Evaluating early warning and coincident indicators of business cycles using smooth trends

• Published date: 01 January 2020
• Author: Antonio García‐Ferrer,Marcos Bujosa,Antonio Martín‐Arroyo,Aránzazu Juan
• DOI: http://doi.org/10.1002/for.2601
• Date: 01 January 2020

Received: 12 December 2018 Revised: 4 April 2019 Accepted: 1 May 2019

DOI: 10.1002/for.2601

RESEARCH ARTICLE

Evaluating early warning and coincident indicators of

business cycles using smooth trends

Marcos Bujosa1Antonio García-Ferrer2Aránzazu de Juan2

Antonio Martín-Arroyo2

1Instituto Complutense del Análisis

Económico—ICAE, Universidad

Complutense de Madrid, Madrid, Spain

2Universidad Autónoma de Madrid,

Madrid, Spain

Correspondence

Marcos Bujosa, Departamento de

Análisis Económico y Economía

Cuantitativa & Instituto Complutense del

Análisis Económico - ICAE, Facultad de

Ciencias Económicas y Empresariales

Universidad Complutense Campus de

Somosaguas 28223 - Pozuelo de Alarcón,

Madrid, Spain.

Email: marcos.bujosa@ccee.ucm.es

Funding information

Spanish Ministry of Economics and

Competitiveness, Grant/AwardNumber:

ECO2015-64l467-R, MINECO/FEDER,

ECO2015-70331-C2-1-R

Abstract

We present a composite coincident indicatordesigned to capture the state of the

Spanish economy. Our approach, based on smooth trends, guarantees that the

resulting indicators are reasonably smooth and issue stable signals, reducing

the uncertainty.The coincident indicator has been checked by comparing it with

the one recently proposed by the Spanish Economic Association index. Both

indexes show similar behavior and ours captures very well the beginning and

end of the official recessions and expansion periods. Our coincident indicator

also tracks very well alternative mass media indicators typically used in the polit-

ical science literature. We also update our composite leading indicator (Bujosa

et al., Journal of Forecasting, 2013, 32(6), 481–499). It systematically predicts the

peaks and troughs of the new Spanish Economic Association index and provides

significant aid in forecasting annual gross domestic product growth rates. Using

only real data available at the beginning of each forecast period, our indicator

one-step-ahead forecast shows improvements over other individual alternatives

and different forecast combinations.

KEYWORDS

business cycles, econometric modeling, forecasting and prediction methods, factor analysis, linear

dynamic harmonic regression, leading and coincident indicators, mathematical and quantitative

methods, simulation methods

1INTRODUCTION

Sound leading and coincident indicators of business

cycles are essential components for firms, investors and

policymakers. Coincident indicators (CIs) are designed to

capture the present state of the economy or of its global

business cycle, while leading indicators (LIs) should be

able to show reliable statistical forecasting power. Not

surprisingly, economists have devoted a large amount of

research in the quest for such indicators following the

early works of Burns and Mitchell (1946) for the US

economy. This intensive research has produced a vast

amount of findings, with both theoretical and empirical

implications as well as additional requirements for the

indexes to fulfill. LIs, for instance, should systematically

provide a precise indication of the future course of the

economy (consistency) and the signals need to arrive early

enough so that prospective policy decisions have time to

be effective timeliness. On the other hand, CIs should

be able to reproduce the present state of the economy

without producing false turning points signals too fre-

quently. The stability of signals is also an important addi-

tional requirement that the literature to date has largely

overlooked (Drehmann & Juselius, 2014). Indicators that

Journal of Forecasting. 2020;39:1–17. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 1

issue stable or persistent signals reduce the uncertainty

regarding trends and avoid confusion for economic agents

in interpreting future directions of change.

At present, there is a large amount of literatureon how to

design CIs and LIs. Methods range from ad hoc weighted

averages of the time series of observed data to model-based

methodologies. In the first approach, the optimality prop-

erties of the index are unknown, so its usefulness is very

limited. Within the model-based approach, however, the

methods of diffusion index forecast (Stock & Watson,2002)

and the other variants of dynamic factor models (DFMs)

have been able to incorporate information from a large

number of predictors into the forecast in a simple and par-

simonious way. As noted by Bujosa, García-Ferrer, and de

Juan (2013), a practical question in this approach, how-

ever, is: How much data is really needed? In other words,

how to find the best way to extract a subset of variables

from a larger data set and how to use it for real-time

forecasting?

