Moving Averages as Support

The average is approached 3 times on this module’s sixty closes, or 11, or 22, and which of those you get depends entirely on how near counts as near — a tolerance your platform applies and never prints. Take the reading with the most evidence in it, 17 approaches within eight tenths of a point of the ten-bar average, and the price continues away from the line on 9 of them. That is 53 per cent. Any bar on the same series continues its own direction two bars later 45 per cent of the time with no line drawn at all, and the same average read five bars stale — a level with no claim on anything — continues away on 5 of its 7. The cross needs no sample to settle, because its lateness is arithmetic: the ten crossed above the twenty at bar 36, which is 12 bars after the low, with 54 per cent of the whole advance already behind it, and lesson 48’s first moment puts a fifty against a two hundred 75 bars further back still. What survives is real and smaller than the folklore: one extra bar of confirmation takes this series from 14 changes of side to 5.

Prerequisites: Lesson 48, which put the mean lag of a ten-bar average at 4.50 bars and a twenty-bar one at 9.50, and which is where the 75 in the claim comes from, lesson 19, whose arithmetic on how many observations a claim needs decides whether 17 approaches can settle anything, and lesson 36, whose efficiency ratio names the stretches in which a line’s description is worth having.

Three lines, and no line at all

Fifty-three per cent sounds like something. The only way to find out whether it is is to run the identical test against lines that have no business working, and against no line whatever. All four rows below use the same sixty closes, the same eight-tenths tolerance and the same two-bar horizon. Only the level changes.

The level	Approaches	Continued away	Share
The ten-bar average	17	9	53%
The same average, its value from five bars earlier	7	5	71%
A flat line at the median close of 102.90	9	5	56%
No level at all: every bar with a direction	49	22	45%

The last row is the one to read first, because it is the price of admission. On this series a bar that has just moved up continues up two bars later 45 per cent of the time, and a bar that has just moved down continues down 45 per cent of the time, with no line involved and nothing to touch. That 45 is what any level has to beat before it has done anything, and the ten-bar average returns 53.

Then read the second row, which is the one that should not work. It is the same average, drawn at the value it held five bars earlier: a level that describes a window ending before the bar it is being tested against, chosen for no reason except that it is the wrong number. It continues away on 5 of its 7 approaches, which is 71 per cent, and it beats the line everybody watches by eighteen points. The flat line at the median beats it too.

The price turned, and the line was nearby.

That is not a claim that the average does nothing. It is a claim about what seventeen observations can carry, and the answer is nothing at all. Nine holds out of seventeen puts the true rate somewhere between 28 and 77 per cent at 95 per cent confidence, which is half the available scale. Lesson 19’s arithmetic gives the other half of the answer: telling a 53 per cent hold rate apart from a 45 per cent one, at the confidence and power that lesson used, takes 609 approaches in each condition. On this series there are seventeen. On a daily chart of one instrument at eight tenths of a point, 609 approaches is a decade.

So the honest finding is not that the claim is false. It is that almost nobody who repeats it has ever been in a position to know, including anybody working from a chart, and that the two lines you would use to check it are already on your screen.

What survives

A description, and it is worth more than the thing that was being claimed. On these sixty closes the price sits above its ten-bar average on 32 of the 51 bars where the average exists, which is 63 per cent, and the sides it takes are not evenly spread: bars 17 to 28 are a continuous run below it and bars 42 to 54 a continuous run above. Those two runs are the shape of the series, and the line found them.

What the line also does, if you let it, is change its mind constantly. Declare the side on every bar and this series changes sides 14 times in 51 bars, with a median run of a single bar. Ask for two consecutive closes on the same side before declaring anything and the 14 becomes 5, with a median run of 11 bars. Three consecutive closes gives 3 declared sides, and four gives 2.

The cost of each of those is exactly one more bar of lateness at every turn, on top of the 4.50 the average already carries, and that is the whole of the trade. Nothing in the persistence rule improves the description. It removes the changes of side that were about to be reversed, at the price of arriving later at the ones that were not, and you can price that in bars before you ever run it.

What this does not settle

That seventeen approaches settle anything, in either direction. The interval around 9 of 17 runs from 28 to 77 per cent, and the interval around the stale line’s 5 of 7 runs from 29 to 96, so the two overlap almost completely and this page cannot tell them apart. Every number in the two tables above is a small sample, and the reason for printing them is not that they establish the claim is false. It is that they establish how much work establishing anything would take, which is 609 approaches, and that number is the actual finding.

