When looking at time series data, such as a stream of prices, it can often be useful to establish a general trend and represent this with a single number. This can be achieved using a linear regression calculation.

Take this series of prices:
4.8, 4.8, 4.5, 3.9, 4.4, 3.6, 3.6, 2.9, 3.5, 3.0, 2.5, 2.2, 2.6, 2.1, 2.2

If you plot on an Excel graph and add a linear trend line, you should get something like this:

We can do the same thing in code:

  1. using System;
  2. class Regression
  3. {
  4.     static void Main(string[] args)
  5.     {
  6.         double[] values = { 4.8, 4.8, 4.5, 3.9, 4.4, 3.6, 3.6, 2.9, 3.5, 3.0, 2.5, 2.2, 2.6, 2.1, 2.2 };
  7.         double xAvg = 0;
  8.         double yAvg = 0;
  9.         for (int x = 0; x < values.Length; x++)
  10.         {
  11.             xAvg += x;
  12.             yAvg += values[x];
  13.         }
  14.         xAvg = xAvg / values.Length;
  15.         yAvg = yAvg / values.Length;
  16.         double v1 = 0;
  17.         double v2 = 0;
  18.         for (int x = 0; x < values.Length; x++)
  19.         {
  20.             v1 += (x – xAvg) * (values[x] – yAvg);
  21.             v2 += Math.Pow(x – xAvg, 2);
  22.         }
  23.         double a = v1 / v2;
  24.         double b = yAvg – a * xAvg;
  25.         Console.WriteLine(“y = ax + b”);
  26.         Console.WriteLine(“a = {0}, the slope of the trend line.”, Math.Round(a, 2));
  27.         Console.WriteLine(“b = {0}, the intercept of the trend line.”, Math.Round(b, 2));
  28.         Console.ReadLine();
  29.     }
  30. }

Now you have the slope of the trend line, this can be used as an input for neural networks analysing time series data. I use something similar in NNATS…

For a complete explanation of linear regression see Wikipedia.

John