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Miha Kralj
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- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
117 lines
5.0 KiB
Markdown
117 lines
5.0 KiB
Markdown
# IMI: Intraday Momentum Index
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The Intraday Momentum Index measures buying and selling pressure using the open-to-close relationship within each bar, rather than the close-to-close changes used by RSI. Each bar is classified as a gain (close > open) or loss (close < open), with the magnitude being the absolute open-close difference. Rolling sums of gains and losses over the lookback period produce an RSI-like ratio scaled to 0-100. This bridges Japanese candlestick analysis with Western oscillator theory: bullish candles contribute to the gain sum, bearish candles contribute to the loss sum. Unlike RSI, IMI does not require a previous close and uses simple rolling sums rather than exponential smoothing, making it more responsive but noisier. Output is bounded 0-100 with conventional overbought (>70) and oversold (<30) zones.
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## Historical Context
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Tushar Chande introduced the Intraday Momentum Index in *The New Technical Trader* (1994), alongside innovations like the Chande Momentum Oscillator. 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 measures a fundamentally different quantity: the directional conviction *within* each bar rather than the change *between* bars. On daily charts, the open-close relationship has clear meaning — it captures overnight positioning gaps plus session direction. The indicator is self-contained within each bar, requiring no previous bar's close, which makes it particularly clean for session-based analysis. The formula structure deliberately mirrors RSI (sum of gains over total) to provide familiar overbought/oversold levels while measuring intra-session momentum.
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## Architecture & Physics
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### 1. Gain/Loss Classification
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Each bar is classified based on the open-close relationship:
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$$G_t = \begin{cases} C_t - O_t & \text{if } C_t > O_t \\ 0 & \text{otherwise} \end{cases}$$
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$$L_t = \begin{cases} O_t - C_t & \text{if } C_t < O_t \\ 0 & \text{otherwise} \end{cases}$$
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Doji bars ($C = O$) contribute zero to both sums.
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### 2. Rolling Sums
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Simple rolling sums over the lookback window (no exponential smoothing):
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$$\text{SumGains}_t = \sum_{i=t-N+1}^{t} G_i$$
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$$\text{SumLosses}_t = \sum_{i=t-N+1}^{t} L_i$$
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Implemented with ring buffers and incremental add/subtract for $O(1)$ per bar.
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### 3. IMI Value
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$$\text{IMI}_t = 100 \times \frac{\text{SumGains}_t}{\text{SumGains}_t + \text{SumLosses}_t}$$
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When both sums are zero (all doji bars in window), IMI defaults to 50.0 (neutral).
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### 4. Complexity
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- **Time:** $O(1)$ per bar — rolling sum add/subtract
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- **Space:** $O(N)$ — two ring buffers for gain and loss history
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- **Warmup:** $N$ bars
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## Mathematical Foundation
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### Parameters
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| Symbol | Parameter | Default | Constraint |
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|--------|-----------|---------|------------|
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| $N$ | period | 14 | $N \geq 1$ |
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### Pseudo-code
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```
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Initialize:
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gainBuf = RingBuffer(period)
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lossBuf = RingBuffer(period)
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gainSum = lossSum = 0
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bar_count = 0
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On each bar (open, close, isNew):
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if !isNew: restore previous state
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// Classify bar
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diff = close - open
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gain = diff > 0 ? diff : 0
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loss = diff < 0 ? -diff : 0
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// Update rolling sums
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if gainBuf is full:
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gainSum -= gainBuf.Oldest
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lossSum -= lossBuf.Oldest
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gainBuf.Add(gain)
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lossBuf.Add(loss)
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gainSum += gain
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lossSum += loss
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// IMI calculation
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total = gainSum + lossSum
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IMI = total > 0 ? 100 × gainSum / total : 50.0
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output = IMI
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```
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### IMI vs RSI Comparison
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| Property | RSI | IMI |
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|----------|-----|-----|
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| Input | Close-to-close change | Open-to-close change |
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| Measures | Inter-session momentum | Intra-session momentum |
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| Smoothing | Wilder's RMA (exponential) | Simple rolling sum |
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| Previous bar | Required ($C_{t-1}$) | Not required (self-contained) |
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| Response | Smoother, more lag | More responsive, noisier |
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| Range | 0-100 | 0-100 |
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### Interpretation
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| IMI Value | Meaning |
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|-----------|---------|
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| > 70 | Overbought — strong bullish intra-session pressure |
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| < 30 | Oversold — strong bearish intra-session pressure |
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| 50 | Neutral — balanced buying/selling within bars |
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| Rising toward 70 | Increasing proportion of bullish candles |
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| Falling toward 30 | Increasing proportion of bearish candles |
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### Timeframe Sensitivity
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On daily charts, the open-close relationship captures overnight gaps plus session direction — the most informative timeframe for IMI. On very short intraday charts (1-minute), the open-close relationship carries less structural information since the open price has minimal gap significance. Choose timeframes where the opening price carries genuine information about session sentiment.
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### OHLC Requirement
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IMI requires both Open and Close prices per bar. It implements `ITValuePublisher` directly rather than `AbstractBase` since it operates on `TBar` (OHLC) input, not single `TValue` input.
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## Resources
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- Chande, T.S. & Kroll, S. — *The New Technical Trader* (John Wiley & Sons, 1994)
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- PineScript reference: `imi.pine` in indicator directory
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