Cybernetic Trading Strategies: Developing a Profitable Trading System with State-of-the-Art Technologies

6

A Trader's Guide to Statistical Analysis

A trader does not have to be a statistical genius, but he or she should have a basic understanding of statistics that are descriptive of various properties of the data being analyzed. This chapter gives an overview of some of the most important statistical concepts that traders should understand. These concepts are as follows:

1. Mean, median, and mode.
2. Standard deviation.
3. Types of distributions and their properties.
4. How mean and standard deviation interact.
5. Hypothesis testing.
6. Mean or variance with two or more distributions.
7. Linearcorrelation.

A trader who has a general idea of these concepts can use statistics to develop trading systems as well as to test patterns and relationships. Let's now discuss each of these concepts in more detail.

MEAN, MEDIAN, AND MODE

The mean is another term for the average. The median of a sample is the middle value, based on order of magnitude. For example, in the number sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, the median is 5 because it is surrounded by four higher values and four lower values. The mode is the most frequently occurring element.

To clarify the definitions of mean, median, and mode, let's look at two different cases:

1. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
2. 1, 2, 3, 4, 5, 100, 150, 200, 300.

In the first case, the mean is 5.5 and the median is either 5 or 6. Hence, in this case, the mean and the median ...