Int. J. Data Analysis Techniques and Strategies, Vol. 5, No. 3, 2013 291 Copyright © 2013 Inderscience Enterprises Ltd. An equivalence between typical spectrographic data analysis and the formulations for time series analysis Leonardo Bennun Departamento de Física, Laboratorio de Física Aplicada, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepcion – Concepcion (41), Chile Fax: 56-41-2224520 E-mail: bennun@yahoo.com Abstract: We have demonstrated the equivalence of two formulations for data processing, which usually are studied separately and independently. Habitually, for time series analysis, like signals processed in communications, electronics, control sciences, etc., mathematical tools based on autocorrelations, cross-correlations or convolutions, etc., are applied. Another sort of formulations is applied for analysis in spectrographic techniques, where the data is usually processed with statistical procedures based on the least square method. The equivalence demonstrated between both methodologies opens new possibilities in time series analysis, in order to find predetermined structures in the acquired data. Also, all of the mathematical criteria often used in spectroscopic analysis (like the limit of detection, or the determination limit), could be applied in methods for analysis of data depending on time. Keywords: data analysis; maximum likelihood principle; processing methods. Reference to this paper should be made as follows: Bennun, L. (2013) ‘An equivalence between typical spectrographic data analysis and the formulations for time series analysis’, Int. J. Data Analysis Techniques and Strategies, Vol. 5, No. 3, pp.291–302. Biographical notes: Leonardo Bennun graduated from the Balseiro Institute, Argentina where he obtained his PhD (2005) and MS (1993) in Nuclear Engineering. He joined the Applied Physics Group at Concepción University, Chile in 2006 as a Research Scientist. His research interests include the development of nuclear methods applied to exploration and exploitation of energetic and mineral resources; metrology, data treatment and the study of stochastic processes. 1 Introduction In the following, we show that two mathematical formulations of analysis, usually considered independent, the first applied to spectroscopic data and the second applied to time series, are absolutely equivalent from a mathematical point of view. There are standard procedures commonly used for the analysis of a time series, which are widely applied to signal processing in communication, mathematical finance, control sciences, etc. These formulations have application areas much more diverse, as many