The Moving Average Convergence Divergence (MACD) is a trading indicator used in technical analysis of securities prices, created by Gerald Appel in the late 1970s. It is designed to reveal changes in the strength, direction, momentum, and duration of a trend in a stock's price.

The MACD indicator (or "oscillator") is a collection of three time series calculated from historical price data, most often the closing price. These three series are: the MACD series proper, the "signal" or "average" series, and the "divergence" series which is the difference between the two. The MACD series is the difference between a "fast" (short period) exponential moving average (EMA), and a "slow" (longer period) EMA of the price series. The average series is an EMA of the MACD series itself.

The MACD indicator thus depends on three time parameters, namely the time constants of the three EMAs. The notation "MACD(a,b,c)" usually denotes the indicator where the MACD series is the difference of EMAs with characteristic times a and b, and the average series is an EMA of the MACD series with characteristic time c. These parameters are usually measured in days. The most commonly used values are 12, 26, and 9 days, that is, MACD(12,26,9).

As true with most of the technical indicators, MACD also finds its period settings from the old days when technical analysis used to be mainly based on the daily charts. The reason was the lack of the modern trading platforms which show the changing prices every moment. As the working week used to be 6-days, the period settings of (12, 26, 9) represent 2 weeks, 1 month and one and a half week. Now when the trading weeks have only 5 days, possibilities of changing the period settings cannot be overruled.

However, it is always better to stick to the period settings which are used by the majority of traders as the buying and selling decisions based on the standard settings further push the prices in that direction.

In signal processing terms, the MACD series is a filtered measure of the derivative of the input (price) series with respect to time. (The derivative is called "velocity" in technical stock analysis.) MACD estimates the derivative as if it were calculated and then filtered by the two low-pass filters in tandem, multiplied by a "gain" equal to the difference in their time constants.

It also can be seen to approximate the derivative as if it were calculated and then filtered by a single low pass exponential filter (EMA) with time constant equal to the sum of time constants of the two filters, multiplied by the same gain. So, for the standard MACD filter time constants of 12 and 26 days, the MACD derivative estimate is filtered approximately by the equivalent of a low-pass EMA filter of 38 days. The time derivative estimate (per day) is the MACD value divided by 14.

The average series is also a derivative estimate, with an additional low-pass filter in tandem for further smoothing (and additional lag). The difference between the MACD series and the average series (the divergence series) represents a measure of the second derivative of price with respect to time ("acceleration" in technical stock analysis). This estimate has the additional lag of the signal filter and an additional gain factor equal to the signal filter constant.

The MACD can be classified as 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 greatly.

Another member of the price oscillator family is the detrended price oscillator (DPO), which ignores long term trends while emphasizing short term patterns.

Exponential moving averages highlight recent changes in a stock's price. By comparing EMAs of different lengths, the MACD series gauges changes in the trend of a stock. The difference between the MACD series and its average is claimed to reveal subtle shifts in the strength and direction of a stock's trend. It may be necessary to correlate the signals with the MACD to indicators like RSI power.

Some traders attribute special significance to the MACD line crossing the signal line, or the MACD line crossing the zero axis. Significance is also attributed to disagreements between the MACD line or the difference line and the stock price (specifically, higher highs or lower lows on the price series that are not matched in the indicator series).

A "signal-line crossover" occurs when the MACD and average lines cross; that is, when the divergence (the bar graph) changes sign. The standard interpretation of such an event is a recommendation to buy if the MACD line crosses up through the average line (a "bullish" crossover), or to sell if it crosses down through the average line (a "bearish" crossover). These events are taken as indications that the trend in the stock is about to accelerate in the direction of the crossover.