 155, (93-106), (2014).
- Hanan Elsaied, Roland Fried, ROBUST FITTING OF INARCH MODELS, Journal of Time Series Analysis, 10.1111/jtsa.12079, 35, 6, (517-535), (2014).
- Yuriy Kharin, Yuriy Kharin, Optimality and Robustness of Vector Autoregression Forecasting Under Missing Values, Robustness in Statistical Forecasting, 10.1007/978-3-319-00840-0, (231-272), (2013).
- M. Eichler, D. Türk, Fitting semiparametric Markov regime-switching models to electricity spot prices, Energy Economics, 10.1016/j.eneco.2012.11.013, 36, (614-624), (2013).
- Byungsoo Kim, Sangyeol Lee, Robust estimation for the covariance matrix of multivariate time series based on normal mixtures, Computational Statistics & Data Analysis, 10.1016/j.csda.2012.06.012, 57, 1, (125-140), (2013).
- Bernhard Spangl, Rudolf Dutter, Robustness in Time Series: Robust Frequency Domain Analysis, Robustness and Complex Data Structures, 10.1007/978-3-642-35494-6, (207-223), (2013).
- B. Spangl, R. Dutter, Analyzing short-term measurements of heart rate variability in the frequency domain using robustly estimated spectral density functions, Computational Statistics & Data Analysis, 10.1016/j.csda.2011.05.010, 56, 5, (1188-1199), (2012).
- Ying Sun, Marc G. Genton, Adjusted functional boxplots for spatio‐temporal data visualization and outlier detection, Environmetrics, 10.1002/env.1136, 23, 1, (54-64), (2011).
- Yuriy S. Kharin, Valeriy A. Voloshko, Robust estimation of AR coefficients under simultaneously influencing outliers and missing values, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2011.04.015, 141, 9, (3276-3288), (2011).
- Olaf Kouamo, Celine Levy-Leduc, Eric Moulines, undefined, 2011 IEEE Statistical Signal Processing Workshop (SSP), 10.1109/SSP.2011.5967757, (553-556), (2011).
- Byungsoo Kim, Sangyeol Lee, Robust estimation for the covariance matrix of multi‐variate time series, Journal of Time Series Analysis, 10.1111/j.1467-9892.2010.00705.x, 32, 5, (469-481), (2010).
- Céline Lévy‐Leduc, Hélène Boistard, Eric Moulines, Murad S. Taqqu, Valderio A. Reisen, Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes, Journal of Time Series Analysis, 10.1111/j.1467-9892.2010.00688.x, 32, 2, (135-156), (2010).
- A.J.Q. Sarnaglia, V.A. Reisen, C. Lévy-Leduc, Robust estimation of periodic autoregressive processes in the presence of additive outliers, Journal of Multivariate Analysis, 10.1016/j.jmva.2010.05.006, 101, 9, (2168-2183), (2010).
- Ta-Hsin Li, A Nonlinear Method for Robust Spectral Analysis, IEEE Transactions on Signal Processing, 10.1109/TSP.2010.2042479, 58, 5, (2466-2474), (2010).
- Marc G. Genton, Anne Ruiz-Gazen, Visualizing Influential Observations in Dependent Data, Journal of Computational and Graphical Statistics, 10.1198/jcgs.2010.09101, 19, 4, (808-825), (2010).
- Robin Nunkesser, Roland Fried, Karen Schettlinger, Ursula Gather, Online analysis of time series by the estimator, Computational Statistics & Data Analysis, 10.1016/j.csda.2008.02.027, 53, 6, (2354-2362), (2009).
- Fabio Fajardo Molinares, Valdério Anselmo Reisen, Francisco Cribari-Neto, Robust estimation in long-memory processes under additive outliers, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2008.12.014, 139, 8, (2511-2525), (2009).
- Olcay Arslan, An alternative multivariate skew Laplace distribution: properties and estimation, Statistical Papers, 10.1007/s00362-008-0183-7, 51, 4, (865-887), (2008).
- Adelchi Azzalini, Marc G. Genton, Robust Likelihood Methods Based on the Skew‐t and Related Distributions, International Statistical Review, 10.1111/j.1751-5823.2007.00016.x, 76, 1, (106-129), (2007).
- Pierre Duchesne, Robust and powerful serial correlation tests with new robust estimates in ARX models, Journal of Time Series Analysis, 10.1111/j.1467-9892.2005.00390.x, 26, 1, (49-81), (2005).
- Mia Hubert, Peter J. Rousseeuw, Stefan Aelst, Robustness, Encyclopedia of Actuarial Science, 10.1002/9780470012505, (2004).
- Pierre Duchesne, On robust testing for conditional heteroscedasticity in time series models, Computational Statistics & Data Analysis, 10.1016/S0167-9473(03)00173-7, 46, 2, (227-256), (2004).
- M. G. Genton, Breakdown-Point for Spatially and Temporally Correlated Observations, Developments in Robust Statistics, 10.1007/978-3-642-57338-5, (148-159), (2003).
- Marc G Genton, Elvezio Ronchetti, Robust Indirect Inference, Journal of the American Statistical Association, 10.1198/016214503388619102, 98, 461, (67-76), (2003).
- M. Imhoff, M. Bauer, U. Gather, R. Fried, Pattern Detection in Intensive Care Monitoring Time Series with Autoregressive Models: Influence of the Model Order, Biometrical Journal, 10.1002/1521-4036(200209)44:6<746::AID-BIMJ746>3.0.CO;2-2, 44, 6, (746-761), (2002).
- Stefan Aelst, Outliers, Encyclopedia of Environmetrics, 10.1002/9780470057339, (2001).
- Yanyuan Ma, Marc G. Genton, Highly Robust Estimation of Dispersion Matrices, Journal of Multivariate Analysis, 10.1006/jmva.2000.1942, 78, 1, (11-36), (2001).
- Xavier de Luna, Marc G Genton, Robust Simulation-Based Estimation of ARMA Models, Journal of Computational and Graphical Statistics, 10.1198/10618600152628347, 10, 2, (370-387), (2001).
- Marc G. Genton, Xavier de Luna, Robust simulation-based estimation, Statistics & Probability Letters, 10.1016/S0167-7152(00)00004-3, 48, 3, (253-259), (2000).
