Moving Average Is More Than What You Think – Part 1

Many traders after being in the business for couple of years will start to dismiss many things they have seen, be that moving average, stochastics, MACD, etc. To these traders, these indicators are just useless, lagging, and somethings simply misleading.

Is that really so?

Moving average is supposed to divide the data series evenly

What moving average suppose to do is to properly partition the data series into 2 halves. 50% above the moving average and the other 50% stay below the moving average.

Most experienced traders already know that this is not true, because the distribution of the prices from the moving average is not really 50/50.

For example, here is a distribution chart of E-mini S&P 45-minute bar data, applied with a 9 period moving average. The distribution chart below will show you the bias,

Price moving avearge 2005

You can see from the chart that the distribution is not really that even and the scale is not good for comparison purpose, say, against data from 1996 where S&P was trading in a completely different range.

Since the moving average is not really doing what it is supposed to do, should we dump it for good?

Normalization against bar range holds the key

Lets look at it in another way before deciding what we are going to do.

Instead of looking at the difference between the moving average and its underlying data, which does not provide a normalized view of the relationship between the data and the moving average, we can look at how far away the data is from the moving average, based on the average range of each bar in the data series, using the same number of periods as the moving average itself.

To be fair, this reference range should be the previous average range as oppose to the current average range, otherwise, the predictive quality would be lost.

The formula to use in the Distribution Plot indicator is,

(data1 – data2) / avgrange (1, data1, 9)

where data1 is the underlying data and data2 is the moving average.

Here is a chart for year 2005, using this new measurement method,

Yaer 2005

Here is the chart for year 2004,

Year 2004

Notice how stable the distributions are when compared against each other.

Here is another look at the distribution based on data from 1996-1999,

1996 - 1999 statistic

Here is the distribution based on data from 2000-2005,

2000 to 2005

Comparing these two drastically different time period, we would have expected somewhat different distributions. But, to most people’s surprise, the distribution of this measurement is stable across all these times.


By properly measuring the moving average and its relationship with the underlying data, the moving average indicator can indeed perform what it is supposed to do. Next time when you read a chart with moving average, you will know what relationship to look for and focus on.

Discuss this article.

4 Comments on “Moving Average Is More Than What You Think – Part 1”

  1. Ted Adams Says:

    How would you create this indicator , in the scrit editor ,so that the parameters can
    be changed ?

  2. Lawrence Chan Says:

    Not sure which indicator you are referring to.

  3. Jonny Garrett Says:

    Normalizing the data in this article was intersting. I’m interested in the concepts behind normalization, how it is done, why and when and when not to use it and anything useful about this. Do you know of any good articles on the web i could look into or would this make good artcile in the blog sometime?

  4. Lawrence Chan Says:

    Normalization of time series is a pretty complex topic by itself. In short, normalization of a time series is to look for 2 functions – one that estimate the mean of a moving window, and the other is a “ruler” that can transform the data, when centered around the first one, resulting in a distribution that belongs to the normal distribution class. The example done in this article provided an answer – a specific moving average paired with a specific average range function, but the process to look for the answer is greatly simplied.
    How useful is such pair? Very useful for estimating the most probably range in near future from the estimation point, much better than the classic binomial method that is common for option volatility estimation.
    It is definitely a great topic to write about because most reference on time series analysis are very boring text books 🙂

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