×
Dürre, Alexander; Fried, Roland; Liboschik, Tobias

Robust estimation of (partial) autocorrelation. (English) Zbl 07912768

Wiley Interdiscip. Rev., WIREs Comput. Stat. 7, No. 3, 205-222 (2015).

Cited in 6 Documents

MSC:

62-08 Computational methods for problems pertaining to statistics

Keywords:

autocovariance; outliers; time series; correlogram

Software:

R
Cite Review PDF
Full Text: DOI

References:

[1] BrockwellPJ. Autocovariance. WIREs Comput Stat2009, 1:187-198.
[2] BoxGEP, JenkinsGM, ReinselGC. Time Series Analysis: Forecasting and Control. 3rd ed.Englewood Cliff, NJ: Prentice Hall; 1994. · Zbl 0858.62072
[3] BrockwellPJ, DavisRA. Time Series: Theory and Methods. 2nd ed.New York: Springer; 2006.
[4] WeiWWS. Time Series Analysis: Univariate and Multivariate Methods. Redwood City: Addison‐Wesley; 1990. · Zbl 0683.62044
[5] VecchiaAV, BalleriniR. Testing for periodic autocorrelations in seasonal time series data. Biometrika1991, 78:53-63. · Zbl 0717.62083
[6] CaiadoJ, CratoN, PeñaD. A periodogram‐based metric for time series classification. Comput Stat Data Anal2006, 50:2668-2684. · Zbl 1445.62222
[7] ChanW‐S. A note on time series model specification in the presence of outliers. J Appl Stat1992, 19:117-124.
[8] DeutschSJ, RichardsJE, SwainJJ. Effects of a single outlier on ARMA identification. Commun Stat Theor Methods1990, 19:2207-2227.
[9] MaronnaRA, MartinRD, YohaiVJ. Robust Statistics. Chichester: John Wiley & Sons; 2006. · Zbl 1094.62040
[10] SchlittgenR, StreitbergBHJ. Zeitreihenanalyse. München: Oldenbourg; 2001, 414-427.
[11] BrockwellPJ. Autoregressive processes. WIREs Comput Stat2011, 3:316-331.
[12] RamseyFL. Characterization of the partial autocorrelation function. Ann Stat1974, 2:1296-1301. · Zbl 0301.62046
[13] MasarottoG. Robust identification of autoregressive moving average models. Appl Stat1987, 36:214-220. · Zbl 0617.62098
[14] MakhoulJ. Lattice methods in spectral estimation. Appl Time Ser Anal1981, 2:301-326. · Zbl 0485.62108
[15] ChanW‐S, WeiWWS. A comparison of some estimators of time series autocorrelations. Comput Stat Data Anal1992, 14:149-163. · Zbl 0875.62420
[16] ChakhchoukhY. A new robust estimation method for ARMA models. IEEE Trans Signal Process2010, 58:3512-3522. · Zbl 1391.62159
[17] BustosOH, YohaiVJ. Robust estimates for ARMA models. J Am Stat Assoc1986, 81:155-168.
[18] MorgenthalerS. Robustness. WIREs Comput Stat2011, 3:85-94.
[19] GarelB, HallinM. Rank‐based autoregressive order identification. J Am Stat Assoc1999, 94:1357-1371. · Zbl 0994.62089
[20] FerrettiNE, KelmanskyDM, YohaiVJ. Estimators based on ranks for ARMA models. Commun Stat Theor Methods1991, 20:3879-3907. · Zbl 0800.62524
[21] BoudtK, CornelissenJ, CrouxC. The gaussian rank correlation estimator: robustness properties. Stat Comput2012, 22:471-483. · Zbl 1322.62129
[22] CrouxC, DehonC. Influence functions of the spearman and kendall correlation measures. Stat Methods Appl2010, 19:497-515. · Zbl 1332.62186
[23] MottonenJ, KoivunenV, OjaH. Robust autocovariance estimation based on sign and rank correlation coefficients. In: Proceedings of the IEEE Signal Processing Workshop on Higher‐Order Statistics, IEEE, 187-190, 1999.
[24] GatherU, BauerM, FriedR. The identification of multiple outliers in online monitoring data. Estadistica2002, 54:289-338. · Zbl 1034.62083
[25] TaskinenS, CrouxC, KankainenA, OllilaE, OjaH. Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices. J Multivar Anal2006, 97:359-384. · Zbl 1085.62078
[26] VakiliK, SchmittE. Finding multivariate outliers with fastPCS. Comput Stat Data Anal2014, 69:54-66. · Zbl 1471.62196
[27] MaronnaRA. Robust M‐estimators of multivariate location and scatter. Ann Stat1976, 4:51-67. · Zbl 0322.62054
[28] TylerDE. A distribution‐free M‐estimator of multivariate scatter. Ann Stat1987, 15:234-251. · Zbl 0628.62053
[29] HubertM, DebruyneM. Breakdown value. WIREs Comput Stat2009, 1:296-302.
[30] DaviesPL. Asymptotic behaviour of S‐estimates of multivariate location parameters and dispersion matrices. Ann Stat1987, 15:1269-1292. · Zbl 0645.62057
[31] Van AelstS, RousseeuwP. Minimum volume ellipsoid. WIREs Comput Stat2009, 1:71-82.
[32] LopuhaaHP. On the relation between S‐estimators and M‐estimators of multivariate location and covariance. Ann Stat1989, 17:1662-1683. · Zbl 0702.62031
[33] Salibian‐BarreraM, YohaiVJ. A fast algorithm for S‐regression estimates. J Comput Graph Stat2006, 15.
[34] HubertM, DebruyneM. Minimum covariance determinant. WIREs Comput Stat2010, 2:36-43.
