# Trix (technical analysis)

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Trix (or 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 (i.e. derivative) of a triple-smoothed exponential moving average. [1] [2] The name Trix is from "triple exponential."

In finance, technical analysis is an analysis methodology for 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 same tools of technical analysis, which, being an aspect of active management, stands in contradiction to much of modern portfolio theory. The efficacy of both technical and fundamental analysis is disputed by the efficient-market hypothesis which states that stock market prices are essentially unpredictable.

An oscillator is a technical analysis indicator that varies over time within a band. Oscillators are used to discover short-term overbought or oversold conditions.

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.

Trix is calculated with a given N-day period as follows:

• Smooth prices (often closing prices) using an N-day exponential moving average (EMA).
• Smooth that series using another N-day EMA.
• Smooth a third time, using a further N-day EMA.
• Calculate the percentage difference between today's and yesterday's value in that final smoothed series.

Like any moving average, the triple EMA is just a smoothing of price data and, therefore, is trend-following. A rising or falling line is an uptrend or downtrend and Trix shows the slope of that line, so it's positive for a steady uptrend, negative for a downtrend, and a crossing through zero is a trend-change, i.e. a peak or trough in the underlying average.

Trend following or trend trading is a trading strategy according to which one should buy an asset when its price trend goes up, and sell when its trend goes down, expecting price movements to continue.

The triple-smoothed EMA is very different from a plain EMA. In a plain EMA the latest few days dominate and the EMA follows recent prices quite closely; however, applying it three times results in weightings spread much more broadly, and the weights for the latest few days are in fact smaller than those of days further past. The following graph shows the weightings for an N=10 triple EMA (most recent days at the left):

 Triple exponential moving average weightings, N=10 (percentage versus days ago)

Note that the distribution's mode will lie with pN-2's weight, i.e. in the graph above p8 carries the highest weighting. An N of 1 is invalid.

The easiest way to calculate the triple EMA based on successive values is just to apply the EMA three times, creating single-, then double-, then triple-smoothed series. The triple EMA can also be expressed directly in terms of the prices as below, with ${\displaystyle p_{0}}$ today's close, ${\displaystyle p_{1}}$ yesterday's, etc., and with ${\displaystyle f=1-{2 \over N+1}={N-1 \over N+1}}$ (as for a plain EMA):

${\displaystyle TripleEMA_{0}=(1-f)^{3}(p_{0}+3fp_{1}+6f^{2}p_{2}+10f^{3}p_{3}+\dots )}$

The coefficients are the triangle numbers, n(n+1)/2. In theory, the sum is infinite, using all past data, but as f is less than 1 the powers ${\displaystyle f^{n}}$ become smaller as the series progresses, and they decrease faster than the coefficients increase, so beyond a certain point the terms are negligible.

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## References

1. "TRIX Uptrend & Downtrend | Stock Buy & Sell Signal |Technical Analysis". Web.archive.org. Archived from the original on 2016-03-05. Retrieved 2018-03-22.
2. "TRIX". Web.archive.org. Archived from the original on 2006-01-08. Retrieved 2018-03-22.CS1 maint: BOT: original-url status unknown (link)