That these sixty closes are anybody’s. They are a teaching series built to be legible on a small chart, and lesson 44 measured their lag-one autocorrelation at minus 0.66, which means they reverse harder than anything you will trade. That is precisely the condition under which a line drawn through the middle of the range gets approached often and holds rarely, so this series is not a neutral place to test a support claim and was never chosen to be one. The tolerance arithmetic transfers. The 53 does not.

That the cross result and the support result are the same kind of statement. They are not, and conflating them is how this lesson could be misread. The support figures are a small sample and are worth what a small sample is worth. The lateness of a cross is a property of two weight vectors, holds on every series, and would still hold if the support claim turned out to be entirely correct. A reader who takes one number away from this page should take the 75.

That support was tested in the form its advocates mean. This page tested closes against one average over one window at five tolerances, because that is the version that can be reproduced from printed numbers. The looser versions are real and were not tested: an area rather than a line, the bar’s low rather than its close, a band around the average, a different period on a different timeframe, or the average of an instrument the reader has watched for years and can read in a way no rule captures. Some of those are testable and this lesson did not test them. One of them is not testable at all, and that is worth saying rather than hiding, because it is the version most people actually hold.

That any of this settles what to do with a line. It settles what a line is entitled to say, which is a narrower thing. The average is a description of a window, late by half that window, that changes its mind fourteen times in fifty-one bars unless you make it wait. What it cannot yet tell you is when its own reading should be read the other way round — and there is an instrument that makes that question unavoidable, because on these same sixty closes it prints thirteen readings above 70 and not one below 30.

Problems

1. Find your own tolerance, then change it. Take one instrument, one moving average and sixty closes. Count the bars whose close is within a tenth of the instrument’s typical daily range of the average, and write the number down. Then count again at half that distance and again at twice it. You now have three counts of the same thing on the same bars, and the spread between them is what the word touch was doing on your chart before you measured it. Ten minutes in a spreadsheet.
2. Compute the hold rate and the base rate in the same sitting. For each approach you counted at your middle tolerance, record whether the close two bars later moved further from the line on the side it approached from. That is your hold rate. Then compute the base rate on the same sixty bars: of every bar that closed up or down, what share continued in that direction two bars later. Write the two numbers side by side. If the first is not clear of the second by more than the width of your sample, you have measured nothing, and the number of approaches you have tells you how far from clear it needs to be.
3. Collect the base rate properly, and the stale line with it. Extend to as much history as you can get and keep counting until you have a hundred approaches rather than seventeen. Then run the identical count on the same average shifted five bars back, which is a level with nothing to recommend it. Two hundred observations and two hold rates, and the honest reading is the difference between them rather than either one alone. This costs an evening, it is the only version of the exercise that can settle anything, and at the end of it you hold a number about your own instrument that nobody has ever quoted at you.

Sources. William Brock, Josef Lakonishok and Blake LeBaron, “Simple Technical Trading Rules and the Stochastic Properties of Stock Returns” (The Journal of Finance, 1992), for the study that gave moving-average rules an academic footing in the first place, which is why the claim is stated fairly at the top of this lesson rather than dismissed. Ryan Sullivan, Allan Timmermann and Halbert White, “Data-Snooping, Technical Trading Rule Performance, and the Bootstrap” (The Journal of Finance, 1999), for the re-examination of those results against the universe of rules that could have been tried instead, which is the same problem the tolerance column above makes visible. Cheol-Ho Park and Scott H. Irwin, “What Do We Know About the Profitability of Technical Analysis?” (Journal of Economic Surveys, 2007), for a survey of ninety-five modern studies and for the finding that early positive results weaken as the tests get stricter. Richard W. Hamming, Digital Filters (Prentice-Hall, 1977), for delay as the first moment of a weight vector, which is where the 4.50, the 9.50 and the 75 come from and why none of them needs a backtest.

A moving average is a description of a window, arriving half that window late, and this lesson has bought it one honest sentence: it says where the price has been sitting relative to its own recent past, and it says so 4.50 bars after the fact on a ten-bar setting and 99.50 on a two-hundred-bar one. It is not support, on any evidence anybody has shown, and the evidence it would take is 609 approaches that nobody has collected. Lesson 51 takes the other instrument on every chart and asks the question this one leaves open. On these same sixty closes a fourteen-bar oscillator prints thirteen readings above 70 and not a single one below 30, and of the twelve that have five bars behind them the price is higher five bars later on 7, which is 58 per cent against a base rate of 58. Overbought is not a level. It is a level read inside a regime, and the regime decides which way to read it.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.