Stocks & Commodities V. 31:10 (26-30): Build A Better Moving Average by Richard D. Ahrens

Build A Better Moving Average by Richard D. Ahrens

Smooth Those Spikes

Is it possible to have a moving average that minimizes zigzags and powers through the occasional price spike? Find out here.

Smoothing market price data sounds like a simple concept, yet it is extremely difficult to do. We apply moving averages to a time series to reduce noise and reveal the underlying trend with as little delay as possible. As such, there are three main elements we have to look at:

* Trend— In digital signal processing (DSP), this is also referred to as the signal.

* Noise—Gyrations inherent in any complex system.

* Delay—How long we have to wait to get an answer.

Moving averages essentially act as low-pass filters, that is, they are supposed to smooth away high-frequency noise and leave the lower-frequency signal for us to view. The problem is that large price changes can overwhelm the smoothing ability of short-term averages, and long-term averages introduce so much delay that the answers are of limited use by the time we get them.

Is there an optimal average?

A 200-day simple moving average (SMA) does a wonderful job of getting rid of noise, but you have to wait 100 days to get an answer. An 11-day simple moving average gets you an answer with only five days of delay, but doesn’t do much to quiet the noise. You can see why it’s difficult to smooth price data!

Averages were originally intended to work with reasonably well-behaved data. Teachers of mathematics and statistics generally warn their students that using an average isn’t useful for every kind of data. An average always gives you an answer, but if the data is badly behaved, the answer may not be very useful.

Market price data is particularly problematic because it is not normally distributed. Discontinuities (sudden jumps in price) happen frequently, and the sudden jumps in price tend to overwhelm moving averages and cause unwanted distortions in their results. Market price data follows a power law distribution, also known as the Laplace double exponential distribution, which means it will have frequent, large jumps (Figure 1). This was documented as early as 1915 by Wesley Claire Mitchell and later by Benoit Mandelbrot in the 1960s. These price discontinuities constitute a special sort of noise, and from time to time it can be a significant issue. Sometimes price will jump, leaving a sizeable gap, and then it gaps back to the previous level a few days later. Other times, it will gap up or down and simply stay at the new level.