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Identification of Seasonal Effects in Impulse Responses Using Score-Driven Multivariate Location Models

Szabolcs Blazsek, Alvaro Escribano and Adrian Licht


For policy decisions, capturing seasonal effects in impulse responses are important for the correct specification of dynamic models that measure interaction effects for policy-relevant macroeconomic variables. In this paper, a new multivariate method is suggested, which uses the score-driven quasi-vector autoregressive (QVAR) model, to capture seasonal effects in impulse response functions (IRFs). The nonlinear QVAR-based method is compared with the existing linear VAR-based method. The following technical aspects of the new method are presented: (i) mathematical formulation of QVAR; (ii) first-order representation and infinite vector moving average, VMA (∞), representation of QVAR; (iii) IRF of QVAR; (iv) statistical inference of QVAR and conditions of consistency and asymptotic normality of the estimates. Control data are used for the period of 1987:Q1 to 2013:Q2, from the following policy-relevant macroeconomic variables: crude oil real price, United States (US) inflation rate, and US real gross domestic product (GDP). A graphical representation of seasonal effects among variables is provided, by using the IRF. According to the estimation results, annual seasonal effects are almost undetected by using the existing linear VAR tool, but those effects are detected by using the new QVAR tool.

JEL classification: C32

Corresponding author: Alvaro Escribano, Department of Economics, Universidad Carlos III de Madrid, Getafe28903, Spain, E-mail:

Funding source: Comunidad de Madrid

Award Identifier / Grant number: MadEco-CM S2015/HUM-3444

Funding source: Ministerio de Economía, Industria y Competitividad

Award Identifier / Grant number: ECO2016-00105-001

Award Identifier / Grant number: MDM 2014-0431

Funding source: Universidad Francisco Marroquín


Previous versions of this paper were presented in “Recent Advances in Econometrics: International Conference in Honor of Luc Bauwens” (Brussels, 19–20 October 2017), GESG Research Seminar (Guatemala City, 9 November 2017), “Workshop in Time Series Econometrics” (Zaragoza, 12–13 April 2018), and “International Conference on Statistical Methods for Big Data” (Madrid, 7–8 July 2018). The authors are thankful to the reviewer and the editor of the journal, Luc Bauwens, Matthew Copley, Antoni Espasa, Eric Ghysels, Joachim Grammig, Andrew Harvey, Søren Johansen, Òscar Jordà, Bent Nielsen, Eric Renault, Genaro Sucarrat, and Ruey Tsay. All remaining errors are our own. Blazsek and Licht acknowledge funding from Universidad Francisco Marroquín. Escribano acknowledges funding from Ministerio de Economía, Industria y Competitividad (ECO2016-00105-001 and MDM 2014-0431), and Comunidad de Madrid (MadEco-CM S2015/HUM-3444).


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Supplementary Material

The online version of this article offers supplementary material (

Received: 2020-02-05
Accepted: 2020-09-17
Published Online: 2020-10-29

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