# Ergodic Oscillator

Also known as: SMI Ergodic.
A Momentum & Oscillators concept (Classic single-name oscillators) in the LuxAlgo Library, with 1 indicator implementation.

## What is the Ergodic Oscillator?

The Ergodic Oscillator comes from William Blau's double-smoothing framework for momentum. Blau took one-bar price change, smoothed it twice with EMAs, and divided by the equally double-smoothed absolute price change, scaling the bounded ratio to plus or minus 100; that construction is his True Strength Index, and 'ergodic' is the label he gave indicators built this way. In the commonly charted form (often named SMI Ergodic) the ergodic line is paired with a signal line, an EMA of the ergodic, and the 'oscillator' variant plots the difference between the two as a histogram.

Blau developed the approach in Technical Analysis of Stocks & Commodities articles in the early 1990s and collected it in his 1995 book Momentum, Direction, and Divergence. His argument was that raw [momentum](https://www.luxalgo.com/library/concept/momentum/) is too noisy to read directly, that a single heavy smoothing arrives too late, and that two successive EMAs applied to one-bar momentum strip noise while keeping more of the turn timing. Normalizing by the double-smoothed absolute change then rescales the result into a bounded oscillator, comparable across instruments the way [RSI](https://www.luxalgo.com/library/concept/rsi/) is and unlike an unbounded [rate of change](https://www.luxalgo.com/library/concept/roc/).

Platform naming is inconsistent: the same construction appears as TSI, Ergodic, or SMI Ergodic, and despite that last label it is distinct from Blau's [Stochastic Momentum Index](https://www.luxalgo.com/library/concept/stochastic-momentum-index/), which measures the close against the midpoint of the high-low range instead. What defines the family is the mechanism: double smoothing strips most bar-to-bar noise, and normalizing by absolute momentum keeps the output bounded, so zero-line position tracks net direction while signal-line crossings mark momentum turns with modest lag.

Parameter conventions vary; SMI Ergodic implementations commonly default to a long smoothing near 20, a short near 5, and a 5-period signal line. Longer first-stage smoothing gives a slower, cleaner line for regime and divergence work; shorter settings act more like a responsive trigger. Because the ratio compares net change to total change, it measures directional consistency rather than size: a drift of small one-way bars can print as strongly as a powerful trend, which deserves skepticism in thin markets.

## How to Identify the Ergodic Oscillator on a Chart

In an indicator pane, the ergodic family has a recognizable signature:

1. Look for a smooth line around a zero centerline, scaled to roughly plus or minus 100 (or 1) rather than 0-100.
2. Find the companion signal line, an EMA of the main line; the pair moves like a slower, rounder MACD.
3. Check for the histogram variant plotting the gap between the ergodic line and its signal.
4. Inspect the inputs: two smoothing lengths plus a signal length, commonly near 20, 5, and 5, mark Blau's double-smoothing design.
5. Confirm the character: notably smoother than RSI or raw momentum at comparable lengths, with rounded turns rather than jagged ones.

## How it's calculated

A double-smoothed ratio of net price change to absolute price change, bounded between -100 and +100 and plotted with a signal line.

```
mtm_t = C_t - C_(t-1)
Erg_t = 100 × EMA_s(EMA_r(mtm_t)) / EMA_s(EMA_r(abs(mtm_t)))
Signal_t = EMA_q(Erg_t)
Osc_t = Erg_t - Signal_t

  C_t: closing price at bar t
  mtm_t: one-bar price change at bar t
  EMA_r(x): r-period exponential moving average of x
  EMA_s(x): s-period exponential moving average of x
  EMA_q(x): q-period exponential moving average of x
  r: first smoothing length (commonly 20)
  s: second smoothing length (commonly 5)
  q: signal line length (commonly 5)
  Erg_t: ergodic (SMI Ergodic) line at bar t
  Signal_t: signal line at bar t
  Osc_t: SMI Ergodic Oscillator, the line minus its signal
  t: bar index
```

Identical in form to William Blau's True Strength Index; TSI defaults r = 25 and s = 13 are also common.

Double-smoothing abs(mtm) in the denominator keeps the output inside -100 to +100.

Some platforms plot only the line and signal and omit the Osc_t histogram.

## How traders use it

- Signal-line crossings as momentum triggers: the ergodic line crossing its EMA signal is read much like a [MACD](https://www.luxalgo.com/library/concept/macd/) cross, typically filtered by zero-line position or a trend gauge to cut counter-trend noise.
- Zero-line regime reads: sustained positive values indicate net upside momentum after heavy smoothing, so the zero cross itself doubles as a slow trend-change cue.
- Divergence analysis: the double smoothing produces clean swing peaks, making [regular divergences](https://www.luxalgo.com/library/concept/regular-bullish-bearish-divergence/) between the ergodic line and price extremes easier to spot ahead of potential exhaustion, with [hidden divergence](https://www.luxalgo.com/library/concept/hidden-divergence/) serving the continuation case.
- Bounded-extreme context: traders mark instrument-specific extreme bands and treat visits as [overbought or oversold](https://www.luxalgo.com/library/concept/overbought-oversold/) conditions, standing down on fresh momentum entries rather than automatically fading.
- Histogram deceleration: a shrinking gap between line and signal flags momentum rolling over before the actual cross, the same early-warning read applied to the MACD histogram.

