Parameter Combinations and Optimisation

Question 1

Counting Parameters

Answer 1

If there are n parameters, and each takes at least k values, then there are at least k^n parameter combinations.

Question 2

Optimisation Criteria / Fitness Function

Answer 2

• maps trading results to fitness.
• higher fitness means better trading strategy results.

Question 3

Example Fitness Function

Answer 3

Profit or return; normally one would incorporate risk too, e.g., via the Sharpe ratio.

Question 4

Grid Search

Answer 4

We define allowable parameter values for each parameter individually, and then look at all combinations.
For a grid search, we must specify parameter ranges for each parameter individually.
We focus on regularly-spaced sequences as returned by the seq function, therefore we need to decide on:
- Endpoints
- Increments

We should also evaluate all parameter combinations.
This is a 2d grid for two parameters, in general a hypergrid, as an example.

Question 5

Regularly-Spaced Sequences

Answer 5

These are sequences of values that are evenly distributed across a specified range.

Question 6

Endpoints

Answer 6

The from and to arguments to seq.
Some parameters have natural upper/lower bounds.
The size of a moving average window is
* lower bounded by 0.
* upper bounded by the length of historical data available.

Question 7

Increments

Answer 7

Suppose you have already decided on endpoints:

1. Estimate backtest time for one parameter combination.
2. Based on how long you have to run the backtest determine the number of parameter combinations to test.
3. Test the same number of parameter values for each parameter to achieve a total close to the target