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WaveTrend

Incremental, causal technical analysis documentation

Summary

WaveTrend is RTTA's streaming LazyBear WaveTrend oscillator: a double-smoothed channel index of HLC3 that produces wt1 / wt2 lines for overbought/oversold and cross signals.

Update API

result = rtta.WaveTrend(
    channel_length=10, average_length=21, signal_length=4, fillna=True,
).update(high, low, close)
Parameter Default Meaning
channel_length 10 EMA length for ESA and absolute deviation
average_length 21 EMA length for WT1
signal_length 4 SMA length for WT2 signal
fillna True If False, NaN until combined warm-up

update(high, low, close) returns wt1, wt2. advance(...) updates state; last() returns the cached result.

Theory Of Operation

WaveTrend is closely related to a commodity channel index on typical price, with extra exponential smoothing:

  1. Typical price \(ap = (h+l+c)/3\).
  2. ESA: EMA of \(ap\).
  3. Mean absolute deviation of \(ap\) from ESA, also EMA-smoothed.
  4. Channel index \(ci = (ap - esa)/(0.015\cdot d)\).
  5. WT1: EMA of \(ci\); WT2: SMA of WT1 (default 4).

Crosses of WT1 through WT2, and extreme levels (commonly near ±60 / ±53 in LazyBear charts), are used for mean-reversion and momentum timing. The constant 0.015 matches the LazyBear / TradingView reference scaling.

Recurrence

\[ap_t = \frac{h_t + l_t + c_t}{3}\]
\[esa_t = \operatorname{EMA}_{n_1}(ap_t)\]
\[d_t = \operatorname{EMA}_{n_1}\big(|ap_t - esa_t|\big)\]
\[ci_t = \frac{ap_t - esa_t}{0.015\, d_t}\]

(safe division when \(d_t=0\)).

\[wt1_t = \operatorname{EMA}_{n_2}(ci_t)\]
\[wt2_t = \operatorname{SMA}_{n_s}(wt1_t)\]

Defaults: \(n_1=10\), \(n_2=21\), \(n_s=4\).

When fillna=False, require \(n_1 + n_2 + n_s\) samples before non-NaN results (conservative warm-up matching the C++ warm_ sum).

Implementation Notes

Reference