Forecasting inflation using univariate continuous‐time stochastic models

• Published date: 01 January 2020
• Author: Kevin Fergusson
• Date: 01 January 2020
• DOI: http://doi.org/10.1002/for.2603

Received: 27 November 2018 Revised: 15 April 2019 Accepted: 10 May 2019

DOI: 10.1002/for.2603

RESEARCH ARTICLE

Forecasting inflation using univariate continuous-time

stochastic models

Kevin Fergusson

Faculty of Business and Economics,

University of Melbourne, Melbourne,

Victoria, Australia

Correspondence

Kevin Fergusson, Facultyof Business and

Economics, University of Melbourne,

Melbourne, Victoria 3010, Australia.

Email: kevin.fergusson@unimelb.edu.au

Abstract

In this paper we investigate the applicability of severalcontinuous-time stochas-

tic models to forecasting inflation rates with horizons out to 20 years. While

the models are well known, new methods of parameter estimation and forecasts

are supplied, leading to rigorous testing of out-of-sample inflation forecasting at

short and long time horizons. Using US consumer price index data we find that

over longer forecasting horizons—that is, those beyond 5 years—the log-normal

index model having Ornstein–Uhlenbeck drift rate provides the best forecasts.

KEYWORDS

inflation rate, log-normal model, maximum likelihood estimation, Vasicekmodel

1INTRODUCTION

Inflation rate forecasting is of much use in economics,

insurance, and pensions. For example, economic policy-

makers need forecasts to monitorand adjust policy settings

to contain excessive inflation. Inflation rate forecasts can

be used as part of wage negotiations so that employees' pur-

chasing powers are maintained. Inflation-linked securities

such as treasury income protected securities (TIPS) require

inflation forecasts to value them. Actuaries in insurance

companies set inflation rate assumptions in their pricing

of insurance products. Additionally,actuaries require fore-

casts of inflation in valuing the inflation-linked liabilities

of pension funds.

As varied are the purposes, forecasting inflation has

many approaches, for example as described in Meyer and

Pasaogullari (2010) and Zhang (2019), which incorporate

into the forecasting model such information as inflation

expectations surveys, Phillips curves, import price indices,

wage indices, commodity prices and interest rates. A sim-

pler approach involves only the inflation time series itself

in computing forecasts.

Along these simpler lines, the focus of this paper

is on forecasts based on continuous-time univariate

stochastic processes. Continuous-time stochastic pro-

cesses, described by stochastic differential equations

(SDEs), can be viewed as limiting cases of discrete-time

stochastic processes, described by discrete time series.

While the tractability of continuous-time SDEs is lim-

ited to a few classes of models, their parsimony allows

precise fitting of model parameters via maximum likeli-

hood estimation; see, for example, Fergusson and Platen

(2015) and Fergusson (2017). In contrast, autoregressive

integrated moving average (ARIMA) and generalized

autoregressive conditional heteroskedasticity (GARCH)

models can contain many parameters, potentially

leading to over-fitting of the models and poor forecast-

ing performances out of sample, and their parameter

estimation times are correspondingly longer. Addi-

tionally, GARCH and its variations are only able to

capture some types of heteroskedastic behavior; see,

for example, Bergstrom (1984).

Typically, inflation forecasts based only a single infla-

tion series employ time series models such as ARIMA

models and nonlinear or time-varying univariate mod-

els such as GARCH. Among the simplest of these is the

random walk model proposed in Atkeson and Ohanian

(2001), in which the forecast of the four-quarter rate of

inflation is the average quarterly inflation rate over the

previous four quarters. These univariate models can also

Journal of Forecasting. 2020;39:37–46. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 37