Forex Indicator - TMACD
(Triangular Moving Average Convergence /
A double-smoothed simple moving average where the middle portion of the data has
MACD (Moving Average Convergence/Divergence) is a technical analysis indicator
created by Gerald Appel in the late 1970s. It is used to spot changes in the strength,
direction, momentum, and duration of a trend in a stock's price.
The MACD is a computation of the difference between two exponential moving averages
(EMAs) of closing prices. This difference is charted over time, alongside a moving
average of the difference. The divergence between the two is shown as a histogram or
Exponential moving averages highlight recent changes in a stock's price. By comparing
EMAs of different periods, the MACD line illustrates changes in the trend of a stock. Then
by comparing that difference to an average, an analyst can chart subtle shifts in the stock's
Since the MACD is based on moving averages, it is inherently a lagging indicator. As a
metric of price trends, the MACD is less useful for stocks that are not trending or are
Note that the term "MACD" is used both generally, to refer to the indicator as a whole, and
specifically, to the MACD line itself.
1 Basic components
2.1 Signal line crossover
2.2 Zero crossover
2.5 False signals
3 Oscillator classification
4 Signal processing theory
7 External links
 Basic components
The graph above shows a stock with a MACD indicator underneath it. The indicator shows
a blue line, a red line, and a histogram or bar chart which calculates the difference
between the two lines. Values are calculated from the price of the stock in the main part of
For the example above this means:
MACD line (blue line): difference between the 12 and 26 days EMAs
signal (red line): 9 day EMA of the blue line
histogram (bar graph): difference between the blue and red lines
MACD = EMA[fast,12] – EMA[slow, 26]
signal = EMA[period,9] of MACD
histogram = MACD – signal
The period for the moving averages on which an MACD is based can vary, but the most
commonly used parameters involve a faster EMA of 12 days, a slower EMA of 26 days,
and the signal line as a 9 day EMA of the difference between the two. It is written in the
form, MACD(faster, slower, signal) or in this case, MACD(12,26,9).
Exponential moving averages highlight recent changes in a stock's price. By comparing
EMAs of different lengths, the MACD line gauges changes in the trend of a stock. By then
comparing differences in the change of that line to an average, an analyst can identify
subtle shifts in the strength and direction of a stock's trend.
Traders recognize three meaningful signals generated by the MACD indicator.
the MACD line crosses the signal line
the MACD line crosses zero
there is a divergence between the MACD line and the price of the stock or between the
histogram and the price of the stock
Graphically this corresponds to:
the blue line crossing the red line
the blue line crossing the x-axis (the straight black line in the middle of the indicator)
higher highs (lower lows) on the price graph but not on the blue line, or higher highs (lower
lows) on the price graph but not on the bar graph
MACD – signal = 0
EMA[fast,12] – EMA[slow,26] = 0
Sign (relative price extremumfinal – relative price extremuminitial) ≠ Sign (relative MACD
extremumfinal – MACD extremuminitial)
 Signal line crossover
Signal line crossovers are the primary cues provided by the MACD. The standard
interpretation is to buy when the MACD line crosses up through the signal line, or sell
when it crosses down through the signal line.
The upwards move is called a bullish crossover and the downwards move a bearish
crossover. Respectively, they indicate that the trend in the stock is about to accelerate in
the direction of the crossover.
The histogram shows when a crossing occurs. Since the histogram is the difference
between the MACD line and the signal line, when they cross there is no difference
The histogram can also help in visualizing when the two lines are approaching a
crossover. Though it may show a difference, the changing size of the difference can
indicate the acceleration of a trend. A narrowing histogram suggests a crossover may be
approaching, and a widening histogram suggests that an ongoing trend is likely to get
While it is theoretically possible for a trend to increase indefinitely, under normal
circumstances, even stocks moving drastically will eventually slow down, lest they go up to
infinity or down to nothing.
 Zero crossover
A crossing of the MACD line through zero happens when there is no difference between
the fast and slow EMAs. A move from positive to negative is bearish and from negative to
positive, bullish. Zero crossovers provide evidence of a change in the direction of a trend
but less confirmation of its momentum than a signal line crossover.
The third cue, divergence, refers to a discrepancy between the MACD line and the graph
of the stock price. Positive divergence between the MACD and price arises when price
hits a new low, but the MACD doesn't. This is interpreted as bullish, suggesting the
downtrend may be nearly over. Negative divergence is when the stock price hits a new
high but the MACD does not. This is interpreted as bearish, suggesting that recent price
increases will not continue.
Divergence may also occur between the stock price and the histogram. If new high price
levels are not confirmed by new high histogram levels, it is considered bearish;
alternatively, if new low price levels are not confirmed by new low histogram levels, it is
Longer and sharper divergences—distinct peaks or troughs—are regarded as more
significant than small, shallow patterns.
The MACD is only as useful as the context in which it is applied. An analyst might apply
the MACD to a weekly scale before looking at a daily scale, in order to avoid making short
term trades against the direction of the intermediate trend. Analysts will also vary the
parameters of the MACD to track trends of varying duration. One popular short-term set-
up, for example, is the (5,35,5).
 False signals
Like any indicator, the MACD can generate false signals. A false positive, for example,
would be a bullish crossover followed by a sudden decline in a stock. A false negative
would be a situation where there was no bullish crossover, yet the stock accelerated
A prudent strategy would be to apply a filter to signal line crossovers to ensure that they
will hold. An example of a price filter would be to buy if the MACD line breaks above the
signal line and then remains above it for three days. As with any filtering strategy, this
reduces the probability of false signals but increases the frequency of missed profit.
Analysts use a variety of approaches to filter out false signals and confirm true ones.
 Oscillator classification
The MACD is an absolute price oscillator (APO), because it deals with the actual prices of
moving averages rather than percentage changes. A percentage price oscillator (PPO),
on the other hand, computes the difference between two moving averages of price divided
by the longer moving average value.
While an APO will show greater levels for higher priced securities and smaller levels for
lower priced securities, a PPO calculates changes relative to price. Subsequently, a PPO
is preferred when: comparing oscillator values between different securities, especially
those with substantially different prices; or comparing oscillator values for the same
security at significantly different times, especially a security whose value has changed
A third member of the price oscillator family is the detrended price oscillator (DPO), which
ignores long term trends while emphasizing short term patterns.
 Signal processing theory
In signal processing terms, the MACD is a filtered measure of velocity. The velocity has
been passed through two first-order linear low pass filters. The "signal line" is that
resulting velocity, filtered again. The difference between those two, the histogram, is a
measure of the acceleration, with all three filters applied. An MACD crossover of the
signal line indicates that the direction of the acceleration is changing. The MACD line
crossing zero suggests that the average velocity is changing direction.
The MACD was invented by Gerald Appel in the 1970s. Thomas Aspray added a
histogram to the MACD in 1986, as a means to anticipate MACD crossovers, an indicator
of important moves in the underlying security.
^ Appel, Gerald (1999). Technical Analysis Power Tools for Active Investors. Financial
Times Prentice Hall. pp. 166. ISBN 0131479024.
^ Murphy, John (1999). Technical Analysis of the Financial Markets. Prentice Hall Press.
pp. 252–255. ISBN 0735200661.