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# Session-Anchored Kaufman's Adaptive Moving Average (AKAMA) Bands Pro (v2.00)
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Quantitative Session-Anchored Volatility & Statistical Dispersion Envelope Suite
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---
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## 1. Summary (Introduction)
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**KAMA Anchored Bands Pro (AKAMA Bands)** is an innovative quantitative envelope indicator that unifies periodic session anchoring with **Perry Kaufman's Adaptive Moving Average** and cumulative **Standard Deviation ($\sigma$) Volatility Bands**.
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While traditional Anchored VWAP (AVWAP) measures volume-weighted average price from an anchor point, **Anchored KAMA (AKAMA) measures directional-efficiency-weighted price dynamics**. It eliminates the overnight low-liquidity noise carryover by resetting its calculation at a user-defined market boundary (such as the **London Stock Exchange (LSE) Open**, **Frankfurt Open**, **New York Cash Open**, or Weekly/Monthly anchors).
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ AKAMA BANDS ARCHITECTURE │
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├────────────────────────────────────────────────────────────────────────┤
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│ Upper Band 3: AKAMA(t) + [3.0 × σ(t)] (Extreme Climax Ceiling) │
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│ Upper Band 2: AKAMA(t) + [2.0 × σ(t)] (Value Area High) │
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│ Upper Band 1: AKAMA(t) + [1.0 × σ(t)] (Dynamic Resistance) │
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│ Centerline: Session-Anchored KAMA (Adaptive Equilibrium) │
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│ Lower Band 1: AKAMA(t) - [1.0 × σ(t)] (Dynamic Support) │
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│ Lower Band 2: AKAMA(t) - [2.0 × σ(t)] (Value Area Low) │
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│ Lower Band 3: AKAMA(t) - [3.0 × σ(t)] (Extreme Climax Floor) │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### Key Capabilities
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* **Periodic & Custom Session Anchoring:** Automatically resets and seeds calculation at Daily Session Open, Weekly Open, Monthly Open, or Custom Institutional Windows (e.g., LSE `08:00 - 16:30`, London/NY Overlap `13:30 - 17:00`).
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* **Intra-Session Efficiency Adaptation:** The KAMA centerline adapts exclusively to price action within the active session, preventing pre-market noise from polluting regular trading hours (RTH).
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* **Anchored Standard Deviation Envelopes:** Projects running statistical dispersion bands ($\pm 1\sigma, \pm 2\sigma, \pm 3\sigma$) accumulated from the exact session anchor bar.
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* **Gapped Odd/Even Line Architecture:** Uses dual alternating buffers (`BufKAMA_Odd`, `BufKAMA_Even`) to eliminate diagonal connecting lines across session resets.
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* **2026 MTF Framework with DataSync Daemon:** Enables higher-timeframe session bands (e.g., M15 or H1 AKAMA Bands) to be mapped onto lower-timeframe execution charts (M1, M5) with flat, non-warping steps.
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---
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## 2. Mathematical Foundations
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```text
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Anchor Bar (Session Open: σ = 0.0)
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│
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├───► Upper Band 3: AKAMA + 3σ (Reversal Exhaustion)
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├───► Upper Band 2: AKAMA + 2σ (Value Area High)
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├───► Upper Band 1: AKAMA + 1σ
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├───► Centerline: AKAMA (Efficiency-Weighted Adaptive Mean)
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├───► Lower Band 1: AKAMA - 1σ
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├───► Lower Band 2: AKAMA - 2σ (Value Area Low)
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└───► Lower Band 3: AKAMA - 3σ (Reversal Exhaustion)
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```
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### 2.1. Anchor Reset & Local Efficiency Ratio
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At each anchor boundary ($t = \text{Anchor Bar}$), the filter re-seeds from the opening price:
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$$\text{AKAMA}_{\text{anchor}} = P_{\text{anchor}}$$
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For any subsequent bar $t$ within the active session ($k_t = t - \text{Anchor Bar}$):
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$$N_{\text{eff}} = \min(k_t, N_{\text{ER}})$$
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$$\text{Direction}_t = | P_t - P_{t - N_{\text{eff}}} |$$
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$$\text{Volatility}_t = \sum_{j=0}^{N_{\text{eff}}-1} | P_{t-j} - P_{t-j-1} |$$
