Forecasting Australia's real house price index: A comparison of time series and machine learning methods

• Author: George Milunovich
• Published date: 01 November 2020
• Date: 01 November 2020
• DOI: http://doi.org/10.1002/for.2678

Received: 2 July 2019 Revised: 8 December 2019 Accepted: 22 February 2020

DOI: 10.1002/for.2678

RESEARCH ARTICLE

Forecasting Australia's real house price index: A

comparison of time series and machine learning methods

George Milunovich

Department of Actuarial Studies and

Business Analytics, Macquarie University,

Sydney,New South Wales, Australia

Correspondence

George Milunovich, Department of

Actuarial Studies and Business Analytics,

Macquarie University, Sydney, NSW 2109,

Australia.

Email: george.milunovich@mq.edu.au

Funding information

Australian Research Council,

Grant/AwardNumber: DP190102049

Abstract

We employ 47 different algorithms to forecast Australian log real house

prices and growth rates, and compare their ability to produce accurate

out-of-sample predictions. The algorithms, which are specified in both single-

and multi-equation frameworks, consist of traditional time series models,

machine learning (ML) procedures, and deep learning neural networks. A

method is adopted to compute iterated multistep forecasts from nonlinear ML

specifications. While the rankings of forecast accuracy depend on the length

of the forecast horizon, as well as on the choice of the dependent variable

(log price or growth rate), a few generalizations can be made. For one- and

two-quarter-ahead forecasts we find a large number of algorithms that out-

perform the random walk with drift benchmark. We also report several such

outperformances at longer horizons of four and eight quarters, although these

are not statistically significant at any conventional level.Six of the eight top fore-

casts (4 horizons ×2 dependent variables) are generated by the same algorithm,

namely a linear support vector regressor (SVR). The other two highest ranked

forecasts are produced as simple mean forecast combinations. Linear autore-

gressive moving average and vector autoregression models produce accurate

olne-quarter-ahead predictions, while forecasts generated by deep learning nets

rank well across medium and long forecast horizons.

KEYWORDS

australian real house price index, autoregression, forecasting, machine learning, neural networks,

time series

1INTRODUCTION

Residential real estate provides shelter, preserves wealth,

and is one of the main drivers of the Australian economy

via construction and finance. Having access to accurate

house price predictions is therefore equally important to

central banks, financial supervision authorities, investors,

and home owners. In this article we explore the ability

of increasingly popular machine learning (ML) and deep

learning (DL) algorithms to forecast quarterly real house

prices in Australia, and comparetheir performance against

a number of traditional time series models. More specifi-

cally, we employ 47 algorithms to generate out-of-sample

predictions of log house prices and growth rates across

the forecast horizons of one, two, four, and eight quarters.

We then measure forecast accuracyaccording to the mean

squared error (MSE), and evaluate each forecast relative

to a benchmark. Statistical tests provide further evidence

regarding any such outperformance. We conclude by

producing a ranking of the forecasting algorithms that is

informative concerning their ability to produce accurate

house price predictions.

1098 © 2020 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/for Journalof Forecasting. 2020;39:1098–1118.

MILUNOVICH 1099

Forecasting national house price indices is challenging

for a number of reasons. The main issue is a relatively short

length of available time series data. House price indices

are typically constructed at monthly and quarterly fre-

quencies, which limits the length of computed indices and

makes model building and testing difficult. The analysis is

further complicated by asymmetric boom and bust cycles

that introduce nonlinear effects (Miles, 2008). As discussed

by Genesove and Mayer (2001) and Engelhardt (2003),

high levels of loss aversion associated with home owner-

ship cause house prices to adjust more quickly when they

rise towards equilibrium value than when they fall. Lastly,

large transaction costs prevalent in the housing markets

tend to amplify any nonlinear dynamics that are present in

the data (Muellbauer & Murphy, 1997).

Despite the modeling difficulties discussed above, there

is a substantial literature on forecasting house prices.

