Symbolic data analysis (SDA) proposes an alternative approach to deal with large and complex data sets. It allows the summarization of these datasets into smaller and more manageable ones retaining the key knowledge. In this framework, we propose an approach for the aggregation of complex time series. This approach is based on a peculiar density plot, called beanplot (Kampstra, 2008). In particular, we explicitly take in account the Density of the data in the underlying temporal interval considered. These types of new data can be fruitfully used where there is an overwhelming number of observations, for example in High Frequency Financial Data (Drago, Scepi, 2009). At the same time, they can be useful for analyzing the complex behavior of the markets where we can discover important patterns in the long time (complex patterns of dependency over the time). In general, Beanplots can be used in the Exploratory Data Analysis framework as a data visualization tool at the same way as Stripcharts, Boxplots and Violinplots, where each one, considered singularly, can be a suitable transformation of histograms. Anyway the interest in this paper is not to explore the structures of data, but to consider the possibility of forecasting complex time series by means of these new type of data. In that sense, the ﬁrst step is to look for a good parameterization of the Complex Objects over the time, by indicators of size, location and shape of our data. In particular we consider a polynomial function as speciﬁc measure of the structure of the object. Successively, the Forecasting process can be performed by using the VAR model (Lutkepohl,2005). We show the usefulness of this strategy by means of simulated data.
- Symbolic Data Analysis,
Available at: http://works.bepress.com/carlo_drago/97/