QuanTAlib/lib/oscillators/rsih/Rsih.md

RSIH: Ehlers Hann-Windowed RSI

By replacing Wilder's exponential smoothing with a Hann window, Ehlers produces an RSI that is zero-mean, bounded, and inherently smooth—no supplemental filtering required.

Property	Value
Category	Oscillator
Inputs	Source (close)
Parameters	period (default 14)
Outputs	Single series (Rsih)
Output range	[-1, +1]
Zero mean	Yes
Warmup	period + 1 bars
PineScript	rsih.pine

• RSIH (Hann-Windowed RSI) is a zero-mean relative strength oscillator that uses Hann window coefficients to weight price differences, producing a bounded [-1, +1] output with inherent smoothing.
• Similar: RSI, LRSI, RRSI | Complementary: Moving averages for trend confirmation | Trading note: Zero crossings signal direction changes; ±0.5 levels indicate strong momentum.
• No external validation libraries implement RSIH. Validated through self-consistency and behavioral testing.

RSIH applies Hann window weighting to consecutive price differences, computes separate weighted sums of up-moves (CU) and down-moves (CD), then normalizes as (CU - CD) / (CU + CD). The Hann window provides inherent smoothing that eliminates the need for supplemental filtering, while the normalization produces a zero-mean output bounded to [-1, +1].

Historical Context

The Hann-Windowed RSI was published by John F. Ehlers in the January 2022 issue of Technical Analysis of Stocks & Commodities magazine under the title "(Yet Another) Improved RSI." Ehlers observed that classic RSI suffers from two fundamental issues: (1) Wilder's exponential smoothing introduces lag and spectral leakage, and (2) the 0–100 output range obscures the zero-mean nature of momentum. By replacing the smoothing with a Hann window FIR filter and using a symmetric [-1, +1] normalization, Ehlers created an RSI variant that is both mathematically cleaner and practically more responsive.

Architecture & Physics

RSIH operates as a single-stage FIR filter:

Hann Window Coefficients

The weighting function is precomputed in the constructor:

w(k) = 1 - \cos\left(\frac{2\pi k}{N + 1}\right) \quad \text{for } k = 1, 2, \ldots, N

where N is the period. Note: Ehlers uses (N + 1) in the denominator, not the standard symmetric Hann formula (N - 1).

Weighted CU/CD Accumulation

For each bar, consecutive price differences are weighted by the Hann coefficients:

\text{CU} = \sum_{k=1}^{N} w(k) \cdot \max(\text{Close}_{t-k+1} - \text{Close}_{t-k}, \; 0) \text{CD} = \sum_{k=1}^{N} w(k) \cdot \max(\text{Close}_{t-k} - \text{Close}_{t-k+1}, \; 0)

Normalization

\text{RSIH}_t = \frac{\text{CU} - \text{CD}}{\text{CU} + \text{CD}}

When \text{CU} + \text{CD} = 0 (flat market), RSIH returns 0.

Implemented with FMA for the coefficient multiplication:

cu = Math.FusedMultiplyAdd(w, diff, cu);

Performance Profile

RSIH is an O(N) FIR filter — each bar requires scanning the full window.

Operation Count (Streaming Mode, Scalar)

Operation	Count	Cost (cycles)	Subtotal
Hann Window Scan
SUB (newer - older)	N	1	N
CMP (diff > 0, diff < 0)	N	1	N
FMA (w × diff + acc)	N	4	4N
Normalization
ADD (CU + CD)	1	1	1
SUB (CU - CD)	1	1	1
DIV (ratio)	1	15	15
Total			~6N + 17 cycles

For default N=14: ~101 cycles per bar.

Dominant cost: FMA loop (4N cycles, ~67%)

Batch Mode (SIMD Analysis)

RSIH is not SIMD-parallelizable across bars because each bar's window overlaps with adjacent bars. However, the inner loop (coefficient × difference accumulation) could potentially benefit from SIMD vectorization within a single bar's computation.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	Hann window provides excellent spectral properties
Timeliness	8/10	FIR filter with minimal lag for oscillator class
Overshoot	9/10	Bounded [-1, +1] — no possibility of divergence
Smoothness	8/10	Hann window provides inherent anti-aliasing

Validation

RSIH is not implemented in mainstream libraries. Validation relies on behavioral testing.

Library	Status	Notes
TA-Lib	N/A	Not implemented
Skender	N/A	Not implemented
Tulip	N/A	Not implemented
Ooples	N/A	Not implemented
Behavioral	✅	Validated: constant→zero, symmetry, mode consistency

Behavioral Test Summary

• Constant Input → Zero: Constant close → all diffs = 0 → CU = CD = 0 → RSIH = 0
• Output Symmetry: RSIH(ascending) = -RSIH(descending) — output is antisymmetric
• Bounded Output: All outputs in [-1, +1] regardless of input magnitude
• Mode Consistency: Streaming, batch, span, and event-driven modes produce identical results
• Bar Correction: Snapshot/Restore via RingBuffer produces exact rollback

Common Pitfalls

1. Warmup Period: RSIH requires Period + 1 bars to fill the close buffer for Period differences. Use IsHot to detect readiness.

2. Hann Window Denominator: Ehlers uses (period + 1) in the Hann formula, NOT the standard symmetric (period - 1). Using the wrong denominator will produce incorrect coefficients.

3. Zero-Mean Output: Unlike classic RSI (0–100), RSIH oscillates around zero with range [-1, +1]. Overbought/oversold levels should be set around ±0.5, not 70/30.

4. FIR Complexity: RSIH is O(N) per bar, not O(1) like IIR indicators. For very large periods, this may impact performance in high-frequency applications.

5. Flat Market Edge Case: When all prices in the window are identical, CU + CD = 0. The implementation returns 0.0 in this case (using an epsilon floor of 1e-10).

6. Period Selection: Ehlers recommends using the dominant cycle period (not half-cycle like classic RSI). Default period of 14 works well for daily charts.

7. Bar Correction: Like all QuanTAlib indicators, RSIH supports bar correction via the isNew parameter. The RingBuffer Snapshot()/Restore() mechanism handles this atomically.