TAR Modeling with Missing Data when the White Noise Process Follows a Student’s t-Distribution

Zhang, Hanwen; Nieto, Fabio H.

doi:10.15446/rce.v38n1.48813

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…for any p > 0. Indeed, the Lévy measure of X is λP A and therefore (55) readily follows from (43). This implies the following result for compound Poisson white noise.…”

Section: Tempered Lévy White Noisesmentioning

confidence: 69%

“…Student's t-distributions and Laplace laws are infinitely divisible. We can therefore consider Student's t-white noises [43], Laplace white noises [24], which are all known to admits to positive absolute moments and are therefore tempered. This is also the case for layered stable white noises [19], tempered stable white noises [17,31], and inverse Gaussian white noises [2].…”

Section: Tempered Lévy White Noisesmentioning

confidence: 99%

See 1 more Smart Citation

On Tempered Discrete and Lévy White Noises

Fageot¹

2022

Preprint

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We study the growth properties of the family of i.i.d. random sequences, also known as discrete white noises, and of their continuous-domain generalization, the family of Lévy white noises. More precisely, we characterize the members of both families which are tempered-i.e., whose asymptotic growth is dominated by some polynomial-in terms of their moment properties. We recover the characterization of tempered Lévy white noises obtained by Robert Dalang and Thomas Humeau and provide a new proof of there fundamental result. Our approach is based on a fruitful connection between the discrete and continuous-domain white noises.

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“…for any p > 0. Indeed, the Lévy measure of X is λP A and therefore (55) readily follows from (43). This implies the following result for compound Poisson white noise.…”

Section: Tempered Lévy White Noisesmentioning

confidence: 69%

Section: Tempered Lévy White Noisesmentioning

confidence: 99%

On Tempered Discrete and Lévy White Noises

Fageot¹

2022

Preprint

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“…This fact can be a limitation in real data analysis because another variable can drive the dynamic of the variable of interest. Then, open-loop TAR models can be used for modeling in that real data applications, see Knotters & De Gooijer (1999), Zhang & Nieto (2015), Gonzalez & Nieto (2020) for examples in univariate open-loop TAR model, and Tsay (1998), Calderón & Nieto (2017), Romero & Calderón (2021) for examples in Multivariate TAR models. The literature of outliers in non-linear time series models has focused mainly on three research lines; the first refers to the detection of non-linearity, the second to robust estimation methods in the presence of outlier data, and the third to methods of detection and modeling of the outlier observations.…”

Section: Introductionmentioning

confidence: 99%

Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study

Calderon

Callamad

2022

Rev. colomb. estad.

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The effect of additive outliers is studied on an adapted non-linearity test and a robust estimation method for autoregressive coefficients in open-loop TAR (threshold autoregressive) models. Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation method, the bias and ratio of mean squared errors are compared between the robust estimator and least squares. Simulation exercises are carried out for different percentages of contamination and the proportion of observations on each model regime. Furthermore, the approximation of the univariate normal distribution to the empirical distribution of estimated coefficients is analyzed along with the coverage level of asymptotic confidence intervals for the parameters. Results show that the adapted non-linearity test does not have size distortions, and it has a superior power than its least-squares counterpart when additive outliers are present. On the other hand, the robust estimation method for the autoregressive coefficients has a better mean squared error than least-squares when this type of observations are present. Lastly, the use of the non-linearity test and the estimation method are illustrated through a real example.

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“…The TAR models can be easily extended, including some exogenous time series and called TARX. The use of Bayesian methods applied to the TAR and SETAR models, can be found in Chen & Lee (1995), So & Chen (2003), Nieto (2005), Nieto (2008), Nieto, Zhang & Li (2013), Zhang & Nieto (2015) and Calderón & Nieto (2017). While to the TARX models, can be found in Chen (1998), So, Chen & Liu (2006), , Chen, Gerlach & Lin (2010), among other works.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

Borja

Sánchez

2020

Rev. colomb. estad.

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Seasonal ﬂuctuations are often found in many time series. In addition, non-linearity and the relationship with other time series are prominent behaviors of several, of such series. In this paper, we consider the modeling of multiplicative seasonal threshold autoregressive processes with exogenous input (TSARX), which explicitly and simultaneously incorporate multiplicative seasonality and threshold nonlinearity. Seasonality is modeled to be stochastic and regime dependent. The proposed model is a special case of a threshold autoregressive process with exogenous input (TARX). We develop a procedure based on Bayesian methods to identify the model, estimate parameters, validate the model and calculate forecasts. In the identiﬁcation stage of the model, we present a statistical test of regime dependent multiplicative seasonality. The proposed methodology is illustrated with a simulated example and applied to economic empirical data.

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TAR Modeling with Missing Data when the White Noise Process Follows a Student’s t-Distribution

Cited by 4 publications

References 12 publications

On Tempered Discrete and Lévy White Noises

On Tempered Discrete and Lévy White Noises

Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study

Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

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