QuanTAlib/lib/dynamics/imi/Imi.md

IMI: Intraday Momentum Index

"RSI measures close-to-close momentum. IMI measures open-to-close momentum. One tracks what happened between sessions; the other tracks what happened inside them."

IMI (Intraday Momentum Index), developed by Tushar Chande, combines candlestick analysis with RSI-like overbought/oversold signals. Unlike RSI, which uses close-to-close price changes, IMI measures the relationship between each bar's open and close prices. This makes it particularly effective for detecting intraday buying/selling pressure and candlestick pattern strength. The result oscillates between 0 and 100, with readings above 70 indicating overbought conditions and below 30 indicating oversold.

Historical Context

Tushar Chande introduced the Intraday Momentum Index in "The New Technical Trader" (1994), alongside other innovations like the Chande Momentum Oscillator (CMO). Chande observed that traditional momentum indicators like RSI ignored the intraday price action captured by candlestick patterns. By using the open-close relationship instead of close-close changes, IMI bridges the gap between Japanese candlestick analysis and Western oscillator theory.

The indicator is particularly useful on daily charts where the open-close relationship has clear meaning (overnight gap vs session direction). On intraday timeframes, its interpretation shifts to measuring buying pressure within each bar. Unlike RSI, IMI does not require a previous close, making it self-contained within each bar.

The formula structure mirrors RSI: sum of gains over sum of gains plus losses, scaled to 0-100. This provides familiar overbought/oversold levels while measuring a fundamentally different quantity.

Architecture & Physics

1. Gain/Loss Classification

Each bar is classified based on the open-close relationship:

\text{Gain}_t = \begin{cases} \text{Close}_t - \text{Open}_t & \text{if Close} > \text{Open} \\ 0 & \text{otherwise} \end{cases}

\text{Loss}_t = \begin{cases} \text{Open}_t - \text{Close}_t & \text{if Close} < \text{Open} \\ 0 & \text{otherwise} \end{cases}

2. Rolling Sum Calculation

The indicator uses O(1) rolling sums via ring buffers:

\text{SumGains}_t = \sum_{i=t-n+1}^{t} \text{Gain}_i

\text{SumLosses}_t = \sum_{i=t-n+1}^{t} \text{Loss}_i

3. IMI Value

\text{IMI}_t = 100 \times \frac{\text{SumGains}_t}{\text{SumGains}_t + \text{SumLosses}_t}

When both sums are zero (flat bars only), IMI defaults to 50.0 (neutral).

4. State Management

The indicator implements ITValuePublisher directly (not AbstractBase) because it requires TBar input (OHLC data). Rolling sums (_gainSum, _lossSum) are saved/restored for bar correction via _savedGainSum / _savedLossSum.

Mathematical Foundation

Core Formula

\text{IMI} = 100 \times \frac{\sum_{i=1}^{n} G_i}{\sum_{i=1}^{n} G_i + \sum_{i=1}^{n} L_i}

where:

• G_i = \max(C_i - O_i, 0) (gain on bullish bars)
• L_i = \max(O_i - C_i, 0) (loss on bearish bars)
• n = lookback period (default 14)

Key Levels

Level	Interpretation
> 70	Overbought: strong bullish intraday pressure
< 30	Oversold: strong bearish intraday pressure
50	Neutral: balanced buying/selling pressure

Comparison with RSI

Property	RSI	IMI
Input	Close-to-close change	Open-to-close change
Measures	Inter-session momentum	Intra-session momentum
Requires previous bar	Yes	No (self-contained)
Smoothing	Wilder's smoothing (EMA)	Simple sum (no smoothing)
Range	0-100	0-100
Default period	14	14

Default Parameters

Parameter	Default	Purpose
period	14	Lookback window for gain/loss sums

Warmup

\text{WarmupPeriod} = \text{period}

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Notes
SUB	1	close - open
CMP	1	classify gain vs loss
ADD/SUB	2	rolling sum update
DIV	1	IMI ratio
MUL	1	scale to 100
Total	~6 ops	O(1) per bar

Batch Mode

Operation	Complexity	Notes
Per-element	O(1)	Rolling sum, no re-scan
Total	O(n)	Linear scan
Memory	O(period)	Two ring buffers

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact arithmetic, no approximation
Timeliness	8/10	No smoothing lag beyond window
Smoothness	5/10	Can be choppy in ranging markets
Simplicity	8/10	Straightforward gain/loss ratio

Validation

Library	Status	Notes
Skender	✅	Matches within tolerance
TA-Lib	N/A	No IMI function
Tulip	N/A	No IMI function
Ooples	✅	Matches within tolerance
CQG	✅	Reference implementation matches

Common Pitfalls

1. TBar input required: IMI needs Open and Close prices. Passing single values (TValue) is not supported. The indicator implements ITValuePublisher directly, not AbstractBase.

2. Doji bars: When Open equals Close, both Gain and Loss are zero. These bars contribute nothing to either sum but still age out of the window.

3. All-zero edge case: If all bars in the window are Dojis, both sums are zero. The implementation returns 50.0 (neutral) to avoid division by zero.

4. Not smoothed: Unlike RSI, which uses Wilder's smoothing (exponential), IMI uses simple sums. This makes it more responsive but also noisier.

5. Timeframe sensitivity: On daily charts, open-close captures overnight gaps plus session direction. On 1-minute charts, the open-close relationship is less meaningful. Choose timeframes where the open price carries information.

6. NaN handling: Non-finite Open or Close values cause the bar to be skipped, preserving the last valid IMI value.

References

• Chande, T. S., & Kroll, S. (1994). "The New Technical Trader." Wiley.
• Investopedia: "Intraday Momentum Index (IMI) Definition."
• CQG: "Intraday Momentum Index (IMI)" Technical Reference.