This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations give raise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling.

Torricelli, L., Barabesi, L., Cerioli, A. (2022). Tempered positive Linnik processes and their representations. ELECTRONIC JOURNAL OF STATISTICS, 16(2), 6313-6347 [10.1214/22-EJS2090].

Tempered positive Linnik processes and their representations

Barabesi, Lucio;Cerioli, Andrea
2022-01-01

Abstract

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations give raise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling.
2022
Torricelli, L., Barabesi, L., Cerioli, A. (2022). Tempered positive Linnik processes and their representations. ELECTRONIC JOURNAL OF STATISTICS, 16(2), 6313-6347 [10.1214/22-EJS2090].
File in questo prodotto:
File Dimensione Formato  
22-EJS2090.pdf

accesso aperto

Tipologia: PDF editoriale
Licenza: Creative commons
Dimensione 452.4 kB
Formato Adobe PDF
452.4 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1224896