Filtering and prediction of noisy and unstable signals: The case of Google Trends data

• Author: Livio Fenga
• DOI: http://doi.org/10.1002/for.2626
• Date: 01 March 2020
• Published date: 01 March 2020

RESEARCH ARTICLE

Filtering and prediction of noisy and unstable signals: The

case of Google Trends data

Livio Fenga

ISTAT—Italian National Institute of

Statistics, Rome, Italy

Correspondence

Livio Fenga, ISTAT—Italian National

Institute of Statistics, Via Cesare Balbo 16,

00184 Rome, Italy.

Email: fenga@istat.it

Abstract

Google Trends data is a dataset increasingly employed for many statistical

investigations. However, care should be placed in handling this tool, especially

when applied for quantitative prediction purposes. Being by design Internet

user dependent, estimators based on Google Trends data embody many

sources of uncertainty and instability. They are related, for example, to techni-

cal (e.g., cross‐regional disparities in the degree of computer alphabetization,

time dependency of Internet users), psychological (e.g., emotionally driven

spikes and other form of data perturbations), linguistic (e.g., noise generated

by double‐meaning words). Despite the stimulating literature available today

on how to use Google Trends data as a forecasting tool, surprisingly, to the best

of the author's knowledge, it appears that to date no articles specifically devoted

to the prediction of these data have been published. In this paper, a novel fore-

casting method, based on a denoiser of the wavelet type employed in conjunc-

tion with a forecasting model of the class SARIMA (seasonal autoregressive

integrated moving average), is presented. The wavelet filter is iteratively cali-

brated according to a bounded search algorithm, until a minimum of a suitable

loss function is reached. Finally, empirical evidence is presented to support the

validity of the proposed method.

KEYWORDS

denoising, forecast, google Trends, SARIMA models, unstable time series, wavelet theory

1|INTRODUCTION

Though they may be built on the basis of reliable and

well‐maintained archives, there is no doubt that none of

the available real‐life time series is ever error free, espe-

cially when it comes to the archives that the statistical

units are extracted from. Consistency checks and

updating procedures are routinely performed by statistical

institutions (e.g., national statistical offices and central

banks) in the attempt to control for bias and other sys-

tematic and nonsystematic errors, which can adversely

affect the quality of the information disseminated. Thank-

fully, a large number of ad hoc statistical tools are

generally available to statistical providers as well as the

technology to use them, both in the form of affordable

hardware resources and freely available computer

routines.

However, there are cases where statistical investiga-

tions are designed to extract valid information on the

basis of unconventional “archives,”for which concepts

such as construction and maintenance are neither appli-

cable nor conceivable. This is the case of the Google

Trends (GT) dataset which, instead of being designed

to meet the traditional inference requirements of the

sample‐to‐population type, is indeed aimed at capturing

the “system status,”the population of reference is at—

Received: 31 October 2017 Revised: 8 July 2019 Accepted: 24 July 2019

DOI: 10.1002/for.2626

Journal of Forecasting. 2020;39:281–295. © 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 281