On the Autocorrelation and Stationarity of Multi-Scale Returns

Carlos Manuel Rodríguez-Martínez, Héctor Francisco Coronel-Brizio, Horacio Tapia-McClung, Manuel Enríque Rodríguez-Achach and Alejandro Raúl Hernández-Montoya ()
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Carlos Manuel Rodríguez-Martínez: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Campus Sur, Calle Paseo No 112, Lote 2, Colonia Nueva Xalapa, Xalapa 91097, Veracruz, Mexico
Héctor Francisco Coronel-Brizio: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Campus Sur, Calle Paseo No 112, Lote 2, Colonia Nueva Xalapa, Xalapa 91097, Veracruz, Mexico
Horacio Tapia-McClung: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Campus Sur, Calle Paseo No 112, Lote 2, Colonia Nueva Xalapa, Xalapa 91097, Veracruz, Mexico
Manuel Enríque Rodríguez-Achach: Unidad Experimental Marista (UNEXMAR), Universidad Marista de Mérida, Mérida 97300, Yucatán, Mexico
Alejandro Raúl Hernández-Montoya: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Campus Sur, Calle Paseo No 112, Lote 2, Colonia Nueva Xalapa, Xalapa 91097, Veracruz, Mexico

Mathematics, 2025, vol. 13, issue 17, 1-12

Abstract: In this article, we conduct a statistical analysis of the autocorrelation functions (ACF) of multi-scale logarithmic returns computed over maximal monotonic uninterrupted trends (runs) in financial indices’ daily data. We analyze the Dow Jones Industrial Average (DJIA) and the Mexican IPC (Índice de Precios y Cotizaciones) over a period from 30 October 1978 to 19 May 2025. We examine how deterministic alternation of signs shapes the ACF of multi-scale returns, and we evaluate covariance stationarity via formal tests (e.g., Augmented Dickey–Fuller and Phillips–Perron). We conclude that, despite the persistent long-memory oscillations in the ACF, multi-scale return series pass the stationarity tests, an outcome with interesting implications for econometric modeling of financial time series.

Keywords: price runs; multi-scale returns properties; empirical analysis; stationarity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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