A key finding is that house price growth rates exhibit

positive serial dependence and predictability over short

horizons (see, e.g., Case & Shiller, 1989; 1990; Gau, 1984;

1985; McIntosh & Henderson, 1989; Schindler, 2013). The

evidence, however, is somewhat mixed regarding the

ability of nonlinear models to outperform linear autore-

gressive moving average (ARMA) specifications. For

instance, Crawford and Fratantoni (2003) reported

that while regime-switching models outperformed

ARMA in-sample, they fell behind when forecasting

out-of-sample. Similarly,Balcilar, Gupta, and Miller (2015)

found that smooth-transition autoregressive models failed

to outperform linear AR specifications over short hori-

zons. These findings are puzzling given that the studies

mentioned above found substantial evidence of nonlinear

behavior in house prices. The literature also investigates

the ability of economic factors to improve the accuracy of

house price forecasts. Rapach and Strauss (2007) found

that autoregressive distributed lag models outperformed

univariate autoregressions in forecasting state house price

indices in the USA. In a similar setting, Bork and Møller

(2015) reported that the best forecasting model varied

over time as well as across US states. Gupta, Kabundi,

and Miller (2011) forecast aggregate US real house price

growth using two sets of explanatory variables: a small

set containing 10 economic factors and a large set of 120

variables. They reported that the small-scale model out-

performed all other specifications, including the random

walk. Bork and Møller (2018) employed factor analysis

with 128 economic time series and showed that macroeco-

nomic fundamentals had strong predictive power for US

house price returns. Their model outperforms predictions

generated from the price–rent ratio, autoregressivebench-

marks, and regression models based on smaller data sets.

Further studies are surveyed by Ghysels, Plazzi, Valkanov,

and Torous (2013).

This paper contributes to the existing literature in

several ways. First, wecompare a large number of forecast-

ing algorithms according to their accuracy in predicting

Australian real house prices and growth rates. In con-

trast, the existing studies typically consider one model at

a time and do not conduct forecast comparisons (see, e.g.,

Abelson, Joyeux, Milunovich, & Chung, 2005; Bourassa &

Hendershott, 1995). Our predictions are generated from

a set of algorithms that include traditional time series

models as well as alternative machine and deep learning

specifications. This is of interest for at least two reasons.

Many of the ML and DL algorithms (i) have the ability

to capture nonlinear relationships, and (ii) employ

cross-validation rather than information criteria for model

selection. Whether such departures from traditional

methods make ML more suitable for forecasting house

prices is an open empirical question. Second, we extend

the idea of multiequation models from linear vector

autoregressions (VARs) to all of our machine learning

specifications. For instance, we construct multiequation

support vector regressors and multiequation random

forests. This is needed in order to compute iterated

multistep-ahead forecasts in a multivariate context. An

advantage of this approach is that only one model needs

to be specified in order to make predictions for all forecast

horizons. Lastly, as is well known, thereare complications

in constructing iterated multistep-ahead predictions from

nonlinear models. We address this issue by adopting a

residual-based procedure of Brown and Mariano (1989) to

generate unbiased multistep forecasts from nonlinear ML

and DL algorithms.

Our data set contains an Australian real house price

index collected at the quarterly frequency over the

1972:Q3–2017:Q3 period. In addition, we obtain data on

seven economic factors that may help improve house price

forecasts. These include inflation, exchange and unem-

ployment rates, house rents, a stock price index, gross

disposable income per capita, and mortgage rates. We

choose the seven predictors largely in consideration of

the existing literature. For instance, a large number of

studies suggest that income often plays a key role in fore-

casting house price growth rates (see, e.g., Case & Shiller,

1990; Favilukis, Ludvigson, & Van Nieuwerburgh, 2017;

Malpezzi, 1999). Similarly, rent is employed as a relevant

predictor by Plazzi, Torous, and Valkanov (2010) and

DiPasquale and Wheaton (1994), and interest rates in

Muellbauer and Murphy (1997). In further literature,

inflation and equities help explain Australian house prices

in Abelson et al. (2005), while employment features in

Abraham and Hendershott (1996).

Weset up our investigation in a fixed estimation window

scheme, which facilitates comparing forecasts from nested

models via the Diebold and Mariano (1995); DM) test.