Authors:
Promise Saro Daewii, Roseline I. Ndu, Lekara-Bayo Ifeoma Better, Deebom Zorle Dum, Jaime Alfonso Flores Navas, Palanivel Rathinasabapathi Velmurugan
Addresses:
Department of Mathematics, Faculty of Science, Rivers State University, Port Harcourt, Rivers State, Nigeria. Department of Statistics, Rivers State University, Port Harcourt, Rivers State, Nigeria. Department of Mathematical Sciences, Open and Distance University of Mexico, Mexico City, Mexico. Faculty of Economics and Business Administration, Berlin School of Business and Innovation, Neukölln, Berlin, Germany.
Abstract:
This research explores the characteristics of distribution, interactions of dynamic volatility, and the conditional covariance framework connecting the All-Share Index (ASI) and Market Capitalization (MC) within the Nigerian capital market, utilizing a hybrid multivariate approach comprising VEC–LSTM–BEKK, VEC–ANN–BEKK, and VEC–SVR–BEKK. Using Python modules (arch, statsmodels, TensorFlow, PyTorch), the research uses 1,799 monthly secondary data points from the Central Bank of Nigeria from January 1996 to June 2024. Preliminary Jarque-Bera tests show non-normality, and the Augmented Dickey-Fuller and Phillips-Perron tests corroborate return stationarity. With low average returns and substantial standard deviations (0.1599 and 0.3839, respectively), ASI (0.0093) and MC (0.0169) demonstrate market capitalization volatility. Both return series display high kurtosis ("ASI"=120.393; "MC"=164.085) and positive skewness ("ASI"=0.7037; "MC"=0.2928). Jarque–Bera tests ("ASI"=207,789.271; "MC"=385,955.456; p=0.000) dispro Unit root tests (p=0.000) and KPSS tests (p=0.100) prove stationarity. Basic raw return correlation is -0.14. MC is more volatile than ASI, with conditional standard deviations of 1.1014 to 1.4059 versus 1.0605 to 1.3075, according to the initial conditional covariance matrices in all three models. VEC–LSTM–BEKK yields the lowest baseline conditional variances (1.1247 for ASI; 1.2130 for MC), middle (1.5908; 1.9225), and highest risk estimates (1.7095; 1.9765). All models had negative off-diagonal covariance factors (-0.2847 to -0.3460), indicating an immediate inverse co-volatility dynamic between aggregate market value and stock index movements
Keywords: All-Share Index (ASI); Phillips-Perron Tests; Python Libraries; Optimizing Portfolios; Non-Normal Distribution; Managing Equity Risk; Market Capitalization (MC).
Received on: 02/05/2025, Revised on: 09/07/2025, Accepted on: 20/08/2025, Published on: 05/06/2026
DOI: 10.64091/ATITP.2026.000334
AVE Trends in Intelligent Technoprise Letters, 2026 Vol. 3 No. 2 , Pages: 89-100