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$$\text{ER}_t = \begin{cases} \frac{\text{Direction}_t}{\text{Volatility}_t}, & \text{if } \text{Volatility}_t > 0 \\ 0.0, & \text{otherwise} \end{cases}$$
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The dynamic smoothing constant is applied recursively from the anchor point:
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$$\text{SC}_t = \left[ \text{ER}_t \cdot (\alpha_{\text{fast}} - \alpha_{\text{slow}}) + \alpha_{\text{slow}} \right]^2$$
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$$\text{AKAMA}_t = \text{AKAMA}_{t-1} + \text{SC}_t \cdot (P_t - \text{AKAMA}_{t-1})$$
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---
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### 2.2. Cumulative Intra-Session Standard Deviation ($\sigma_t$)
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Standard deviation is calculated by accumulating the squared deviations of price relative to the dynamic AKAMA line strictly within the session:
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$$\text{Variance}_t = \frac{1}{k_t + 1} \sum_{j=\text{Anchor Bar}}^{t} \left( P_j - \text{AKAMA}_j \right)^2$$
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$$\sigma_t = \sqrt{\text{Variance}_t}$$
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### 2.3. Volatility Band Multipliers
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$$\text{Upper Band } n_t = \text{AKAMA}_t + (M_n \cdot \sigma_t)$$
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$$\text{Lower Band } n_t = \text{AKAMA}_t - (M_n \cdot \sigma_t)$$
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*where $M_1 = \text{InpBand1Mult}$ (default: $1.0$), $M_2 = \text{InpBand2Mult}$ (default: $2.0$), and $M_3 = \text{InpBand3Mult}$ (default: $3.0$).*
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---
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## 3. MQL5 Architecture & Engineering Standards
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```text
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┌────────────────────────────────────────────────────────┐
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│ KAMA_Anchored_Calculator.mqh │
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│ (Core Engine: Stateless Anchor & Local KAMA Engine) │
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs AKAMA Odd/Even & Price Series (O(1))
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▼
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┌────────────────────────────────────────────────────────┐
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│ KAMA_Anchored_Bands_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Buffer Layer (8) │ MTF & Session Management │
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│ • 2 Centerline Plots │ • DataSync_Tools.mqh │
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│ • 6 Volatility Bands │ • Staircase Flat-Force │
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│ • Current Session Mask │ • Odd/Even Gapped Engine │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **Stateless Deterministic Engine:** `CKamaAnchoredCalculator` processes session transitions deterministically, eliminating static variable corruption during real-time tick recalculations.
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2. **Session Lifetime & Active Retention:** The indicator identifies the active or most recently completed session and maintains its bands continuously, ensuring the session range remains visible during post-session hours until the next session opens.
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3. **2026 MTF Framework with Staircase Solution:** Higher-timeframe session bands map into flat, synchronized steps on lower-timeframe charts via `first_bar_of_forming_htf` anchoring and `DataSync_Tools.mqh`.
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---
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## 4. Parameters Reference
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### Timeframe Settings
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* `InpTimeframe` (*default: `PERIOD_CURRENT`*): Calculation timeframe. When set to `PERIOD_CURRENT`, it runs in native zero-lag mode. When set to a higher timeframe (e.g., `PERIOD_M15`, `PERIOD_H1`), it activates the synchronized MTF engine.
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### Anchor Settings
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* `InpResetPeriod` (*default: `ANCHOR_PERIOD_SESSION`*): Anchor mode (`ANCHOR_PERIOD_SESSION`, `ANCHOR_PERIOD_WEEK`, `ANCHOR_PERIOD_MONTH`, `ANCHOR_PERIOD_CUSTOM_SESSION`).
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* `InpTzShift` (*default: `0`*): Timezone offset in hours to align midnight resets with broker server time.
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* `InpCustomStart` (*default: `"08:00"`*): Session start time (`HH:MM`) when using `ANCHOR_PERIOD_CUSTOM_SESSION` (e.g., LSE Open).
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* `InpCustomEnd` (*default: `"17:00"`*): Session end time (`HH:MM`) when using `ANCHOR_PERIOD_CUSTOM_SESSION` (e.g., LSE Close).
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### KAMA Core Settings
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* `InpErPeriod` (*default: `10`*): Lookback period ($N$) for the KAMA Efficiency Ratio.
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* `InpFastEmaPeriod` (*default: `2`*): Fastest smoothing period ($F$) during high directional efficiency.
