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:

- using System;
- class Regression
- {
- static void Main(string[] args)
- {
- 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 };
- double xAvg = 0;
- double yAvg = 0;
- for (int x = 0; x < values.Length; x++)
- {
- xAvg += x;
- yAvg += values[x];
- }
- xAvg = xAvg / values.Length;
- yAvg = yAvg / values.Length;
- double v1 = 0;
- double v2 = 0;
- for (int x = 0; x < values.Length; x++)
- {
- v1 += (x - xAvg) * (values[x] - yAvg);
- v2 += Math.Pow(x - xAvg, 2);
- }
- double a = v1 / v2;
- double b = yAvg - a * xAvg;
- Console.WriteLine("y = ax + b");
- Console.WriteLine("a = {0}, the slope of the trend line.", Math.Round(a, 2));
- Console.WriteLine("b = {0}, the intercept of the trend line.", Math.Round(b, 2));
- Console.ReadLine();
- }
- }

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