Methods for backcasting, nowcasting and forecasting using factor‐MIDAS: With an application to Korean GDP

• Published date: 01 April 2018
• Author: Norman R. Swanson,Hyun Hak Kim
• Date: 01 April 2018
• DOI: http://doi.org/10.1002/for.2499

Received: 3 January 2017 Revised: 21 September 2017 Accepted: 24 September 2017

DOI: 10.1002/for.2499

RESEARCH ARTICLE

Methods for backcasting, nowcasting and forecasting using

factor-MIDAS: With an application to Korean GDP

Hyun Hak Kim1Norman R. Swanson2

1Department of Economics, Kookmin

University, Seoul, Korea

2Department of Economics, Rutgers

University, NewBrunswick, NJ, USA

Correspondence

Hyun Hak Kim, Department of

Economics, Kookmin University,77

Jeongneung-Ro, Seongbuk-Gu, Seoul

02707, Korea.

Email: hyunhak.kim@kookmin.ac.kr

Abstract

We utilize mixed-frequency factor-MIDAS models for the purpose of carrying

out backcasting, nowcasting, and forecasting experiments using real-time data.

We also introduce a new real-time Korean GDP dataset, which is the focus of

our experiments. The methodology that we utilize involves first estimating com-

mon latent factors (i.e., diffusion indices) from 190 monthly macroeconomic

and financial series using various estimation strategies. These factors are then

included, along with standard variables measured at multiple different frequen-

cies, in various factor-MIDAS prediction models. Our key empirical findings as

follows. (i) When using real-time data, factor-MIDAS prediction models outper-

form various linear benchmark models. Interestingly, the “MSFE-best” MIDAS

models contain no autoregressive (AR) lag terms when backcasting and now-

casting. AR terms only begin to play a role in “true” forecasting contexts. (ii)

Models that utilize only one or two factors are “MSFE-best” at all forecasting

horizons, but not at any backcasting and nowcasting horizons. In these latter

contexts, much more heavily parametrized models with many factors are pre-

ferred. (iii) Real-time data are crucial for forecasting Korean gross domestic

product, and the use of “first available” versus “most recent” data “strongly”

affects model selection and performance. (iv) Recursively estimated models are

almost always “MSFE-best,” and models estimated using autoregressiveinterpo-

lation dominate those estimated using other interpolation methods. (v) Factors

estimated using recursive principal component estimation methods have more

predictive content than those estimated using a variety of other (more sophis-

ticated) approaches. This result is particularly prevalent for our “MSFE-best”

factor-MIDASmodels, across virtually all forecast horizons, estimation schemes,

and data vintages that are analyzed.

KEYWORDS

backcasting, forecasting, factor model, MIDAS, nowcasting

1INTRODUCTION

In this paper, we utilize a combination of real-time data

and mixed-frequency modeling methods together with

a variety of principal component analyses, in order to

provide new evidence on the usefulness of these tech-

niques for forecasting. More specifically, we introduce

a new real-time Korean gross domestic product (GDP)

Journal of Forecasting. 2018;37:281–302. wileyonlinelibrary.com/journal/for Copyright © 2017 John Wiley & Sons, Ltd. 281

282 KIM AND SWANSON

dataset, which is used together with a large monthly

dataset including 190 variables,1to backcast, nowcast,

and forecast Korean GDP. Our prediction models combine

the mixed data sampling (MIDAS) framework of Ghysels,

Santa-Clara, and Valkanov (2004), which allows for the

incorporation of variables of differing frequencies,with the

diffusion index framework of Stock and Watson (2002).

The difference between backcasting, nowcasting, and

forecasting can be explained as follows. Suppose that the

objective is to predict GDP for 2016:Q2, using a simple

autoregressive model of order one, say. In a conventional

setting where real-time data are not available,it is assumed

that information up to 2016:Q1 is available at the time the

prediction is made, so that 

GDP2016:Q2 = +

GDP2016:Q1,

where  and 

are parameters estimated using maximum

likelihood based on recursive or rolling data windows. In

a real-time context, however, this prediction is not feasi-

ble. Namely, if the prediction is to be made in April or

even May of 2016, then GDP2016:Q1 is not yet available,even

in preliminary release. This issue leads to the convention

of defining three different types of predictions, includ-

ing backcasts (predicting past observations, which are not

yet available in real time), nowcasts (predicting concur-

rent observations), and forecasts (see Giannone, Reichlin,

and Small (2008) for a comprehensive discussion of back-

casting and nowcasting). One advantage of carefully ana-

lyzing the data structure used in the formulation of

prediction models is that we are able to simulate real-time

decision-making processes. In addition to Giannone et al.