[35] RousseeuwPJ. Multivariate estimation with high breakdown point. Math Stat Appl B1985, 8:283-297. · Zbl 0609.62054
[36] RousseeuwPJ, Van DriessenK. A fast algorithm for the minimum covariance determinant estimator. Technometrics1999, 41:212-223.
[37] CrouxC, HaesbroeckG. Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. J Multivar Anal1999, 71:161-190. · Zbl 0946.62055
[38] GerviniD. A robust and efficient adaptive reweighted estimator of multivariate location and scatter. J Multivar Anal2003, 84:116-144. · Zbl 1038.62051
[39] HadiAS, ImonAHM, WernerM. Detection of outliers. WIREs Comput Stat2009, 1:57-70.
[40] DonohoDL. Breakdown properties of multivariate location estimators. Technical report, Harvard University, Boston; 1982. Available at: http://statweb.stanford.edu/
[41] StahelWA. Robust estimation: infinitesimal optimality and covariance matrix estimators. PhD Thesis, ETH, Zurich, Switzerland, 1981.
[42] GnanadesikanR, KettenringJR. Robust estimates, residuals, and outlier detection with multiresponse data. Biometrika1972, 28:81-124.
[43] MaY, GentonMG. Highly robust estimation of the autocovariance function. J Time Ser Anal2000, 21:663-684. · Zbl 0970.62056
[44] RousseeuwPJ, CrouxC. Alternatives to the median absolute deviation. J Am Stat Assoc1993, 88:1273-1283. · Zbl 0792.62025
[45] MaronnaRA, ZamarRH. Robust estimates of location and dispersion for high‐dimensional datasets. Technometrics2002, 44:307-317.
[46] MasreliezC. Approximate non‐Gaussian filtering with linear state and observation relations. IEEE Trans Automat Control1975, 20:107-110. · Zbl 0298.93018
[47] MartinRD, ThomsonDJ. Robust‐resistant spectrum estimation. Proc IEEE1982, 70:1097-1115.
[48] R Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2012.
[49] TodorovV, FilzmoserP. An object‐oriented framework for robust multivariate analysis. J Stat Softw2009, 32:1-47.
[50] NordhausenK, SirkiaS, OjaH, TylerDE. ICSNP: Tools for Multivariate Nonparametrics. R package version 1.0‐9, 2012.
[51] SirkiaS, MiettinenJ, NordhausenK, OjaH, TaskinenS. SpatialNP: Multivariate nonparametric methods based on spatial signs and ranks. R package version 1.1‐0, 2012.
[52] RousseeuwP, CrouxC, TodorovV, RuckstuhlA, Salibian‐BarreraM, VerbekeT, KollerM, MaechlerM. Robustbase: Basic Robust Statistics. R package version 0.90‐2, 2014.
[53] BrentRP. Algorithms for Minimization Without Derivatives. Englewood Cliffs, NJ: Prentice‐Hall; 1973. · Zbl 0245.65032
[54] Al‐HomidanS. Semidefinite and second‐order cone optimization approach for the toeplitz matrix approximation problem. J Numer Math2006, 14:1-15. · Zbl 1096.65052
[55] DavisR, ResnickS. Limit theory for the sample covariance and correlation functions of moving averages. Ann Stat1986, 14:533-558. · Zbl 0605.62092
[56] LoretanM, PhillipsPCB. Testing the covariance stationarity of heavy‐tailed time series: An overview of the theory with applications to several financial datasets. J Empir Financ1994, 1:211-248.
[57] PolitisDN. Financial time series. WIREs Comput Stat2009, 1:157-166.
[58] RojoJ. Heavy‐tailed densities. WIREs Comput Stat2013, 5:30-40. · Zbl 1540.62020
[59] DavisRA, MikoschT. The sample autocorrelations of heavy‐tailed processes with applications to ARCH. Ann Stat1998, 26:2049-2080. · Zbl 0929.62092
[60] FoxAJ. Outliers in time series. J R Stat Soc Ser B Methodol1972, 34:350-363. · Zbl 0249.62089
[61] MaY, GentonMG. Highly robust estimation of dispersion matrices. J Multivar Anal2001, 78:11-36. · Zbl 1013.62065
[62] BollerslevT. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics1986, 31:307-327. · Zbl 0616.62119
[63] BollerslevT, ChouRY, KronerKF. ARCH modeling in finance: a review of the theory and empirical evidence. J Econom1992, 52:5-59. · Zbl 0825.90057
[64] DuanJ‐C. The GARCH option pricing model. Math Finance1995, 5:13-32. · Zbl 0866.90031
[65] LamoureuxCG, LastrapesWD. Heteroskedasticity in stock return data: volume versus GARCH effects. J Financ1990, 45:221-229.
[66] BasrakB, DavisRA, MikoschT. Regular variation of GARCH processes. Stochastic Processes and their Applications2002, 99:95-115. · Zbl 1060.60033
[67] BaillieRT, ChungH. Estimation of GARCH models from the autocorrelations of the squares of a process. J Time Ser Anal2001, 22:631-650. · Zbl 0984.62063
[68] ChangCC, PolitisDN. Robust autocorrelation estimation. Journal of Computational and Graphical Statistics, (just‐accepted), 2014.
[69] FriedR, LiboschikT, ElsaiedH, KitromilidouS, FokianosK. On outliers and interventions in count time series following GLMs. Aust J Stat2014, 43:181-193.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.