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* `InpSlowEmaPeriod` (*default: `30`*): Slowest smoothing period ($S$) during low efficiency.
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* `InpSourcePrice` (*default: `PRICE_CLOSE_STD`*): Applied price source (Standard OHLC or Synthetic Heikin Ashi).
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### Standard Deviation Bands Settings
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* `InpBand1Mult` (*default: `1.0`*): Multiplier for Band 1 ($\pm 1.0\sigma$).
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* `InpBand2Mult` (*default: `2.0`*): Multiplier for Band 2 ($\pm 2.0\sigma$).
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* `InpBand3Mult` (*default: `3.0`*): Multiplier for Band 3 ($\pm 3.0\sigma$).
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* `InpCurrentSessionOnly` (*default: `true`*): When enabled, purges historical session bands to keep the chart clean and focused on the active session.
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### Visual Settings
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* Full independent customization for centerline color, style, and width, as well as distinct colors for Band 1, Band 2, and Band 3.
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---
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## 5. Institutional Trading Playbooks (LSE & Session Ranges)
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ LSE & INSTITUTIONAL SESSION PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. LSE Open Breakout: Enter in direction of candle close outside +1σ │
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│ when AKAMA slope accelerates at 08:00 London. │
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│ 2. Value Area Fade: When AKAMA is flat during midday, fade rejections│
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│ at +2σ / -2σ back toward the AKAMA centerline. │
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│ 3. Climax Exhaustion: Spikes into ±3σ indicate unsustainable momentum. │
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│ Look for mean-reversion reversal entries. │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The London Opening Range Breakout (LSE ORB)
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* **Configuration:** Set `InpResetPeriod = ANCHOR_PERIOD_CUSTOM_SESSION`, `InpCustomStart = "08:00"`, `InpCustomEnd = "16:30"`.
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* **Execution:** At the 08:00 London open, watch the expansion of the AKAMA centerline. A strong candle break beyond `Upper Band 1 (+1.0σ)` with an accelerating AKAMA confirms that European institutional capital is driving a directional trend.
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### 5.2. Session Value Area Mean Reversion
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* **Context:** During midday trading (e.g., 11:30 - 13:30 London time), the AKAMA centerline flattens into horizontal equilibrium.
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* **Short Trigger:** Price tests `Upper Band 2 (+2.0σ)` and forms a rejection candle $\rightarrow$ Target: AKAMA Centerline.
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* **Long Trigger:** Price tests `Lower Band 2 (-2.0σ)` and forms a rejection candle $\rightarrow$ Target: AKAMA Centerline.
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### 5.3. Statistical Climax Reversal ($\pm 3.0\sigma$)
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* Price touching or exceeding `Band 3 (±3.0σ)` represents a 3-standard-deviation tail event for the active session ($99.7\%$ Gaussian probability threshold).
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* When a $3.0\sigma$ extension coincides with exhaustion on `KAMA_Acceleration_Pro`, it signals an institutional blow-off top or panic flush, offering high-reward counter-trend reversal opportunities.
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---
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## 6. Indicator Buffer Map (For Developers & EA Integration)
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| Buffer Index | Name | Type | Description |
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| :---: | :---: | :---: | :--- |
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| **0** | `BufKAMA_Odd` | `INDICATOR_DATA` | Anchored KAMA Centerline (Odd Periods) |
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| **1** | `BufKAMA_Even` | `INDICATOR_DATA` | Anchored KAMA Centerline (Even Periods - Gapped) |
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| **2** | `BufUp1` | `INDICATOR_DATA` | Upper Volatility Band 1 ($+1.0\sigma$) |
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| **3** | `BufDn1` | `INDICATOR_DATA` | Lower Volatility Band 1 ($-1.0\sigma$) |
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| **4** | `BufUp2` | `INDICATOR_DATA` | Upper Volatility Band 2 ($+2.0\sigma$) |
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| **5** | `BufDn2` | `INDICATOR_DATA` | Lower Volatility Band 2 ($-2.0\sigma$) |
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| **6** | `BufUp3` | `INDICATOR_DATA` | Upper Volatility Band 3 ($+3.0\sigma$) |
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| **7** | `BufDn3` | `INDICATOR_DATA` | Lower Volatility Band 3 ($-3.0\sigma$) |
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring instant compatibility with Expert Advisors and scanner dashboards via `iCustom()`.*
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