MACD Indicator Deep Dive

Go: open a terminal in a folder you can write to — cd ~/Desktop on macOS or Linux, cd %USERPROFILE%\Desktop on Windows.

Do: save this as prices.py and run python3 prices.py.

"""Build a price series once, so every later step works on the same numbers."""
import random

random.seed(11)                     # fixed, so your figures match this page exactly

# Eight regimes of 50 bars: up, down, flat, repeating. The turns are at
# bar 50, 100, 150, 200, 250, 300, 350 -- known, because we put them there.
REGIMES = [0.35, -0.30, 0.0, 0.35, -0.30, 0.0, 0.35, -0.30]

price, series = 100.0, []
for bar in range(400):
    drift = REGIMES[bar // 50]
    price += drift + random.uniform(-1.2, 1.2)
    series.append(round(price, 2))

with open("closes.txt", "w") as f:
    for p in series:
        f.write("%.2f\n" % p)

print("bars written :", len(series))
print("first 5      :", series[:5])
print("last 5       :", series[-5:])
print("high / low   : %.2f / %.2f" % (max(series), min(series)))
print("regime turns : bars 50, 100, 150, 200, 250, 300, 350")
print()
print("Three kinds of market on purpose -- rising, falling and flat, each")
print("appearing more than once. Most indicator advice is written as if only")
print("the first two exist.")

You should see: four hundred bars with known turning points:

bars written : 400
first 5      : [100.24, 100.73, 102.1, 102.36, 102.73]
last 5       : [116.86, 116.63, 115.51, 114.5, 114.51]
high / low   : 134.48 / 92.25
regime turns : bars 50, 100, 150, 200, 250, 300, 350

Three kinds of market on purpose -- rising, falling and flat, each
appearing more than once. Most indicator advice is written as if only
the first two exist.

The turns are known because they were placed deliberately. That is what makes step 5 possible — with real market data you can see what an indicator did, but never how late it was.

If not: PermissionError means the folder is not writable — cd somewhere you own. Different first values mean random.seed(11) is missing.

Go: the same folder.

Do: save this as macd.py and run python3 macd.py.

"""MACD is three numbers, and only two of them are calculated."""

closes = [float(line) for line in open("closes.txt")]

def ema(values, period):
    k = 2.0 / (period + 1)
    out = [None] * (period - 1)
    out.append(sum(values[:period]) / period)
    for v in values[period:]:
        out.append(v * k + out[-1] * (1 - k))
    return out

fast, slow = ema(closes, 12), ema(closes, 26)
macd = [None if None in (f, s) else f - s for f, s in zip(fast, slow)]

defined = [v for v in macd if v is not None]
sig_raw = ema(defined, 9)
offset = len(macd) - len(defined)
signal = [None] * offset + sig_raw
hist = [None if None in (m, s) else m - s for m, s in zip(macd, signal)]

print("bar   close     EMA12     EMA26      MACD    signal      hist")
for i in (25, 33, 34, 100, 250):
    row = [closes[i], fast[i], slow[i], macd[i], signal[i], hist[i]]
    print("%3d %s" % (i, "".join("%10s" % ("%.4f" % v if v is not None else "--") for v in row)))

print()
print("MACD line   = EMA(12) - EMA(26)      -- a difference, not an average")
print("signal line = EMA(9) of the MACD line")
print("histogram   = MACD - signal          -- not calculated, just subtracted")

You should see: the MACD line defined from bar 25 and the signal only from bar 33:

bar   close     EMA12     EMA26      MACD    signal      hist
 25   106.8400  106.9168  105.0485    1.8683        --        --
 33   109.8800  107.9414  106.4272    1.5142    1.4963    0.0179
 34   110.1300  108.2781  106.7015    1.5766    1.5124    0.0642
100    95.5700   98.3459  101.2788   -2.9329   -2.6548   -0.2780
250   106.6600  108.9754  111.0338   -2.0584   -1.8185   -0.2398

MACD line   = EMA(12) - EMA(26)      -- a difference, not an average
signal line = EMA(9) of the MACD line
histogram   = MACD - signal          -- not calculated, just subtracted

Notice the two different starting points. The MACD line needs 26 bars, because EMA(26) does; the signal line then needs a further nine of those, so it does not exist until bar 33. Anything at the left edge of a MACD panel is warm-up, not signal.

The last three lines are the definition worth memorising. MACD is a difference, not an average — which is the fact step 4 turns into a practical consequence.

If not: if the signal column stays --, the offset arithmetic is wrong: the signal is an EMA of the defined MACD values only, then padded back out to the full length so the indexes line up with the price bars.

Go: the same folder.

Do: save this as identity.py and run python3 identity.py.

