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        Short Definition

          Parameter stability is a concept where we investigate how the performance of strategies changes with altered input values. 
 

This article is an extension of our article on curve fitting. If you have not read it, we recommend you do so here.

A trading edge often consists of several optimizable inputs. It could be how many days you wait until you sell, how high the RSI-indicator needs to go to generate a signal, or anything else that is related to the logic of the strategy. 

An edge that has optimizable inputs varies in performance and characteristic depending on what input values you use.  If you choose to sell after 20 days instead of 10, that would alter the behavior of the strategy. When evaluating the robustness of a strategy we can do so by looking at  how these variations in parameter values affect the performance.

 

Optimal Parameters Change Throughout Time

When we design strategies, we are looking for robust edges that we think will work into the future. What many traders do to achieve this, is that they optimize the inputs  to find the best parameters for their strategy.  Often they believe that they have delimited specific market behavior by choosing the best parameter values.

This could be true in certain cases. Sometimes there are very specific tendencies in markets that need to be defined through very exact parameter settings. For example if  you want to measure volatility on a weekly basis. you would not want to use a 7 day lookback period, since  one week is 5 trading days.

However, in most cases the selected parameter settings do not mirror any specific behavior.  This means that we might need more evidence to support our trust in the edge. It is in such cases parameter stability comes into play.

What is Parameter stability?

A strategy with inputs enables us to change how the strategy calculation is carried out. With each change, the strategy is altered somewhat.  Since the optimum values for strategies often change over time, testing parameter stability  becomes a way of simulating what happens when we are not trading optimal values. This is what we will be doing most of the time in real trading.

Parameter stability simply means that an edge performs well under many different parameter combinations.

Clarification

Let us say that we have a system that buys when RSI crosses over a certain value and sells after a certain number of days. We set up the following input ranges:

RSI threshold level: 50-90 in steps of 10

Buy after X number of days: 1-10 in steps of 1

 

In this case, we have 5*10= 50 variations of the same strategy.

Ideally, all of them should be profitable.  If that is the case, it is an indication that we have a good and robust system that we might consider trading.

Conversely, if we find that very few of the variations have produced desirable results, we are warned that our edge might be curve fit!

 

Curve Fit Optimization Ranges

When testing  parameter stability, we must be aware of one common pitfall; the one of curve fit optimization ranges. In short, it means that we decide what values to include in our parameter stability test, knowing beforehand that there is a narrow optimum of values.

For example, we could know that the optimum values are between 6 and 8. If we use that knowledge to set the optimization range in our parameter stability test to 6-8, the optimization range is curve fit.

 

Conclusion

Parameter stability is powerful method to discern curve fit strategies from true ones. By determining how well the strategy behaves when it is slightly off its optimum parameter, we can anticipate how well it will perform in the future.

However, it is important to recognize that all types of arbitrary choices of what to include and not, could be subject to curve fitting. Of course, this also applies to optimization ranges which could endanger the usefulness of testing parameter stability.