Predictive power of Markovian models: Evidence from US recession forecasting

• Date: 01 September 2019
• DOI: http://doi.org/10.1002/for.2579
• Author: Ruilin Tian,Gang Shen
• Published date: 01 September 2019

Received: 15 March 2018 Revised: 1 February 2019 Accepted: 3 February 2019

DOI: 10.1002/for.2579

RESEARCH ARTICLE

Predictive power of Markovian models: Evidence from US

recession forecasting

Ruilin Tian1Gang Shen2

1Department of Transportation, Logistics

and Finance, North Dakota State

University, Fargo,North Dakota

2Department of Statistics, North Dakota

State University, Fargo,North Dakota

Correspondence

Ruilin Tian, Department of

Transportation, Logistics and Finance,

North Dakota State University,PO Box

6050, Fargo, ND 58108.

Email: ruilin.tian@ndsu.edu

Abstract

This paper provides extensions to the application of Markovian models in pre-

dicting US recessions. The proposed Markovian models, including the hidden

Markov and Markov models, incorporatethe temporal autocorrelation of binary

recession indicators in a traditional but natural way. Considering interest rates

and spreads, stock prices, monetary aggregates, and output as the candidate pre-

dictors, we examine the out-of-sample performance of the Markovian models

in predicting the recessions 1–12 months ahead, through rolling window exper-

iments as well as experiments based on the fixed full training set. Our study

shows that the Markovian models are superior to the probit models in detecting

a recession and capturing the recession duration. But sometimes the rolling win-

dow method may affect the models' prediction reliability as it could incorporate

the economy's unsystematic adjustments and erratic shocks into the forecast.

In addition, the interest rate spreads and output are the most efficient predictor

variables in explaining business cycles.

KEYWORDS

forecast recession, GDI, hidden Markov model, Markov model, probit model, rollingwindow

1INTRODUCTION

In the existing literature, research for predicting business

cycles forecasts either economic growth through continu-

ous models or recessions through binary models. Estrella,

Rodrigues, and Schich (2003) find that binary models are

typically more stable than continuous models. A major-

ity of studies have implemented one of two models:

logit/probit and/or Markovian models. This paper extends

the methodology of modeling and forecasting binary time

series through a set of proposed Markovian models.

Early studies with logit/probit models such as Canova

(1994) investigates the natureof financial crises in the USA

for the period 1880–1914. He finds that the out-of-sample

forecasting ability is poor as only two out of eight investi-

gated financial crises are predicted. Estrella and Mishkin

(1998) point out that the in-sample and out-of-sample

performance can differ greatly, and parsimonious models

work best out of sample. Traditional static models for pre-

dicting recessions simply ignore information about past

states of the economy.

Since there exists autocorrelation in the binary recession

indicator time series, static models are clearly inappro-

priate. The temporal correlation of binary recession sig-

nals should be considered in statistical models for future

recession prediction. Dynamic extension of static models

has attracted attention in recent years; see, among oth-

ers, Jacob and Lewis (1978), Chang, Kavvas, and Delleur

(1984), Durland and McCurdy (1994), Dueker (1997,

2005), Chauvet and Potter (2005), Kauppi and Saikkonen

(2008), and Nyberg (2010). Dynamic models typically

encompass autocorrelation among recession signals by

Journal of Forecasting. 2019;38:525–551. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 525

526 TIAN AND SHEN

linking recession probability with lagged recession indi-

cators and other explanatory variables. Although it is

arguable that the lagged recession indicator in some

dynamic models is statistically significant, dynamic mod-

els often reportedly outperform static models.

Starting with Neftçi (1984) and Hamilton (1989),

Markov switching methodology for business cycle fore-

casting has been suggested in the literature. Neftçi devel-

ops a second-order Markov model to capture the binary

upswings and downswings in the unemployment rate

when analyzing the asymmetric behavior of the unemploy-

ment rate. Hamilton introduces a hidden Markov model

(HMM) to describe economic regime changes as an unob-

served first-order Markov process via observed macroeco-

nomic data.

