Stochastic modelling for evolution of stock prices by means of functional principal component analysis (Q2711689)

Financial prices are usually recorded once for every day that an appropriate market is open. It is known that the financial time series so obtained do not conform with the usual requirements for orthodox time series analysis. In fact, stochastic processes generating financial prices are generally agreed to be not stationary. NEWLINENEWLINENEWLINEThe purpose of this paper is to model and forecast the stock price process avoiding some of the restrictive hypothesis imposed by classical methodologies such as stationarity, equally spaced observations, etc. Also, the objective of this paper is to apply functional principal component analysis to model and forecast financial prices of the banking in Madrid Stock Market from weekly observations of a random sample of banks. The evolution of stock prices along the time can be modelled as a sample path of a continuous-time stochastic process so that the sample information about stock markets is a set of curves rather than the vectors of the standard multivariate analysis. By the reason, in this paper, it is proposed to apply forecasting models based on functional principal component analysis. The resulting principal component prediction models are based on linear regression of the principal components associated to the process in the future against the principal components in the past.