The versatility of spectrum analysis for forecasting financial time series

• Date: 01 April 2018
• Author: Pierre Rostan,Alexandra Rostan
• DOI: http://doi.org/10.1002/for.2504
• Published date: 01 April 2018

RESEARCH ARTICLE

The versatility of spectrum analysis for forecasting financial

time series

Pierre Rostan | Alexandra Rostan

Department of Finance, Prince Sultan

University, Riyadh, Saudi Arabia

Correspondence

Pierre Rostan, Department of Finance,

Prince Sultan University, Rafaha Street,

Salah Ad Din, P.O. Box 66833, Riyadh

11586, Kingdom of Saudi Arabia.

Email: rostan.pierre@gmail.com

Abstract

The versatility of the one‐dimensional discrete wavelet analysis combined with

wavelet and Burg extensions for forecasting financial times series with distinc-

tive properties is illustrated with market data. Any time series of financial assets

may be decomposed into simpler signals called approximations and details in

the framework of the one‐dimensional discrete wavelet analysis. The simplified

signals are recomposed after extension. The final output is the forecasted time

series which is compared to observed data. Results show the pertinence of

adding spectrum analysis to the battery of tools used by econometricians and

quantitative analysts for the forecast of economic or financial time series.

KEYWORDS

econometric modeling, financial econometrics, financial time series, forecasting and prediction

methods, mathematical and quantitative methods, spectrumanalysis

1|INTRODUCTION

“Want a hedge fund job? Knowing about wavelets

improves your odds!”(Kishan, 2016). Nowadays, securities

analysts are left on the backburner, whereas quants nib-

bling with wavelets are the primary target of hedge funds

such as Renaissance Technologies and Two Sigma Invest-

ments using mathematical models for investing. In a war

for quantitative talent, UBS Group AG doubled the num-

ber of quants in the past two years and plans to hire even

more (Voegeli, 2016). Other banks and investment funds

—for instance, Credit Suisse Group AG and GAM Hold-

ing—are heavily recruiting quants trained in physics or

mathematics. Wavelet analysis is the focus of planet

Investment looking for answers to lackluster returns. Fore-

casting is a key investment strategy and risk analysis tool.

In this paper, one‐dimensional discrete wavelet analy-

sis is applied to stationary and nonstationary financial

time series forecasting. The intuition behind the use of

wavelet analysis for times series forecasting is simple.

Many physical phenomena such as electrical, audio, or

seismic signals propagate through space in waveforms.

In finance and economics, interest rates, exchange rates,

volatility of asset returns, gross domestic product, levels

of employment, or consumer spending propagate through

time in waveforms. For example, Rostan, Belhachemi,

and Racicot (2016) showed that interest rates might be

forecasted with spectrum analysis due to their valuable

property of propagating through time in waveforms.

Population estimates also follow waveform patterns and

may be forecasted using spectrum analysis (Rostan,

Belhachemi, & Rostan, 2015). The challenge in spectrum

analysis is how to apply its methodology to asset prices

time series when they do not follow waveform patterns:

for example, the nonstationary S&P 500 index. The intui-

tive idea will be to decompose the original signal of S&P

500 index prices (i.e., the initial time series) in waveform

signals, then to apply spectrum analysis to these

decomposed signals, since waveform patterns are easily

captured by spectrum analysis.

Section 2 reviews previous studies related to forecast-

ing with spectrum analysis. Section 3 presents the meth-

odology. Section 4 gathers the results and Section 5

concludes.

Received: 28 September 2016 Revised: 1 June 2017 Accepted: 16 November 2017

DOI: 10.1002/for.2504

Journal of Forecasting. 2018;37:327–339. Copyright © 2017 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 327