"""Prove the histogram carries no information the other two lines lack."""

closes = [float(line) for line in open("closes.txt")]

def ema(values, period):
    k = 2.0 / (period + 1)
    out = [None] * (period - 1)
    out.append(sum(values[:period]) / period)
    for v in values[period:]:
        out.append(v * k + out[-1] * (1 - k))
    return out

fast, slow = ema(closes, 12), ema(closes, 26)
macd = [None if None in (f, s) else f - s for f, s in zip(fast, slow)]
defined = [v for v in macd if v is not None]
offset = len(macd) - len(defined)
signal = [None] * offset + ema(defined, 9)
hist = [None if None in (m, s) else m - s for m, s in zip(macd, signal)]

hist_zero, macd_cross, both = 0, 0, 0
for i in range(1, len(closes)):
    if None in (hist[i], hist[i-1], macd[i], macd[i-1], signal[i], signal[i-1]):
        continue
    h = (hist[i-1] <= 0) != (hist[i] <= 0)
    c = (macd[i-1] <= signal[i-1]) != (macd[i] <= signal[i])
    hist_zero += h
    macd_cross += c
    both += (h and c)

print("histogram crossed zero        :", hist_zero, "times")
print("MACD crossed its signal line  :", macd_cross, "times")
print("both happened on the same bar :", both, "times")
print()
print("identical:", hist_zero == macd_cross == both)
print()
print("They are the same event, always, by construction: hist = MACD - signal,")
print("so hist = 0 is exactly MACD = signal. The histogram is a redrawing of")
print("a crossing you can already see, not a third opinion about it.")
print()
print("This matters when a strategy claims confirmation from 'MACD crossover")
print("AND histogram turning positive'. That is one condition counted twice,")
print("and counting a condition twice does not make it more likely to be right.")

You should see: three counts that are the same number:

histogram crossed zero        : 13 times
MACD crossed its signal line  : 13 times
both happened on the same bar : 13 times

identical: True

They are the same event, always, by construction: hist = MACD - signal,
so hist = 0 is exactly MACD = signal. The histogram is a redrawing of
a crossing you can already see, not a third opinion about it.

This matters when a strategy claims confirmation from 'MACD crossover
AND histogram turning positive'. That is one condition counted twice,
and counting a condition twice does not make it more likely to be right.

Thirteen, thirteen, thirteen. Not approximately — identically, on every bar, and it could not be otherwise: the histogram is MACD minus signal, so it crosses zero exactly when MACD crosses signal. There is no arrangement of prices for which one happens and the other does not.

This is a general habit worth more than the specific fact. Before combining two indicators for “confirmation”, check whether they are computed from the same inputs. Two views of one calculation agree with each other for reasons that have nothing to do with the market, and stacking them raises your confidence without raising your accuracy — which is the worst possible combination.

If not: if the three counts differ, the comparison operators are inconsistent — both tests must treat the boundary the same way, which is why each uses <= and compares the resulting booleans rather than testing signs directly.

Go: the same folder.

Do: save this as unbounded.py and run python3 unbounded.py.

"""RSI has a ceiling. MACD does not -- and that changes how you may use it."""

closes = [float(line) for line in open("closes.txt")]

def ema(values, period):
    k = 2.0 / (period + 1)
    out = [None] * (period - 1); out.append(sum(values[:period]) / period)
    for v in values[period:]:
        out.append(v * k + out[-1] * (1 - k))
    return out

def macd_of(values):
    f, s = ema(values, 12), ema(values, 26)
    return [None if None in (a, b) else a - b for a, b in zip(f, s)]

# The same shape of market, priced in three different units.
INSTRUMENTS = [("a share at ~100", 1.0), ("an index at ~10,000", 100.0),
               ("a currency pair at ~1.10", 0.011)]

print("%-26s %10s %10s %10s" % ("INSTRUMENT", "MIN MACD", "MAX MACD", "RANGE"))
print("-" * 60)
for label, scale in INSTRUMENTS:
    scaled = [c * scale for c in closes]
    m = [v for v in macd_of(scaled) if v is not None]
    print("%-26s %10.4f %10.4f %10.4f" % (label, min(m), max(m), max(m) - min(m)))

print()
print("Identical price movement. The MACD values differ by a factor of ~10,000,")
print("because MACD is a price difference and inherits the price's units.")
print()
print("So 'MACD above 2 is strong' is meaningless without saying which")
print("instrument, and a threshold copied from someone else's chart is")
print("copied along with their instrument's price scale. RSI does not have")
print("this problem: it is a ratio, so it is always between 0 and 100.")

You should see: the same market producing MACD values four orders of magnitude apart:

INSTRUMENT                   MIN MACD   MAX MACD      RANGE
------------------------------------------------------------
a share at ~100               -3.2272     4.3345     7.5618
an index at ~10,000         -322.7227   433.4538   756.1765
a currency pair at ~1.10      -0.0355     0.0477     0.0832

Identical price movement. The MACD values differ by a factor of ~10,000,
because MACD is a price difference and inherits the price's units.

So 'MACD above 2 is strong' is meaningless without saying which
instrument, and a threshold copied from someone else's chart is
copied along with their instrument's price scale. RSI does not have
this problem: it is a ratio, so it is always between 0 and 100.

The three rows are the identical price series multiplied by a constant — the same percentage moves, the same shape, the same turning points. The MACD values differ by a factor of roughly ten thousand, because MACD is a price difference and carries the price's units with it.

