Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects

Tinbergen Institute Discussion Paper 20-004/III

38 Pages Posted: 24 Feb 2020

See all articles by Paolo Gorgi

Paolo Gorgi

VU University Amsterdam - Faculty of Economics and Business Administration; University of Padova

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Date Written: January 20, 2020

Abstract

We consider a general class of observation-driven models with exogenous regressors for double bounded data that are based on the beta distribution. We obtain a stationary and ergodic beta observation-driven process subject to a contraction condition on the stochastic dynamic model equation. We derive conditions for strong consistency and asymptotic normality of the maximum likelihood estimator. The general results are used to study the properties of a beta autoregressive process with threshold effects and to establish the asymptotic properties of the maximum likelihood estimator. We employ the threshold autoregressive model with leverage effects to analyze realized correlations for several sets of stock returns. We find that the impact of past values of realized correlation on future values is at least 10% higher when stock returns are negative rather than positive. This finding supports the conjecture that correlation between stock returns tends to be higher when stock prices are falling, and lower when there is a surge in stock prices. Finally, we conduct an out-of-sample study that shows that our model with leverage effects can enhance the accuracy of point and density forecasts of realized correlations.

Keywords: Double bounded time series, financial econometrics, leverage effects, observation- driven models, realized correlation

JEL Classification: C32, C52, C58

Suggested Citation

Gorgi, Paolo and Koopman, Siem Jan, Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects (January 20, 2020). Tinbergen Institute Discussion Paper 20-004/III, Available at SSRN: https://ssrn.com/abstract=3526417 or http://dx.doi.org/10.2139/ssrn.3526417

Paolo Gorgi (Contact Author)

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

University of Padova ( email )

Via 8 Febbraio, 2
Padova, Vicenza 35122
Italy

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

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

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