Wavelet Analysis of Non-Stationary Financial Time Series: An Application to Nigerian Stock Exchange Data

This study applies wavelet analysis to decompose and characterise the non-stationary behaviour of equity return time series from the Nigerian Exchange Group, filling a methodological gap in the Nigerian financial econometrics literature where standard Fourier-based and ARIMA approaches have been the predominant analytical tools despite their limitations for non-stationary processes. The Nigerian equities market has exhibited episodic structural breaks, long-memory dynamics, and heteroscedastic volatility clustering, particularly during the 2016 currency crisis, the 2020 COVID-19 shock, and the post-subsidy-removal turbulence of 2023, each of which generates non-stationarities that violate assumptions of classical time series methods. Daily closing prices for the Nigerian Exchange Group All-Share Index and the five largest market capitalisation equities are sourced for the period January 2010 to December 2023. Continuous wavelet transform and discrete wavelet transform decompositions using Daubechies wavelets are applied to extract time-frequency representations of return dynamics. Wavelet coherence analysis is conducted to examine time-varying co-movement between individual equity returns and the market index across different frequency scales. Wavelet variance decomposition reveals the relative contribution of short-run, medium-run, and long-run fluctuations to total return variance across different market episodes. Results confirm long-memory properties in squared returns at medium and long scales, and document increased cross-sectional coherence during crisis periods. Keywords: wavelet analysis, financial time series, Nigerian Exchange Group, non-stationarity, equity returns