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Unformatted text preview: Autocorrelation function of the daily histogram time series of SP500 intradaily returns Gloria GonzlezRivera & University of California, Riverside Department of Economics Riverside, CA 92521 Javier Arroyo Universidad Complutense de Madrid Department of Computer Science and Arti&cial Intelligence 28040 Madrid, Spain & Corresponding author: gloria.gonzalez@ucr.edu, tel (951) 8271590, fax (951) 8275685. G. GonzlezRivera acknowledges the &nancial support of the UCR University Scholar award and the Academic Senate grants. 1 ABSTRACT Histogram time series (HTS) and interval time series (ITS) are symbolic data sets. Though there are methodological developments for a crosssectional environment, those for time series data are scarce. Arroyo, GonzlezRivera, and Mat (2009) analyze forecasting methods for HTS and ITS adapting smoothing &lters and nonparametric algorithms like the kNN. Though these methods are very exible, they may not be the true underlying data generating process (DGP). We present the &rst building block towards the search for a DGP by focusing on the autocorrelation functions (ACF) of HTS and ITS. We analyze the ACF of the daily histogram of 5minute intradaily returns to the SP500 index in 2007 and 2008. There are clusters of high/low activity that generates a strong, positive, and persistent au tocorrelation pointing towards some autoregressive process for HTS. Though smoothing and kNN may not be the true DGPs, we &nd that they are very good approximations because they are able to capture almost all the original autocorrelation. However, there seems to be some structure left in the data that will require new modelling techniques. As a byproduct, we also analyze the [90,100%] quantile interval. By using the full information contained in the histogram, we &nd that there are advantages in the estimation and prediction of a speci&c interval. Key Words : Symbolic data, Intervalvalued data, Histogramvalued data, Autocorrelation, Intradaily returns JEL Classi&cation: C22, C53 2 1 Introduction Histogramvalued time series (HTS) and intervalvalued time series (ITS) are examples of symbolic data sets as opposed to classical data sets. The sample information of classical data sets, crosssectional or/and time series, consists of a collection of singlevalued observations. In symbolic data sets the sample information is a collection of more complex and richer objects. For instance, in a time series context, the datum at time t could be an interval, like the high/low price interval of a given stock in a given day, so that the collection of intervals indexed by t constitutes an interval time series. In the same fashion, we can think of a daily histogram of intradaily prices or returns, so that the collection of histograms indexed by t form a histogram time series. The analysis of symbolic data sets is a very promising tool to deal with massive information sets. Billard and Diday (2006) and Diday and Noirhomme (2008) provide an extensive review of this new &eld.(2008) provide an extensive review of this new &eld....
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 Fall '08
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 Economics

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