So any rule of the form “enter when MACD exceeds N” is instrument-specific by construction, and a number taken from a video about one market is meaningless on another. RSI does not have this problem because it is a ratio: gains divided by losses cancels the units, which is why 70 means the same thing on every chart. That difference — bounded ratio versus unbounded difference — decides which questions each indicator can answer.

If not: if the three ranges are identical, the scale is not being applied — the list comprehension must multiply each close before the MACD is computed, not after.

Go: the same folder.

Do: save this as lag.py and run python3 lag.py.

"""Compare like with like: how many bars after the turn does each CROSSOVER fire?"""

closes = [float(line) for line in open("closes.txt")]

def ema(values, period):
    k = 2.0 / (period + 1)
    out = [None] * (period - 1); out.append(sum(values[:period]) / period)
    for v in values[period:]:
        out.append(v * k + out[-1] * (1 - k))
    return out

def sma(values, period):
    return [None if i < period-1 else sum(values[i-period+1:i+1])/period
            for i in range(len(values))]

fast, slow = ema(closes, 12), ema(closes, 26)
macd = [None if None in (f, s) else f - s for f, s in zip(fast, slow)]
defined = [v for v in macd if v is not None]
offset = len(macd) - len(defined)
signal = [None] * offset + ema(defined, 9)

TRUE_TURN = 50

def first_cross_down(a, b, start):
    """First bar at or after `start` where series a drops below series b."""
    for i in range(max(start, 1), len(a)):
        if None in (a[i], b[i], a[i-1], b[i-1]):
            continue
        if a[i-1] >= b[i-1] and a[i] < b[i]:
            return i
    return None

CANDIDATES = [
    ("MA(5) crosses below MA(20)",   sma(closes, 5),  sma(closes, 20)),
    ("EMA(12) crosses below EMA(26)", fast,           slow),
    ("MACD crosses below signal",     macd,           signal),
]

print("the trend actually reverses at bar :", TRUE_TURN)
print()
print("%-32s %8s %10s" % ("CROSSOVER", "AT BAR", "BARS LATE"))
print("-" * 52)
for label, a, b in CANDIDATES:
    bar = first_cross_down(a, b, TRUE_TURN)
    print("%-32s %8s %10s" % (label, bar, bar - TRUE_TURN if bar else "never"))

print()
print("MACD fires FIRST here, which is the opposite of what 'an average of")
print("averages must be slower' would predict. The reason is worth having:")
print("MACD does not wait for either average to turn down. It measures the")
print("GAP between them, and the gap starts narrowing while both are still")
print("rising -- a change of acceleration, not of direction.")
def count_crosses(a, b):
    n = 0
    for i in range(1, len(a)):
        if None in (a[i], b[i], a[i-1], b[i-1]): continue
        if (a[i-1] > b[i-1]) != (a[i] > b[i]): n += 1
    return n

print()
print("And the price of firing early, over all 400 bars:")
for label, a, b in CANDIDATES:
    print("   %-32s %2d crossings" % (label, count_crosses(a, b)))
print()
print("That is what 'momentum indicator' actually means: acceleration changes")
print("constantly inside a trend that never reverses, so the earliest signal")
print("is also the noisiest. Early and reliable are the same trade-off the")
print("moving-average page measured, seen from another angle.")

You should see: MACD firing first, and producing the most signals:

the trend actually reverses at bar : 50

CROSSOVER                          AT BAR  BARS LATE
----------------------------------------------------
MA(5) crosses below MA(20)             59          9
EMA(12) crosses below EMA(26)          66         16
MACD crosses below signal              52          2

MACD fires FIRST here, which is the opposite of what 'an average of
averages must be slower' would predict. The reason is worth having:
MACD does not wait for either average to turn down. It measures the
GAP between them, and the gap starts narrowing while both are still
rising -- a change of acceleration, not of direction.

And the price of firing early, over all 400 bars:
   MA(5) crosses below MA(20)        9 crossings
   EMA(12) crosses below EMA(26)     5 crossings
   MACD crosses below signal        13 crossings

That is what 'momentum indicator' actually means: acceleration changes
constantly inside a trend that never reverses, so the earliest signal
is also the noisiest. Early and reliable are the same trade-off the
moving-average page measured, seen from another angle.

This result surprised me while writing the page, and the first version of it was wrong. I had assumed — and written — that MACD must be the slowest, since it is built from averages of averages. The measurement said two bars against nine and sixteen, so the prose was wrong, not the code.

The explanation is the useful part. MACD does not wait for an average to turn down. It tracks the gap between two averages, and that gap begins narrowing while both are still rising — a change in acceleration, which necessarily precedes a change in direction. That is what “momentum indicator” means, stated precisely.

And the bottom table is the price. Thirteen crossings against five for the slower pair: the earliest signal is the noisiest one, because acceleration changes constantly inside a trend that never reverses. Early and reliable are two ends of one dial, and every indicator on every chart is a position on it.

If not: if MACD reports never, the signal array is misaligned with the price bars — the padding in step 2 is what keeps index i meaning bar i in every series. The exact bar numbers depend on the seeded series and will match this page.