Time series and stochastic differential equations as a tool to model the volatility of an asset

Abstract

In the problem of estimating the prices of electricity markets, different forecast models have been proposed for the short term, among the most outstanding are the works by Francisco Nogales, which uses autoregressive integrated moving average methodology to analyses time series in the California market. Peninsular Spain. Nogales and Contreras use time series models applied to the markets of California and Spain, the applied series were carried out to estimate the hourly price of the following day using two methodologies, the first a dynamic regression and the second transfer function models. In he proposes a prediction based on Autoregressive conditional heteroscedasticity models generalized conditional autoregressive heteroscedasticity Rabbit use the wavelet transform to decompose the data series, then applying an autoregressive integrated moving average model to the transformed series, taking advantage of the existing advantages in the domain of the frequency. The techniques have a high correlation with problems of physics which can be approached in a similar way, we must highlight the fact of using stochastic differential equations which are modern techniques in mathematics and physics.