## Ergodic Oscillator vs related concepts

- **MACD** (https://www.luxalgo.com/library/concept/macd/): MACD subtracts two EMAs of price, so it is unbounded and its scale drifts with price level. The ergodic normalizes double-smoothed momentum by absolute momentum, giving a bounded, comparable line at the cost of an extra smoothing stage.
- **Stochastic Momentum Index** (https://www.luxalgo.com/library/concept/stochastic-momentum-index/): Also Blau, but a different question: SMI double-smooths the close's distance from the midpoint of the high-low range. The SMI Ergodic label on many platforms actually denotes the TSI-style construction, so check the formula, not the name.
- **RSI** (https://www.luxalgo.com/library/concept/rsi/): RSI averages gains against losses over one window, reacting faster but printing far more texture. The ergodic's two-stage smoothing trades that immediacy for cleaner swings, which is what makes its crosses and divergences easier to read.

## FAQ

### Is the Ergodic Oscillator the same as the True Strength Index?

At the core, yes. Blau's ergodic construction and the True Strength Index share the same formula: double-EMA-smoothed momentum divided by double-EMA-smoothed absolute momentum. The differences are packaging: platforms vary default lengths, add a signal line, or plot the line-minus-signal histogram, and 'SMI Ergodic' usually labels the version with the signal line included. If the smoothing lengths match, the values match.

### What does 'ergodic' mean in this indicator's name?

It is Blau's own label, borrowed loosely from statistics, for momentum that has been double-smoothed enough that its ratio to smoothed absolute momentum gives a stable, bounded reading. It is not a claim that markets are ergodic in the formal mathematical sense, so treat the name as branding for the double-smoothing technique rather than as a statistical property of prices.

### What are common settings for the SMI Ergodic oscillator?

Implementations frequently default to a long smoothing around 20, a short around 5, and a 5-period signal EMA, though Blau varied lengths freely by market and timeframe. Longer first-stage settings favor slower regime reads; shorter ones favor triggers. Settings redistribute lag; none remove it.

### Is the Ergodic Oscillator leading or lagging?

Lagging by construction: two EMA stages plus a signal EMA all defer to past data, so crosses arrive after the turn they describe. Divergences can precede reversals, the closest the tool comes to leading behavior, but that is an inference from waning momentum, not a forecast. Treat it as a momentum-state descriptor and pair it with structure for timing.

### How is the Ergodic Oscillator different from the Stochastic Oscillator?

The [stochastic oscillator](https://www.luxalgo.com/library/concept/stochastic-oscillator/) locates the close within the recent high-low range on a 0-100 scale, a position measure that pins to extremes during trends. The ergodic is a smoothed momentum ratio centered on zero, measuring directional consistency of price changes. They can disagree for long stretches; the zero-centered scale is the quickest visual tell.

### Can the Ergodic Oscillator be applied to inputs other than price?

Yes. The construction is input-agnostic: any series can be fed through the double-smoothed ratio, the same substitution habit behind [RSI of other sources](https://www.luxalgo.com/library/concept/rsi-of-other-sources/). Feeding it an already-smoothed input stabilizes the line further but lengthens the chain between reading and price, so the pipeline is best kept short.

## Implementations in the Library

- Ergodic Oscillator (LuxAlgo): https://www.luxalgo.com/library/indicator/ergodic-oscillator/

## Related concepts

- Balance of Power: https://www.luxalgo.com/library/concept/balance-of-power/
- CCI: https://www.luxalgo.com/library/concept/cci/
- Williams %R: https://www.luxalgo.com/library/concept/williams-percent-r/
- Ultimate Oscillator: https://www.luxalgo.com/library/concept/ultimate-oscillator/
- True Strength Index: https://www.luxalgo.com/library/concept/true-strength-index/
- Relative Vigor Index: https://www.luxalgo.com/library/concept/relative-vigor-index/
- Awesome Oscillator: https://www.luxalgo.com/library/concept/awesome-oscillator/
- Accelerator Oscillator: https://www.luxalgo.com/library/concept/accelerator-oscillator/
- Gator Oscillator: https://www.luxalgo.com/library/concept/gator-oscillator/
- Elder Ray: https://www.luxalgo.com/library/concept/elder-ray/

---

Source: https://www.luxalgo.com/library/concept/ergodic-oscillator/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/