2. The Empirical Data

The data for AAAYX, ydata, is loaded as follows.

The descriptive statistics for our data are given by using Statistics`DescriptiveStatistics`.

These reports show that the usual normal distribution is not suitable for our data and that the negative skewness requires extra care in interpreting the results. To illustrate graphically, mathStatica can be used for nonparametric kernel density estimation in two steps. First, we specify the kernel as the Gaussian kernel. The second step is to choose the bandwidth denoted here by c.

Since the kernel and have now been specified, we can plot Figure 1 as our smoothed nonparametric kernel density estimate using the NPKDEPlot[data,K,c] function.

Figure 1.

The preceding discussion and plot illustrate a common situation: normality is often not suitable for many financial time series including ours. mathStatica can effectively implement a wide range of nonnormal densities for applications in finance.