(2008), the reader is referred to Girardi et al. (2017) for an

overview of this literature, within the context of nowcast-

ing euro area GDP in pseudo real time using dimension

reduction techniques.

There are several approaches to forecasting lower fre-

quency variables using higher frequency variables. The

first approach involves use of the so-called “bridge” model,

which aggregates higher frequency variables with lower

frequency variables, such as GDP. This aggregation is

called a “bridge,” and this method is commonly used

by central banks, since implementation and interpreta-

tion are straightforward (see, e.g., Golinelli & Parigi, 2005;

Rünstler & Sédillot, 2003; Zheng & Rossiter,2006). Indeed,

this approach offers a very convenient solution for fil-

tering, or aggregating, variables characterized by differ-

ent frequencies. However, aggregation may lead to the

loss of useful information. This issue has led to the

recent development of alternative mixed frequency mod-

eling approaches. One important approach, which is men-

tioned above, is called MIDAS. This approach involves

1This large monthly Korean macroeconomic dataset, which resembles

the well-knownUS Stock and Watson (2002) dataset, is introduced in Kim

(2017).

the use of a regression framework that directly includes

variables sampled at different frequencies. Broadly speak-

ing, MIDAS regression offers a parsimonious means by

which lags of explanatory variables of differing frequen-

cies can be utilized; and its use for macroeconomic fore-

casting is succinctly elucidated by Clements and Galvao

(2008). Additional recent papers in this area of forecasting

include Kuzin, Marcellino, and Schumacher (2011), who

predict euro area GDP, Ferrara and Marsilli (2013), who

predict French GDP, and Pettenuzzo, Timmermann, and

Valkanov (2014), who discuss Bayesianimplementation of

MIDAS. One interesting feature of MIDASis that the tech-

nique readily allows for the inclusion of diffusion indices.

For discussion of the combination of factor and MIDAS

approaches, see Marcellino and Schumacher (2010) and

Section 5 of this paper.For an interesting application to the

prediction of German GDP, see Schumacher (2007). The

reader is additionally referred to Giannone et al. (2008),

Ba ´

nbura, Giannone, and Reichlin (2012), and Ba ´

nbura and

Modugno (2014) for interesting discussions on the use of

mixed-frequency modeling for nowcasting, and to Kuzin,

Marcellino, and Schumacher (2013), Aastveit, Gerdrup,

Jore, and Thorsrud (2014), and Mazzi, Mitchell, and

Montana (2014) for a discussion on forecast combination

in the current context.

Our empirical findings can be summarized as fol-

lows. First and foremost, real-time data make a differ-

ence. The utilization of real-time data in a recursive

estimation framework, coupled with MIDAS, leads to

the “MSFE-best” predictions in our experiments. Sec-

ond, models that utilize only one or two factors are

“MSFE-best” at all forecasting horizons, but not at any

backcasting and nowcasting horizons. In these latter con-

texts, much more heavily parametrized models with many

factors are preferred. In particular,while one or two factors

are selected around half of the time in the cases, five or six

factors are also selected around half of the time. Third, the

variable being predicted makes a difference. For Korean

GDP, the use of “first available” versus “most recent”

data “strongly” affects model selection and performance.

One reason for this is that “first available” data are never

revised, and can thus in many cases be viewed as “noisy”

versions of later releases of observations for the same cal-

endar date. This is particularly true if rationality holds (see,

e.g., Swanson & van Dijk, 2006). Fourth, recursively esti-

mated models are almost always “MSFE-best,” and mod-

els estimated using autoregressive interpolation dominate

those estimated using other interpolation methods. Fifth,

factors constructed using recursive principal component

estimation methods have more predictive content than

those estimated using a variety of other (more sophisti-

cated) approaches. This result is particularly prevalent for

our “MSFE-best” factor-MIDAS models, across virtually