Abstract
The study of the evolution of financial series has always been a complex problem because of the nature of stock market series that usually are close to a random walk. The most usual approach has been to apply ARCH and GARCH models, as well as methods that attempt to capture stochastic volatility. In this paper we present an alternative way of approximating this problem, that consists of modeling these series by functional principal components analysis of the financial process up to a certain time frame. The study focused on the Spanish index IBEX35 over a broad period (2007–2013) and, based on continuous market trading, the sample paths were considered integrable square curves. The objective of the work is the estimation of explanatory models for the different bonds as well as the correlation between them.
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Acknowledgements
This research has been supported by project MTM2017-88708-P of Ministerio de Economía y Competitividad, Government of Spain and project P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa, Junta de Andalucía, Spain. Authors are very grateful for the invitation to participate in this volume that is a tribute to our dear master, colleague and friend Pedro Gil, whose memory will live forever.
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Valderrama, M.J., Escabias, M., Galán, F., Gil, A. (2018). A Functional Stochastic Model for the Evolution of Spanish Stock Market. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_39
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DOI: https://doi.org/10.1007/978-3-319-73848-2_39
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