In
financial technical analysis
In finance, technical analysis is an analysis methodology for analysing and forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis use many of the sam ...
, momentum (MTM) and rate of change (ROC) are simple
indicators showing the difference between today's
closing price
An open-high-low-close chart (also OHLC) is a type of chart typically used to illustrate movements in the price of a financial instrument over time. Each vertical line on the chart shows the price range (the highest and lowest prices) over one un ...
and the close N days ago. Momentum is the absolute difference in stock, commodity:
:
Rate of change scales by the old close, so as to represent the increase as a fraction,
:
''"Momentum"'' in general refers to prices continuing to trend. The momentum and ROC indicators show trend by remaining positive while an uptrend is sustained, or negative while a downtrend is sustained.
A crossing up through zero may be used as a signal to buy, or a crossing down through zero as a signal to sell. How high (or how low when negative) the indicators get shows how strong the trend is.
The way momentum shows an absolute change means it shows for instance a $3 rise over 20 days, whereas ROC might show that as 0.25 for a 25% rise over the same period. One can choose between looking at a move in dollar terms, relative point terms, or proportional terms. The zero crossings are the same in each, of course, but the highs or lows showing strength are on the respective different bases.
The conventional interpretation is to use momentum as a trend-following indicator. This means that when the indicator peaks and begins to descend, it can be considered a sell signal. The opposite conditions can be interpreted when the indicator bottoms out and begins to rise. Momentum signals (e.g., 52-week high) have been shown to be used by financial analysts in their buy and sell recommendations.
SMA
Momentum is the change in an N-day
simple moving average
In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is ...
(SMA) between yesterday and today, with a scale factor N+1, i.e.
:
This is the slope or steepness of the SMA line, like a
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
. This relationship is not much discussed generally, but it's of interest in understanding the signals from the indicator.
When momentum crosses up through zero it corresponds to a trough in the SMA, and when it crosses down through zero it's a peak. How high (or low) momentum gets represents how steeply the SMA is rising (or falling).
The
TRIX indicator is similarly based on changes in a moving average (a triple exponential in that case).
Other moving average trading rules
The relationship between different moving average trading rules is explained in the paper "Anatomy of Market Timing with Moving Averages".
Anatomy of Market Timing with Moving Averages
/ref> Specifically, in this paper the author demonstrates that every trading rule can be presented as a weighted average of the momentum rules computed using different averaging periods.
References
Technical indicators
External links
Fidelity, Rate of Change Indicator
Tuned, Using the Rate of Change Indicator Programmatically
Investopedia definition, Momentum Indicator
Tuned, Using the Momentum Indicator Programmatically
{{technical analysis
Technical indicators