Momentum (technical analysis)
Encyclopedia
Momentum and rate of change (ROC) are simple technical analysis
Technical analysis
In finance, technical analysis is security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis incorporate technical analysis, which being an aspect of active management stands...

 indicators showing the difference between today's closing price 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.

SMA

Momentum is the change in an N-day simple moving average (SMA) between yesterday and today, with a scale factor N+1, ie.


This is the slope or steepness of the SMA line, like a derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

. 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
Trix (technical analysis)
Trix is a technical analysis oscillator developed in the 1980s by Jack Hutson, editor of Technical Analysis of Stocks and Commodities magazine. It shows the slope of a triple-smoothed exponential moving average...

indicator is similarly based on changes in a moving average (a triple exponential in that case).
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