The problem with technical indicators is that they suffer lag, resulting in signals appearing after events have occurred in time series context. Recently I’ve been investigating ways of reducing lag in these filters, building upon the results from a previous post which shows the workings of a zero-lag indicator derived from first principles. It seems something can be done, although the technique as it stands needs further refining. The graph below shows how it compares with the Exponential Moving Average (EMA) and the Moving Average (MA):
The thing with this filter is that it has negative lag when the market is trending but has high gain when the market is in cycle mode. The reason for this is that in the filtering algorithm there is a part where I multiply the actual price by itself which results in noise components being amplified. To understand this let us consider the following:
Price data can be seen as comprising of two components: a signal part which is useful and a noise part which is not useful.
The effect of multiplying Price by itself is a quadratic equation with signal and noise terms:
We have three noise terms, two of which affect our signal. I think this is the cause of the laggish behavior when the market is cyclic because the high frequency noise components are amplified.
Now there are two ways I can think of improving the performance of this filter
- Find a means of modifying the value of alpha when the filter detects that the market is no longer trending. This will require an additional algorithm to estimate whether the market is in trend mode or cycle mode - something which the Hilbert Transform can take care of.
- Find an alternative to multiplying the price by itself so that additional noise terms are not introduced.
I am biased towards 1 so shall spend more time on that. Because I consider this work in progress, I am tempted to discuss the actual workings of the filtering algorithm at a future date when we have some acceptable performance.
