# Evgeny Slutzky and Moving Averages, from Phil McDonnell

September 27, 2008 |

All moving averages have to be based on a backward looking window of time. So a 10 day average is the average of the last 10 days and so on. But the center in time for that average is really about five days ago. To be more precise it is (n+1) / 2 days ago or 5.5 days ago.

So comparing two moving averages of different lengths is really comparing apples and oranges. If we compare a 10 day to a 30 day average, for example, then we are comparing the average of 5.5 days ago to 15.5 days. In other words they are not the same point in time. Mr. Glazier's enlightening 3D representation of moving averages of various lengths shows that the longer windows respond more slowly to ripples in price than do the shorter moving averages because of this lag effect.

Another feature visible in the chart is the apparently cyclical undulations. The problem with that is that it may simply be a manifestation of the Slutzky - Yule effect. Essentially Slutksy-Yule says that any series, when averaged, will show sinusoidal oscillations as a result of the averaging process. This is true even if the original series was composed of random numbers which could not possibly be sinusoidal in nature.

Another common pitfall when using moving averages is to think that all one has to do is to find the magic combination such as a 19, 27 and 79 day triple crossover with a minimum threshold of 1%. The problem with any such system is that there are an infinite number of these combinations. We quickly fall into the data mining trap where we will appear to find something even if it is merely a product of chance.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008

Another interesting point about moving averages is that the daily change in an N period moving average is caused by the difference between the values of the Nth day and the current day:

MA(t) = (1/N) * ( p(t) + p(t-1) + … + p(t-N+1) )

MA(t) - MA(t-1) = (1/N) * ( p(t) - p(t-N) )

So in cases where N is small, and where the p(t-N) value that fell out of the calculation is large, the moving average can experience sudden drops. This causes that cognitive dissonance when one sees a moving average fall even as the values are climbing between yesterday and today.This also provides the intuition to Slutzky Yule - for any given set of observations, there exists a cluster of points that has the highest average of all similar sized clusters, so while that cluster is passing through the calculation period of the moving average, there will be a peakedness, with two troughs surrounding it.

## Alice Allen remarks:

While we’re talking about moving averages, a practical caution from my own experience with a popular commercial trading platform: If you are in a fast trading situation, monitoring a price graph with less than a 1-day display unit (e.g., 60-min, 30-min, 15-min), a line labeled “200-Day Moving Average Study” may not be the true 200-Day MA but perhaps the MA of the last 200 ticks. Under these circumstances, you may visually note that the price has crossed your MA line, but it will not necessarily be a true MA crossover as calculated by programs. Maybe this is obvious, but it took me a while to figure out and perhaps is unique to the platform I use.

## Anatoly Veltman writes:

The best use of MAs that I know has nothing to do with crossovers. And it happens to be essential to one’s daily/weekly chart perspective. Extremely useful! I first saw it described by Stan Weinstein; then the periods and trading signals were optimized by a few proprietary shops. I believe it to be one of the better tools; if not for all markets, then at least for stocks.

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