How to understand if past financial data could be used for future forecast
Understand the concept of information
Purpose of an information is to communicate message and support reasoning.
Best way to achieve that purpose is by using summaries and visuals. In our case we will use only summary numbers.
Calculate mean
Mean is a single value that represent typical value of a dataset.
Means is calculated as adding all item values (x1, x2, ...) and then dividing that sum by the number of items
Mean of dataset: 1, 2, 3, 4, 5 is (1+2+3+4+5) / 5 = 3.
Calculate relative standard deviation (RSD)
Standard deviation is an average difference between the observed value and the mean. Wording 'relative' compares that standard deviation with the mean.
RSD is calculated using 2 numbers: mean and standard deviation.
1) Every value in a datasets is subtracted from the mean and the result is then squared.
(1-3)^2,
(2-3)^2,
(3-3)^2,
(4-3)^2,
(5-3)^2
2) Results from the first step are added together.
3) Sum from second step is divided by the number of items in a dataset (if sample is used, second number ie. denominator is subtracted by 1).
4) The square root is taken from the third step result.
5) The result from the fourth step is divided by the mean and multiplied by 100 (note that if mean is a negative value instead of relative standard deviation we call the result coefficient of variation).
Make conclusion
In our dataset (1, 2, 3, 4, 5) mean is 3, and RSD is 47%.
What that means? It means that for observations like in our dataset typical future value will be around 3 with 47% imprecision.
Smaller RSD means higher precision of dataset. In practice up to 25% RSD is satisfactory.