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RelativeVolatilityIndex

Incremental, causal technical analysis documentation

Summary

RelativeVolatilityIndex is RTTA's streaming Donald Dorsey Relative Volatility Index (RVI). It applies RSI-style smoothing to upward and downward standard deviation of close, and also emits an EMA signal line of the RVI.

Update API

result = rtta.RelativeVolatilityIndex(
    std_window=10, smooth_window=14, fillna=True
).update(close)
# result.rvi, result.signal

With fillna=False, both fields are NaN until std_window + smooth_window samples have been seen.

Theory Of Operation

Dorsey's RVI looks like RSI but replaces price change with rolling standard deviation of close, assigned to the up side when close rises and the down side when close falls. The result measures the direction of volatility rather than the direction of price: high RVI means volatility is occurring more on up moves; low RVI means more on down moves. RTTA also smooths RVI with a same-length EMA as a signal line.

Recurrence

Let \(c_t\) be close, \(n_s\) be std_window (default \(10\)), and \(n_e\) be smooth_window (default \(14\)).

\[\sigma_t = \operatorname{StdDev}_{n_s}(c_t)\]

Assign volatility to up/down sides (first bar contributes zeros):

\[(u_t, d_t) = \begin{cases} (\sigma_t,\, 0), & c_t > c_{t-1} \\ (0,\, \sigma_t), & c_t < c_{t-1} \\ (0.5\,\sigma_t,\, 0.5\,\sigma_t), & c_t = c_{t-1} \end{cases}\]
\[U_t = \operatorname{EMA}_{n_e}(u_t), \qquad D_t = \operatorname{EMA}_{n_e}(d_t)\]
\[RVI_t = 100 \cdot \frac{U_t}{U_t + D_t} \quad\text{(safe divide)}\]
\[\operatorname{signal}_t = \operatorname{EMA}_{n_e}(RVI_t)\]

Nested StdDev and EMAs use fillna=True. Outer warm count is \(n_s + n_e\).

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class RelativeVolatilityIndex with members std_, up_, down_, and signal_. Result fields are rvi and signal. See also Inertia, which regresses RVI.

Reference