  ## All flavors of moving average!

The moving average is perhaps the most popular  technical analysis tool of markets. According to this article, its use for smoothing data goes back to the early 20th century. Its use to define the market trend is everywhere, on traders screen  as well as specialized media screens. It is impossible to find a book of technical analysis that does not speak about moving average and it seems that strategies based on the crossing of two moving averages are the few classics that continue to work. “The variations on moving average indicators are so numerous that a book could be devoted exclusively to their various flavors.” Mechanical trading systems, p.18.

The goal of this article is to let you taste some flavors of this popular indicator. However, in order to be brief, I limit the discussion to the use of a single moving average. We will return later in other articles to the use of two or even three moving averages.

The tests are done on the EURUSD, with an initial capital of \$ 10,000 for the period from 01-01-2008 until 01-01-2012 and the time frame of M15. Volume of trade = 1 mini lot (\$ 10K). But before presenting the test results, I’d tell you a trick I use to make a sweep of a broad spectrum of time intervals without crashing my computer. During the optimization process, I use a single time frame M15, but instead of varying the period of a fixed step (linear scale), rather I use a logarithmic scale. So I vary what I call MaPeriodPower from 3 to 15 which corresponds to a period of 2 ^ 3 to 2 ^ 15 times M15. I hope this is clear, otherwise I will return to in the next article.

1 – The calculation method (simple, exponential, smoothed, balanced)

The goal is not to show you how to calculate the moving average, first of all, because you do not need to do so and second, because there are lots of websites that already do this, but to evaluate the best method for a trading strategy. Certain authors, each according to their employed strategy, see no advantage in using other one but Simple Moving Average. Others, prefer the exponential for its ability to respond to recent changes. Personally, I prefer to pass the test and “let the best guy win” …

The test protocol:

• Stop and Reverse: Buy when the price crosses, from bottom to top, its moving average. Sell ​​when the price crosses, from top to bottom, its moving average.
• Evaluate the strategy on a wide range of time frame, from (2 ^ 3)xM15 = 8xM15 to (2 ^ 15)xM15 = 32768xM15 = 341xD1
• Calculate the average value of profits and the standard deviation and the ratio (profit/standard deviation) will be used to compare four methods for calculating the moving average (higher the ratio will be, better the method of calculation for our strategy will be)

 SMA EMA Smoothed Weighted Average -2215 -1707 -1126 -2335 Std 5234 5246 4682 5660 Ratio -0.423 -0.325 -0.241 -0.413

The winner of the first test is the smoothed moving average. For the following tests, I’ll take this type of calculation.

2- Calculation applied to … (Close, Thypical price, Weighted close)

Thypical price = (High + Low + Close)/3

Weighted close = (High + Low + Close x 2)/4

 Close Typical Weighted Average -1126 -1118 -1125 Std 4682 4686 4693 Ratio -0.241 -0.239 -0.240

The difference is in no way significant. It is useless to display the graph.

3- The price crosses moving average or the slope?

The two most popular strategies using a single moving average are:

• The price crosses its moving average
• The moving average slope changes
 Price slope Average -1126 -57 Std 4682 4442 Ratio -0.241 -0.013 Figure 2 : Profit / Loss for both strategies (the price crosses and the slope of the moving average)
Conclusion
According to test results, the best combination to use for a strategy based on a single moving average is :  a smooth type calculation applied to the closing price and to trade the average slope instead of the crossing of the price with its average.
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