ECIG 2007 Modeling www time series

2007Stéphane Gauvin

FSA - ULaval

ECIG 2007

Modeling www time series

The research opportunity

A word on time series models

Data Models Results

What have we learned? Next steps


FSA - ULaval

Research opportunity

CSR: Organizations manage a widening set of stakeholders

Power of exit Power of voice

The digital sphere has become the Übermedia

Voices are innumerable Which voice will become dominant? (eg: anti-smoking, fat lawsuits, vegetarianism)

General question is:

Can we measure and forecast real-world opinions merely by listening to the digital sphere?

Today’s question is:

How strong is the signal in the digital sphere?


FSA - ULaval

A word on timeseries models

Marketing is concerned with theory building

Data mining is atheoretical Trends are as a nuisance

First step is to take first and second differences VAR and/or co-integration

Dekimpe & Hanssens IJRM 2000, WP 2006 Franses JMR 2005


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Into the looking glass

The digital sphere is invisible. It is queried (googled)

We all google all the time to retrieve specific instances

Swammer searches to count instances


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Swammer

Build an intelligent set of queries to compute index

Shown to be close to survey data


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Illustrative data


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Robust or else


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Storms obscure trends


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French presidental


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Royal / Sarkozy


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Industry data


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Models

Parametric trend models

Robust estimator (M-reg)


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SSA Singular Spectrum Analysis (SSA) (Golyandina et al.

2000)

Non parametric applications to the digital sphere Bagchi & Mukhopadhyay (2006) (overall growth of the Internet) Papagiannaki et al. (2005) (overall backbone traffic)

SSA applications Ghil et al. (2002) (climatology) Balazs & Chaloupka (2004) (biology) Koelle & Pascual (2004) (epidemiology)

Antoniou et al. (2003) (wavelet model / Internet traffic) Edwards (2006) (dissertation / US Navy related series)


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Caterpillar-SSA

It is based on the idea of time series embedding into finite-dimensional space and following application of singular value decomposition (SVD) to the trajectory matrix (that is the result of time series embedding). The components of SVD are uniquely juxtaposed to the additive components of the original time series. Thereby we obtain the decomposition of the time series into additive components together with the information about them. This information is represented by the collection of singular vectors and signular values of the SVD.


FSA - ULaval

Caterpillar-SSA

Opérationnellement

1. Construire une matrice de vecteurs décalés (dim L/2)2. Extraire les valeurs propres3. Regrouper les eigen-vecteurs en trois groupes

1. Tendance (auto-corrélations varient lentement)2. Cycles (auto-corrélations varient rapidement)3. Bruit (cycles de fréquence arbitraire)


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Caterpillar-SSA


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Results - presidential


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Results - presidental


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Results - Industry


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Results - Industry


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Results - Industry


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Conclusions

Good signal-to-noise ratio

Estimation must be robust

SSA

Trend is easily extracted and follows closely the original series Not robust to extreme values

M-NL

Dominant technique for large scale scenario Sometimes, sensitive to seed values


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Next

Build a tracking system

M-NL to signal shifts autoSSA to produce rich trend summaries

Explore forecasting models

Fitting and forecasting are not the same Longer series to test rolling holdout samples

Validity issues

Anecdotal evidence of close tracking Presidential series raises questions as to what the signal means

ECIG 2007 Modeling www time series

Documents

original time series

idea of time series

result of time series

samelonger series

components of svd

additive components

industryconclusionsgood

signal means