A new unique impulse response function in linear vector autoregressive models

• Published date: 01 June 2023
• Author: Yanlin Shi
• Date: 01 June 2023
• DOI: http://doi.org/10.1111/irfi.12396

SHORT REPORT

A new unique impulse response function in linear

vector autoregressive models

Yanlin Shi

Department of Actuarial Studies and Business

Analytics, Macquarie University, Sydney,

New South Wales, Australia

Correspondence

Yanlin Shi, Department of Actuarial Studies

and Business Analytics, Macquarie University,

Sydney, NSW 2109, Australia.

Email: yanlin.shi@mq.edu.au

Abstract

This article proposes a new unique impulse response func-

tion (IRF) measure, or MIRF, based on the popular vector

autoregressive model to study interdependency of multivar-

iate time series. Same as the orthogonal IRF, the estimator

of MIRF has an analytical form with well-established asymp-

totics, and is invariant to ordering of series. Compared to

alternative unique IRF measures, MIRF does not depend on

extreme identifications, and the associated forecast error

variance measure is explainable. An illustrative empirical

example is also provided.

KEYWORDS

eigendecomposition, forecast error variance decomposition,

impulse response function, vector autoregressive

JEL CLASSIFICATION

C32, C58

1|INTRODUCTION

The popularity of the vector autoregressive (VAR) model starts from the seminal work of Sims (1980), which is a nat-

ural extension of the AR model to the multivariate framework. For novel finance practices, VAR is still a methodology

to investigate the interdependency of multivariate time series (see, e.g., Caraiani et al. (2021), among others).

Impulseresponse function (IRF)is one of the most importantmetrics based on VAR.For instance, togetherwith the

associated forecast error variance decomposition (FEVD), IRF may describe how interested finance and/or economic

series reactover time to exogenous impulses (Da Fonseca & Gottschalk, 2020; Scherrer & Fernandes, 2021).However,

Received: 9 January 2022 Revised: 9 May 2022 Accepted: 14 September 2022

DOI: 10.1111/irfi.12396

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which

permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no

modifications or adaptations are made.

© 2022 The Author. International Review of Finance published by John Wiley & Sons Australia, Ltd on behalf of International Review

of Finance Ltd.

460 International Review of Finance. 2023;23:460–468.

wileyonlinelibrary.com/journal/irfi