The Markov switching model of Hamilton (1989) is

widely used for time series in which the autoregressive

parameters switch between different time regimes. Studies

that implement HMMs include, among others, Hamilton

(1990), Lahiri and Moore (1991), Lahiri and Wang

(1994), Hamilton and Perez-Quiros (1996), Layton (1996),

Gregoir and Lenglart (2000), Ivanova, Lahiri, and Seitz

(2000), Marsh (2000), Kontolemis (2001), Koskinen and

Öller (2003), Giampieri, Davis, and Crowder (2005),

Andersson, Bock, and Frisén (2005), Banachewicz and

Lucas (2008), Banachewicz, Lucas, and Vaart (2008),

Chen, So, and Lin (2009), Parikakis and Merika (2009),

Pinson and Madsen (2012), Nunes, Natário, and Carvalho

(2013), Collet and Leonardi (2014), Dorosiewicz (2016),

Hou (2017), Nystrup, Madsen, and Lindström (2017), and

Nguyen (2018).

Besides the above-mentioned studies that adopt HMMs,

the following Markov switching models also showed their

success in forecasting economic time series. Batchelor

(2001) uses a time-varying parameter Markov switching

model to measure linkages between business confidence,

consumer confidence, and the state of the economy

in the USA and the UK. Kanas (2003) examines the

out-of-sample performance of the standard regime switch-

ing and the Markov regime switching models in forecast-

ing stock returns. Chauvet and Hamilton (2006) study a

Markov switching model in which the binary recession sig-

nals interlace with gross domestic product (GDP) growth

rates and form a Markov chain. Nalewaik (2011) incor-

porates vintage differences and forecasts into the Markov

switching models described by Hamilton (1994). Barsoum

and Stankiewicz (2015) analyze business cycle patterns

in macroeconomic time series with Markov switch-

ing mixed data sampling (MIDAS) models. Recently,

Camacho, Perez-Quiros, and Poncela (2018) extended the

Markov switching dynamic factor model to account for

some of the specificities of the day-to-day monitoring of

economic developments from macroeconomic indicators.

More applications of Markov switching models can be

found in Nikolsko-Rzhevskyy and Prodan (2012), Foroni,

Guérin, and Marcellino (2015), Ardia, Bluteau, Boudt, and

Catania (2018), and Nyberg (2018).

This paper provides an extension to the application

of Markovian models in forecasting the US recessions.

We propose a set of variants of hidden Markov and

Markov models, treating the temporal dependency in

a traditional but natural way. Our proposed hidden

Markov models use a latent variable to represent the

impact of unknown driving factors on economy reces-

sions, while our proposed Markov models reallocate

the probabilities between recession and nonrecession

regimes in the transition matrix to strengthen the mod-

els' ability to detect a recession. In addition, the first

two proposed variants of HMMs (i.e., the DAR-HMM

and DAR-DHMM) can estimate the long-term proba-

bility of recession—a unique feature that other models

do not possess.

We assess the out-of-sample predictability of the pro-

posed Markovian models at horizon 1 to 12 months by con-

sidering six potential explanatory variables that include

the yield spread, money market spread, junk bond spread,

money supply, stock price, and gross domestic income

(GDI). The 1-month-ahead forecast is actually close to

“nowcast,” which predicts the present, the very recent

past, or the very near future. There has been increasing

interest in nowcasting. Studies like Giannone, Reichlin,

and Small (2008), Liebermann (2013), Mazzi, Mitchell,

and Montana (2013), and Chen, So, Wu, and Yan (2014),

and Garbellano (2016) nowcast business cycles, GDP, or

some other macro variables. Nowcast is also applied to

the real-time prediction of influenza excess deaths (Nunes,

2011; Nunes et al., 2013) and supply management (Lahiri

& Monokroussos, 2013).

Using the monthly data from 07/1964 to 12/2017, we

analyze the predictive performance of the probit and

Markovian models (including the hidden Markov and

Markov models) based on (1) the full training set from

07/1964 to 12/1989 and (2) the 10-year rolling window

training sets. All diagnostic statistics except the rolling

average Akaike information criterion (AIC) recommend

the Markovian models. The rolling average AIC recom-

mends the dynamic probit model since the model has a

strong ability to incorporate up-to-date information from

explanatory variables for prediction. However, the erratic

messages from predictors may ruin the model's recession

forecast, making its prediction too volatile to be trusted.

The rolling window method typically yields lower AIC

and in-sample mean absolute error (MAE), while the

impact of rolling reestimation on the out-of-sample MAE

is mixed. When the forecast horizon is shorter than a year,

the out-of-sample MAEs for most of the Markovian models