- Composite oscillator built from **six parallel MACD histograms** at Fibonacci EMA periods (34, 55, 89, 144, 233, 377), all sharing fast period 8.
- Groups into three wave bands: **A** (short-term), **B** (medium-term), **C** (long-term), giving a single-pane momentum spectrum across cycle lengths.
- When all three bands share the same sign, momentum is **unanimous**. When they diverge, the market is arguing with itself.
- Matches the **thinkorswim TTM_Wave_A/B/C** thinkScript studies with TOS-compatible property mapping.
- No configurable parameters: the Fibonacci period structure is the design, not a tunable choice.
John Carter introduced TTM Wave in *Mastering the Trade* (2005, revised 2012) as part of his "Trade The Markets" (TTM) suite alongside TTM Squeeze and TTM Trend. The indicator descends from Gerald Appel's MACD (1979) but extends it by running six parallel MACD channels whose periods follow the Fibonacci sequence: 8, 34, 55, 89, 144, 233, 377.
The design philosophy is straightforward: a single MACD channel captures momentum at one timescale. Stack six of them and you get a momentum spectrum. When short-term waves (A) fire first and medium/long-term waves (B, C) follow suit, the trend has legs. When A waves reverse while C waves persist, you are looking at a pullback, not a reversal.
Carter's original implementation appeared as thinkScript studies on the thinkorswim platform. No external TA libraries (Skender, TA-Lib, Tulip, OoplesFinance) implement TTM Wave, making this a first-principles implementation validated through self-consistency tests.
TTM Wave measures momentum acceleration at six different timescales simultaneously. Each channel computes a MACD histogram (the difference between the MACD line and its signal line), which is a second-order momentum measure: it tracks the rate of change of the fast-minus-slow EMA spread relative to its own smoothed average. Positive histogram means momentum is accelerating bullishly; negative means bearishly.
The multi-timeframe structure is the indicator's core value proposition. A single MACD can only tell you about momentum at one scale. TTM Wave tells you whether short-term, medium-term, and long-term momentum agree. Agreement (all six histograms positive or all negative) identifies high-conviction trend environments. Disagreement (A waves positive while C waves negative, or vice versa) identifies pullbacks and potential reversals.
The slowest channel (8, 377, 377) dictates the warmup. [`IsHot`](lib/oscillators/ttm_wave/TtmWave.cs:71) is the conjunction of all six MACD `IsHot` flags.
[`TtmWave`](lib/oscillators/ttm_wave/TtmWave.cs:29) is implemented as a composition of six internal [`Macd`](lib/oscillators/ttm_wave/TtmWave.cs:43) instances rather than manual EMA management. This delegates bar correction, NaN handling, and state management to the battle-tested `Macd` class. The trade-off: six redundant fast EMA computations (all share period 8). The benefit: zero additional state synchronization bugs.
The six histograms map to three wave bands, each containing an inner (smaller period) and outer (larger period) envelope. Within each group, the inner channel reacts faster, the outer channel slower. When the inner crosses zero before the outer, momentum is accelerating at that timescale.
Because `TtmWave` subscribes to a source publisher's events, it implements [`IDisposable`](lib/oscillators/ttm_wave/TtmWave.cs:29) to properly unsubscribe and dispose all six internal MACD instances.
### 5. Edge Cases
- **Zero parameters**: No user-configurable parameters exist; the Fibonacci structure is fixed by design.
- **Insufficient warmup**: All six channels must be hot before `IsHot` returns true. Early values are computed but unreliable.
- **NaN/Infinity inputs**: Handled by each internal MACD instance independently.
- **Bar correction**: `isNew=false` propagates to all six channels, each of which rolls back independently.
## Interpretation and Signals
### Signal Zones
| Condition | Meaning |
|-----------|---------|
| All 6 histograms positive | Strong bullish alignment across all timeframes |
| All 6 histograms negative | Strong bearish alignment across all timeframes |
| A positive, B/C negative | Short-term bounce within a bearish trend |
| A negative, B/C positive | Short-term pullback within a bullish trend |
| A/B positive, C negative | Medium-term rally against long-term bearish bias |
| Mixed within groups | Transitional; no clear directional conviction |
### Signal Patterns
- **Full alignment**: All waves share the same sign. Highest probability trend continuation environment.
- **A-wave reversal**: A waves cross zero while B and C persist. Signals a pullback, not a trend change (unless B follows).
- **Sequential ignition**: A fires first, then B, then C. The strongest trends develop when waves "ignite" in sequence from short to long.
- **C-wave divergence**: C waves weakening while A waves strengthen in the opposite direction. Early warning of a potential macro trend change.
- **Inner/outer spread**: Within a wave band, the inner channel crossing zero before the outer confirms momentum acceleration.
### Practical Notes
- Do not trade A-wave zero-crosses in isolation. They fire frequently in choppy markets and carry no conviction without B/C confirmation.
- C waves respond glacially to price changes (period 377). A sudden 5% move barely registers. Use Wave A for timing, Wave C for directional bias.
- Histogram magnitudes are not comparable across wave bands. Longer-period channels naturally produce larger absolute values because the fast-slow EMA spread grows with period.
## Related Indicators
- [**AO**](../ao/Ao.md): Awesome Oscillator, a single-channel momentum histogram (SMA-based rather than EMA).
- [**APO**](../apo/Apo.md): Absolute Price Oscillator, single dual-EMA difference without signal line.
- [**TRIX**](../trix/Trix.md): Triple EMA rate-of-change, another approach to multi-smoothed momentum.
1.**Confusing wave numbering with channel numbering.** WaveA1 is the *outer* A wave (channel 2, period 55), not channel 1. WaveA2 is the *inner* (channel 1, period 34). This matches the TOS naming where the larger envelope gets the "1" suffix.
2.**Expecting C waves to react to short-term moves.** Channel 6 (period 377) needs roughly 752 bars to warm up and responds glacially to price changes. Use Wave A for timing, Wave C for bias.
3.**Trading A-wave zero-crosses in isolation.** Wave A zero-crosses fire frequently in choppy markets. Without confirming B/C wave direction, you are trading noise.
4.**Ignoring the warmup period.** With 752 bars needed, daily charts require three years of history. On 1-minute charts, that is 12.5 hours. Insufficient warmup produces misleading histogram values.
5.**Comparing histogram magnitudes across wave bands.** Longer-period channels naturally produce larger absolute histograms. Normalize by channel period if you need cross-wave magnitude comparison.
6.**Over-optimizing by sharing the fast EMA.** All six channels use fast period 8, so sharing one EMA(8) seems logical. However, the MACD class manages state atomically (previous state rollback). Sharing breaks independent bar correction.
A: The Fibonacci period structure (8, 34, 55, 89, 144, 233, 377) is the design itself, not a tunable choice. Changing the periods would produce a different indicator, not a different configuration of TTM Wave. Carter designed these specific ratios to capture momentum at Fibonacci-harmonic timescales.
**Q: Why does Last return WaveA2 instead of an aggregate?**
A: TOS convention. The primary `Wave1` plot on thinkorswim is the channel 1 (8, 34, 34) histogram, which corresponds to `WaveA2`. All six wave outputs are available as separate properties for multi-wave analysis.
A: Look for alignment. When all six histograms share the same sign, momentum is unanimous across timescales. When A waves flip while C waves persist, it is a pullback, not a reversal. Sequential ignition (A fires, then B, then C) confirms a developing trend.
