Permutation entropies of short‐term interest rates as an early‐warning signal

• Published date: 01 December 2019
• Date: 01 December 2019
• DOI: http://doi.org/10.1111/infi.12348
• Author: Daeyup Lee,Hail Park

DOI: 10.1111/infi.12348

ORIGINAL ARTICLE

Permutation entropies of short‐term interest

rates as an early‐warning signal

Daeyup Lee

1

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Hail Park

2

1

Financial & Monetary Economics Team,

Economic Research Institute, Bank of

Korea, Seoul, Republic of Korea

2

Department of International Business &

Trade, Kyung Hee University, Seoul,

Republic of Korea

Correspondence

Hail Park, Department of International

Business & Trade, Kyung Hee University,

26 Kyungheedae‐ro, Dongdaemun‐gu,

Seoul, 02447 Republic of Korea.

Email: hailpark@khu.ac.kr

Funding information

Kyung Hee University, Grant/Award

Number: KHU‐20171277

Abstract

This paper proposes a new method for detecting abnormal

movements of short‐term interest rates by using permuta-

tion entropy (PE) as a complementary early‐warning

signal. Empirical results have shown that the PEs of the

US T‐Bill rates plunged below the thresholds of normal

movements before the financial crisis of 2007–2009, and

the PE of 3‐month Euribor similarly dropped before the

European sovereign debt crisis of 2010. Additionally, it was

found that the PEs of spreads of both domestic interest

rates and Libors dropped against the US T‐Bill rates below

the thresholds in 2005. This evidence could serve as useful

information for policymakers in crisis periods.

KEYWORDS

complexity, early‐warning signal, permutation entropy

JEL CLASSIFICATION

C46, E44, G15

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INTRODUCTION

The pivotal role of financial stability in maintaining sustainable economic growth was made

clear by the global financial crisis of 2007–2009. The direct welfare loss from financial crises is

enormous. Reinhart and Rogoff (2008) reported that the average drop in real output growth per

capita was over 2 percentage points during 18 postwar banking crises. Moreover, Cerra and

Saxena (2008) showed that crises have indirect and long‐lasting effects on economic growth.

The 2007–2009 financial crisis highlighted the necessity of developing tools to provide early‐

warning signals of systemic failures in the financial markets (Gray, 2009). The burgeoning

literature on early‐warning indicators suggests that credit‐related variables are the best indicators

(Schularick & Taylor, 2012). Although credit‐related indicators have been successful in predicting

financial crises, a remaining issueis that the interpretation of theseindicators could be somewhat

International Finance. 2019;22:323–340. wileyonlinelibrary.com/journal/infi © 2019 John Wiley & Sons Ltd

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ambiguous. A higher credit‐to‐GDPratio, one of the most popular measures for credit booms,can

be interpreted as a result of changes in fundamentals such as financial development or other

institutional changes (the so‐called “This time is different syndrome,”as in the work of Reinhart

& Rogoff, 2010). To complement the current literature on early‐warning indicators, this paper

develops an approach based on the extraordinary dynamics of short‐term interest rates, whereas

the focus of the current literature has been on the extraordinary levels of financial variables.

For a period known as the Great Moderation, it seems difficult to find strong early‐warning

signals in terms of volatility, even though measurements of volatility are common in evaluating

financial‐market stability. It is better to have early‐warning signals that are independent of data

volatility. If misalignments in the financial markets grow during booms, then the distribution of

data may differ from this in normal times, particularly in terms of temporal dependence. It would

thus be helpful to have a measurement to detect an increase in temporal dependence. Several

related papers have documented the effects of heterogeneous beliefs on financial markets.

Badarinza and Buchmann (2011) argued thathigher levels of disagreement in the beliefs of agents

about interest rates can be a signal of distress in bond markets. Nimark (2010) also showed that

speculative behaviour driven by heterogeneity in beliefs among tradersplays an important role in

the term structure dynamics of US bond yields. Scheinkman and Xiong (2003) showed that

overconfidence causes disagreements between agents regarding asset prices and that disagree-

ments generate asset price bubbles. Meanwhile, Sims (2009) noted that rational inattention and

different opinions about the courseof future inflation can lead to distortions in real assetmarkets.

There are at least two reasons why abnormally high temporal dependence may be viewed as

a warning signal. First, abnormally high temporal dependence may be the result of herd

behaviour or feedback trading in the financial markets, which makes them fragile. As noted by

Cipriani and Guarino (2010), herd behaviour may result in temporal dependence on trading

patterns.

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Second, the overly predictable movement of asset prices may induce excessive risk‐

taking by financial investors. Regarding this issue, Altunbas, Gambacorta, and Marges‐Ibanez

(2010) indicated the pitfall of a highly predictable monetary policy in the sense that the

resulting lower uncertainty may induce higher risk‐taking by banks.

A simple and popular measure of temporal dependence is autocorrelation. According to

Scheffer et al. (2009), higher autocorrelation is included as a possible early‐warning signal of the

bifurcation of dynamic systems. However, autocorrelation has the following weak points. First,

it can detect only linear dependence. In this regard, Mishkin (2011) highlighted the nonlinearity

of the macroeconomy as one of the lessons from the 2007–2009 financial crisis. Carpenter et al.

(2011) reported the presence of nonlinear dynamics in an experiment on “catastrophic

ecological regime shifts.”Second, autocorrelation may be driven by some outliers. Third, it is

sensitive to structural breaks such as changes of means.

Klonowski, Olejarczyk, and Stepien (2004) suggested using methods developed in medical

diagnosis (especially with regard to epileptic seizures) to diagnose economic sickness given the

similarity between economic systems and living organisms and the fact that both generate state‐

dependent signals. The complexity measures used in medical diagnosis include dimensions

(permutation), entropies, and Lyapunov exponents. Eckmann and Rulle (1985) provided a

classic discussion of these complexity measures. Among them, permutation entropy (PE) is the

most recent and computationally affordable measure. This paper investigates the potential of PE

as a measure of the temporal dependence of financial variables.

In general, a higher PE means that the data‐generating process is more complex and

unpredictable. If the PE of a financial variable is significantly low, it implies market inefficiency

because the efficient market hypothesis suggests the unpredictability of future movements of

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