This example demonstrates the use of data filters in analyzing stock prices.

Consider the following function that generates a sample stock path over N time periods.  The stock is considered to have initial cost S0, trend parameter r and fluctuation parameter sigma.

Generate a sample stock path over 500 time periods and plot.

The data smoothing functions provided in the Statistics library now give us a means to analyze the overall trend of the data while disregarding small fluctuations. Consider the moving average function, which calculates the average value of a window around each data point.

Exponential smoothing can also be applied.  This method works by 'smoothing' out rough edges, generally caused by cyclic or irregular patterns in the data.

This example demonstrates the use of data filters in analyzing sales at a department store.

Consider the following function that randomly generates the times of n sales at a department store.  The rate of sales is represented by the parameter r and the deviation in this rate by the parameter theta.

Consider the first 100 sales with rate parameter 0.5 and deviation parameter 0.2.

The overall trend is readily apparent with the application of the moving average filter.

The Gaussian kernel should be used with continuous data that is defined on the whole real line. It possesses the familiar bell shape and is based on the Gaussian probability density function.

The triangular kernel is a piecewise function related to the triangular distribution.  This kernel generally creates a kernel density estimate with sharp edges, although remaining relatively smooth.

The rectangular kernel is a piecewise function related to the uniform distribution.  This kernel creates a kernel density estimate that resembles a staircase function.

The biweight kernel is a smooth kernel that is defined on a finite interval, unlike the gaussian kernel.  It should be used for bounded data that is smooth along the interval it is defined upon.

The Epanechnikov kernel is the standard kernel for kernel density estimation. It generally provides the closest match to a probability density function under most circumstances. The kernel itself is a rounded function similar to the biweight, except it is not differentiable at its boundaries.