Wilder Swing Index (SI)

Summary

Wilder's Swing Index: one number rating each bar against the bar before it, from both bars' open and close and the current bar's high and low, signed by the direction of the swing. A strong close above the prior close on a wide range reads high and positive, a strong down swing reads high and negative. It is scaled against the limit move, the largest one-bar move the market allows, and stays between -100 and +100 while every move is within that limit. J. Welles Wilder Jr. introduced it in 1978 and trades its running total, ASI.

Formula

\mathrm{SI}_t = 50 \cdot \frac{N_t}{R_t} \cdot \frac{K_t}{T}, \text{ or } 0 \text{ when } R_t = 0

N_t = (C_t - C_{t-1}) + \tfrac{1}{2}(C_t - O_t) + \tfrac{1}{4}(C_{t-1} - O_{t-1}) \qquad K_t = \max(a, b)

R_t = \begin{cases} a - \tfrac{1}{2}b + q & \text{if } a \ge b \text{ and } a \ge d \\ b - \tfrac{1}{2}a + q & \text{else if } b \ge d \\ d + q & \text{otherwise} \end{cases}

where $a = |H_t - C_{t-1}|$ , $b = |L_t - C_{t-1}|$ , $d = |H_t - L_t|$ , $q = \tfrac{1}{4}|C_{t-1} - O_{t-1}|$ , and $T$ is optInLimitMove (Wilder writes it $L$ ).

Notes

Wilder rounds each value to a whole number when working by hand; the output is not rounded.
A bar that moves more than the limit move can read beyond -100 or +100; the output is not clamped.

Inputs

inOpen — Open price of each bar
inHigh — High price of each bar
inLow — Low price of each bar
inClose — Close price of each bar

Outputs

outReal — Swing index of the bar against the previous bar

Parameters

Parameter	Type	Default	Accepted values	Description
`optInLimitMove`	real	3	≥ 0.00000001	Limit move, the largest one-bar price move the index is scaled against, in price units

Properties

Numerical Stability: Start-Independent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: si.c · si.yaml

Native	File
C	`ta_SI.c`
Rust	`si.rs`
Java	`Core_SI.java`
C#	`Core_SI.cs`

TA-Lib is also available for Python, R and more using a wrapper.

References

J. Welles Wilder Jr., New Concepts in Technical Trading Systems, Trend Research, 1978, section VIII "The Swing Index", pp.87-106