Wavelet Analysis of Financial Time Series
Also known as: wavelet coherence, continuous wavelet transform, time-frequency analysis, Dalgacık (Wavelet) Finansal Analiz
Wavelet financial analysis decomposes a financial time series into different frequency bands (time scales) so short- and long-term relationships can be studied at the same time. Drawing on the treatments of Gençay, Selçuk and Whitcher (2001) and Aguiar-Conraria and Soares (2014), wavelet coherence then visualises how the relationship between two series shifts across both time and frequency.
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When to use it
Use it for continuous financial time series (returns, prices, volatility) when you suspect the relationship between variables changes across both time and horizon. A reasonably long series is needed — at least about 128 observations, and ideally a length close to a power of two (padding can help). The Morlet wavelet is the usual finance choice, edge regions inside the cone of influence should be reported with caution, and wavelet coherence is the standard tool for time-frequency correlation between two series.
Strengths & limitations
- Resolves short- and long-term dynamics simultaneously in one time-frequency picture.
- Captures relationships that are localised in time, revealing when co-movement strengthens or breaks down.
- Wavelet coherence and phase difference reveal both the strength and the lead-lag direction of co-movement across horizons.
- Requires a fairly long series (at least about 128 points), with a power-of-two length being ideal.
- Edge effects within the cone of influence make estimates near the start and end of the series unreliable.
- Results depend on the chosen mother wavelet and smoothing, and the time-frequency maps require careful interpretation.
Frequently asked
What does wavelet coherence tell me?
It is a localised correlation between two series in the time-frequency plane, ranging from 0 to 1. High coherence in a region means the two series move together at that horizon during that period; the accompanying phase difference indicates which series leads.
Why is the Morlet wavelet used in finance?
The Morlet wavelet gives a good balance between time and frequency localisation and yields a clear phase, which makes it the common default for analysing financial series and computing coherence.
What is the cone of influence?
It marks the region near the start and end of the series where the wavelet transform is distorted by edge effects. Coherence and power inside this cone are unreliable and should be reported with that caveat.
How long does my series need to be?
At least about 128 observations, and ideally a length close to a power of two. Shorter series leave too little room across scales and make the lower-frequency bands hard to estimate; padding can help meet the power-of-two ideal.
Sources
- Gençay, R., Selçuk, F. & Whitcher, B. (2001). An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press. DOI: 10.1016/b978-012279670-8.50004-5 ↗
- Aguiar-Conraria, L. & Soares, M.J. (2014). The Continuous Wavelet Transform: Moving Beyond Uni- and Bivariate Analysis. Journal of Economic Surveys, 28(2), 344-375. DOI: 10.1111/joes.12012 ↗
How to cite this page
ScholarGate. (2026, June 1). Wavelet Analysis of Financial Time Series. ScholarGate. https://scholargate.app/en/finance/wavelet-finance
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