SYMARMA: a new dynamic model for temporal data on conditional symmetric distribution. (English) Zbl 1416.62509

The authors propose a new class of models under the assumption that the random component has conditionally a continuous symmetric distribution, while the dynamic component has the form of ARMA structure. A conditional maximum likelihood estimator of the unknown parameter is derived and an iterative procedure for the estimation is presented. Some simulation studies are given to present the performances of the obtained estimator. The application on the time series of excess return in the daily closing prices in some indexes is discussed.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics


SYMARMA; bootstrap; R
Full Text: DOI


[1] Benjamin, MA; Rigby, RA; Stasinopoulos, M, Generalized autoregressive moving avarege models, J Am Stat Assoc, 98, 214-223, (2003) · Zbl 1047.62076
[2] Cao, CZ; Lin, JG; Zhu, LX, Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors, Stat Pap, 51, 813-836, (2010) · Zbl 1247.62218
[3] Chen, C; Liu, LM, Joint estimation of model parameters and outlier effects in time series, J Am Stat Assoc, 88, 284-297, (1993) · Zbl 0775.62229
[4] Cox, DR, Statistical analysis of time series: some recent developments, Scand J Stat, 8, 93-115, (1981) · Zbl 0468.62079
[5] Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman and Hall, London · Zbl 0334.62003
[6] Creal, D; Koopman, SJ; Lucas, A, Generalized autoregressive score models with applications, J Appl Econom, 28, 777-795, (2013)
[7] Cysneiros, FJA; Paula, GA, Restricted methods in symmetrical linear regression models, Comput Stat Data Anal, 49, 689-708, (2005) · Zbl 1429.62285
[8] Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York · Zbl 0835.62038
[9] Fang KT, Kotz S, Ng KW (1990) Symmetric multivariate and relates distributions. Chapman and Hall, London · Zbl 0699.62048
[10] Galea, M; Paula, GA; Uribe-Opazo, M, On influence diagnostic in univariate elliptical linear regression models, Stat Pap, 44, 23-45, (2003) · Zbl 1010.62066
[11] Heyde, CC; Feigin, PD, On efficiency and exponential families in stochastic process estimation, Stat Distrib Sci Work, 1, 227-240, (1975)
[12] Li, WK, Time series model based on generalized linear models: some further results, Biometrics, 50, 506-511, (1994) · Zbl 0825.62606
[13] Ljung, GM; Box, GEP, On a measure of a lack of fit in time series models, Biometrika, 65, 297-303, (1978) · Zbl 0386.62079
[14] Lucas, A, Robustness of the student-t based M-estimator, Commun Stat, Theory Methods, 26, 1165-1182, (1997) · Zbl 0920.62041
[15] Paula, GA; Cysneiros, FJA, Systematic risk estimation in symmetric models, Appl Econ, 16, 217-221, (2009)
[16] Paula, GA; Leiva, V; Barros, M; Liu, S, Robust statistical modeling using Birnbaum-Saunders-\(t\) distribution applied to insurance, Appl Stoch Model Bus Ind, 28, 16-34, (2012) · Zbl 06292429
[17] Peña, D, Influential observations in time series, J Bus Econ Stat, 8, 235-241, (1990) · Zbl 0800.62557
[18] Ruppert D (2004) Statistics and finance. Springer, New York · Zbl 1049.91083
[19] R Core Team. R (2012) A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN: 3-900051-07-0, http://www.R-project.org · Zbl 0386.62079
[20] Rocha, AV; Cribari-Neto, F, Beta autoregressive moving avarege models, Test, 18, 529-545, (2009) · Zbl 1203.62160
[21] Zeger, SL, A regression model for time series of counts, Biometrics, 75, 621-629, (1988) · Zbl 0653.62064
[22] Zeger, SL; Qaqish, B, Markov regression models for time series: a quasi-likelihood approach, Biometrics, 44, 1019-1031, (1988) · Zbl 0715.62166
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