M-regression spectral estimator for periodic ARMA models. An empirical investigation

Sarnaglia, Alessandro José Queiroz; Reisen, Valdério Anselmo; Bondon, Pascal; Lévy‐Leduc, Céline

doi:10.1007/s00477-020-01958-y

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…Chang, Tiao, and Chen (1988) and Chen and Liu (1993) demonstrated that the estimated parameters of the ARMA model become biased when the data contains outliers. In the case of long-memory and periodic time series, see, for example, the recent papers by Reisen, Lévy-Leduc, and Taqqu (2017) and Sarnaglia, Reisen, Lévy-Leduc, and Bondon (2021).…”

Section: Introductionmentioning

confidence: 99%

Heteroscedastic Process: A M-quantile Approach

Patrocinio,

Reisen,

Bondon

et al. 2022

Preprint

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As is well known, outliers are quite common observations in different application areas and these types of data can cause large biases in the estimates of the mean, variance, correlation and, consequently, in the parameter estimates. Thus, robust estimation methods are needed to obtain reliable statistical models. There are empirical evidence that the financial time series and the distributions of returns are not well approximated by Gaussian models, which is an assumption generally considered to model these data. Therefore, both quantile and M-regression methods have been suggested to estimate GARCH model. In this paper, these two methodologies are combined to obtain a robust estimator for conditional volatility. Empirical evidence indicates that the proposed method seems to be more resistant to additive outliers than the M- and Quantile regressor estimators. Some technical issues are addressed, and an application illustrates the usefulness of the method in a real data set.

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Section: Introductionmentioning

confidence: 99%

Heteroscedastic Process: A M-quantile Approach

Patrocinio,

Reisen,

Bondon

et al. 2022

Preprint

Self Cite

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“…The considered problem in the context of the PARMA models was discussed in [46] where the authors proposed to use the robust algorithms for PARMA models' parameters estimation without changing the estimation procedures. See also [47][48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

New estimation method for periodic autoregressive time series of order 1 with additive noise

Żuławiński

Wyłomańska

2021

Int J Adv Eng Sci Appl Math

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The periodic behavior of real data can be manifested in the time series or in its characteristics. One of the characteristics that often manifests the periodic behavior is the sample autocovariance function. In this case, the periodically correlated (PC) behavior is considered. One of the main models that exhibits PC property is the periodic autoregressive (PARMA) model that is considered as the generalization of the classical autoregressive moving average (ARMA) process. However, when one considers the real data, practically the observed trajectory corresponds to the “pure” model with the additional noise which is a result of the noise of the measurement device or other external forces. Thus, in this paper we consider the model that is a sum of the periodic autoregressive (PAR) time series and the additive noise with finite-variance distribution. We present the main properties of the considered model indicating its PC property. One of the main goals of this paper is to introduce the new estimation method for the considered model’s parameters. The novel algorithm takes under consideration the additive noise in the model and can be considered as the modification of the classical Yule–Walker algorithm that utilizes the autocovariance function. Here, we propose two versions of the new method, namely the classical and the robust ones. The effectiveness of the proposed methodology is verified by Monte Carlo simulations. The comparison with the classical Yule–Walker method is presented. The approach proposed in this paper is universal and can be applied to any finite-variance models with the additive noise.

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