Thursday 5 June 2008

Hilbert Sine Wave - Which Version is Best?

OK I'm gonna warn you now - this post is all about the Hilbert Sine Wave and contains 8 chart examples. So if you're not interested, hit the delete button. But if you are…

Before I start - how about that 30 point up move on the Emini today? If you didn't read yesterday's post, then here it is - trend line congestion & winding up for a big move.

Hilbert Sine Wave and Pull Back in Trend

First off, a couple of charts that show the Hilbert Sine Wave in action today. I use multiple time frames to day trade - 233 tick, 699 tick and 2,097 tick.

Emini Hilbert Sine Wave Image

Hilbert Sine Wave: Pull Back in Trend (Emini 2,097 tick)

In the highest time frame (2,097 tick) we're in an up trend and then have a cyclical low turning point - signaling a possible pull back in trend entry point.

Emini Hilbert Sine Wave Image

Hilbert Sine Wave: End of Trend (Emini 233 tick)

Then looking at the lowest time frame (233 tick) we have possible downside exhaustion with an "end of trend" warning signal. This is the end of a down trend - essentially a counter-trend move. We overshoot slightly (white dot) but then the Emini rallies strongly to finish the day on the highs.

Which Hilbert Sine Wave Should You Use?

Thanks to Victor H. and Rick J. for suggesting I look at the different Hilbert Sine Wave versions available. John Ehlers, the developer of the Hilbert Sine Wave, has created 4 different versions of this indicator and there are another 2 possible variations:

Original code from "Rocket Science for Traders" using weighted moving average
Original code using Jurik moving average smoothing (what I use)
Original code using Hull moving average smoothing (fast & free moving average)
Updated code from "Cybernetic Analysis for Stocks and Futures" book
Alternative approach using Discrete Fourier Transform (DFT)
Alternative approach using Bandpass Filters

I assessed all 6 versions on 2 criteria. First comparing support and resistance level signals generated by the Better Sine Wave algorithm visually on a 233 tick chart of the Emini. Each version was given a visual score, relative to the original weighted moving average version (score zero).

Then I back-tested 4 different systems on a 699 tick Emini chart over 60,000 bars:

Cycle trades (buy at support, sell at resistance)
"Overshoot" trades (buy at overshoot of support, sell at overshoot of resistance)
Breakout trades (buy at overshoot of resistance, sell at overshoot of support)
5th Wave trades (buy at pullback in up trend, sell at pullback in down trend)

The results of all the systems were then added together. Don't expect great results for these systems - it's taking EVERY trade with no filtering - but it does allow us to compare between different versions of the Hilbert Sine Wave.

The results are summarized below:

	WMA	JMA	Cyber.	Hull	DFT	B'pass
Visual Score	0	-1	-3	-2	-5	-7
Profit	$6.7k	$2.4k	$1.4k	$0	($3.0k)	($3.4k)
Profit Factor	1.07	1.07	1.01	1.04	0.97	0.97
No. Trades	1,675	1,747	1,883	1,997	1,666	2,057
% Profitable	53%	53%	49%	52%	52%	45%
Bottom Line	BEST	2nd

Hilbert Sine Wave: Visual Score & System Results Trading 1 Emini Contract

Bottom line - the original code using a weighted moving average to smooth input data was best overall! Wow, with all the hard work gone into improved versions - the original still works best.

Now, am I going to change from the Jurik moving average version I use day-to-day? Probably not, the pull-back in trend (or 5th wave) signals are very important for my day trading and I think the JMA version in superior in this regard. But the analysis was enlightening.

The visual score charts are shown below with my annotations. Hope this article was useful to those traders who use the Hilbert Sine Wave.

Emini Hilbert Sine Wave WMA Image