Justification for using a very large number of variables

has been solely based on statistical properties of final

estimates. For instance, if the DFM is estimated using

principal components, the number of variables included

in the model needs to be large to achieve consistency

(Bai & Ng, 2002). Therefore, a large number of papers

in the literature tend to include hundreds of variables

without offering a systematic good record of forecasting

performance (Stock & Watson, 2003). However, (Poncela

& Ruiz, 2015) showed that when the DFM is directly esti-

mated from the Kalman filter equations, no more than

a small number of variables is needed to achieve con-

sistency. They also showed that, when model parameters

have to be estimated, the parameter and total uncer-

tainties could increase when the number of indicators

increases. The related question is then: Do we really need

consistency when our main goal is forecasting? In this

regard, García-Ferrer and Poncela (2002), Boivin and Ng

(2006), and Poncela and García-Ferrer (2014), among oth-

ers, found that expanding the sample size adding data

that bear little information about the factor components

does not necessarily improve forecasts. Similar results

are found in Álvarez, Camacho, and Pérez-Quirós (2016)

regarding the use of aggregated versus disaggregated

data.

This last issue (reduction search) is central when try-

ing to deal with the permanent disease that afflicts all

real forecasting exercises with nonexperimental data: too

many predictors without enough data. Leamer (2012)

offers an interesting proposal by acknowledging that old

and new methods to deal with the overparametriza-

tion problem can work well sometimes but not always.

Understanding the economic circumstances where each

approach is successful becomes a crucial starting point.

Then it is the context that determines which procedure

to use.1

There are other important issues when building com-

posite indicators. Independent of the method used—either

spectral methods (Altissimo, Cristadoro, Forni, Lippi, &

Veronese,2010) or principal components (Stock & Watson,

2002)—estimation of DFM is based on two features:

the assumption of stationarity and the use of seasonally

adjusted data. Both of them may have potential prob-

lems. Because economic data are nonstationary, authors

prefilter all series to make each one plausibly station-

ary by taking first or second differences. But getting rid

of nonstationarity by differencing individual series, when

the series are cointegrated, throws away vast amount of

information and may distort inference (Corona, Poncela,

& Ruiz, 2017; Sims, 2012). The issue of using seasonally

adjusted data is also open to controversy (Ghysels, Osborn,

& Rodrigues, 2006; Matas-Mir,Osborn, & Lombardi, 2008).

In recent years severalresearchers have found the presence

of residual seasonality of the US real GDP and other US

macroeconomic variables (Bujosa & García-Ferrer, 2014).

In an attempt to reduce the residual seasonality, the US

Bureau of Economic Analysis (BEA) revised GDP during

the period 2013–2015, seasonally adjusting more of the

input data in the aggregated series. In spite of these adjust-

ments, (Phillps & Boldin, 2017) found that the first quarter

data were still, on average, 0.6%too weak.2

For the above reasons, in this paper we will be using

a small number of original (or log-transformed) monthly

seasonally unadjusted data to build and analyze CIs and

LIs for the Spanish business cycles from 1982 to 2014. Our

goals in this paper are threefold. Firstly, we will obtain a

composite coincident indicator (CCI) using monthly tar-

geted predictors and DFMs with the aim of reproducing

the official dating of Spanish business cycles and its rela-

tion with mass media indexes. Secondly, and using the

same methodology, we will update our composite lead-

ing indicator (CLI) (see Bujosa et al., 2013) that success-

fully anticipates the onset of Spanish recessions. Finally,

we will evaluate our CLI in comparison with alternative

1When analyzing US business cycles a few years ago, Leamer (2009)

found that for macroeconomic variables the borderline between features

that repeat and features that do no repeat is constantly changing and,

how the contribution to gross domestic product (GDP) growth of certain

economic indicators was radically different during the expansions and

during recessions. This empirical finding allowed him to use the so-called

cycle drivers that systematically anticipated a large percentage of the US

recessions. Interestingly,this finding was solely based on detailed exami-

nation and monitoring of disaggregated macroeconomic data using very

simple methods.

2Prior to the revision in mid-2016 directlyseasonally adjusting the official

seasonally adjusted GDP would revise the first-quarter growth since 2013

upward by an average of about 1.5%.

BUJOSA ET AL.

2