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http://dx.doi.org/10.1145/1102351.1102366

has been cited by the following article:

• TITLE: Forecasting Density Function: Application in Finance

  AUTHORS: Rituparna Sen, Changie Ma

  KEYWORDS: Density Estimation, Functional Data Analysis, Principal Components Analysis, Vector ARMA

  JOURNAL NAME: Journal of Mathematical Finance, Vol.5 No.5, November 26, 2015

  ABSTRACT: With increasing availability of data, in many situations it is now possible to reasonably estimate the probability density function (pdf) of a random variable. This is far more informative than using a few summary statistics like mean or variance. In this paper, we propose a method of forecasting the density function based on a time series of estimated density functions. The proposed method uses kernel estimation to pre-process the raw data followed by dimension reduction using functional principal components analysis (FPCA). Then we fit Vector ARMA models to the reduced data to make a prediction of the principal component scores, which can then be used to obtain the forecast for density function. We need to transform and scale the forecasts to ensure non-negativeness and integration to one. We compared our method to [1] for histogram forecasts, on simulated data as well as real data from S&P 500 and the Bombay Stock Exchange. The results showed that our method performed better on both the datasets and the simulation using uniform and Hilbert distance. The time dependence and complexity of density function are different for the two markets, which is captured by our analysis.