Semiparametric Modeling of Multiple Quantiles

30 Pages Posted: 16 Dec 2019

See all articles by Leopoldo Catania

Leopoldo Catania

Aarhus University - School of Business and Social Sciences; Aarhus University - CREATES

Alessandra Luati

University of Bologna - Department of Statistics

Date Written: November 28, 2019

Abstract

We develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time varying quantiles at each probability level is based on the gradient of the check loss function, that forms a martingale difference sequence. Theoretical properties of the proposed model are derived, such as weak stationarity of the quantile process and consistency and asymptotic normality of the estimators of the fixed parameters. The model can be applied for filtering and prediction. We also illustrate a number of possible applications such as: i) semiparametric estimation of dynamic moments of the observables, ii) density prediction, and iii) quantile predictions.

Keywords: Dynamic Quantiles, Score Driven Models, Risk Management

Suggested Citation

Catania, Leopoldo and Luati, Alessandra, Semiparametric Modeling of Multiple Quantiles (November 28, 2019). Available at SSRN: https://ssrn.com/abstract=3494995 or http://dx.doi.org/10.2139/ssrn.3494995

Leopoldo Catania (Contact Author)

Aarhus University - School of Business and Social Sciences ( email )

Fuglesangs Allé 4
Aarhus V, DK-8210
Denmark
+4587165536 (Phone)

HOME PAGE: http://pure.au.dk/portal/en/leopoldo.catania@econ.au.dk

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Alessandra Luati

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

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