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# Session-Anchored Kaufman's Adaptive Z-Score (AK-Score) Pro (v1.00)
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Quantitative Session-Anchored Statistical Dispersion & Elasticity Oscillator
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---
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## 1. Summary (Introduction)
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**KScore Anchored Pro (AK-Score Pro)** is an institutional-grade statistical momentum oscillator that measures intra-session price deviation from **Session-Anchored Kaufman's Adaptive Moving Average (AKAMA)** normalized in units of cumulative session standard deviation ($\sigma$).
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While traditional rolling Z-Score indicators compute standard deviation across a fixed lookback window that inadvertently blends overnight low-volume drift with regular market hours, **AK-Score calculates dispersion strictly accumulated from the session anchor point**:
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* **At Session Open (Anchor Bar):** AK-Score is initialized to $0.0\sigma$ (Neutral Gray), establishing an unpolluted baseline at market opens (such as the **London Stock Exchange (LSE)**, **Frankfurt**, or **New York Cash Open**).
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* **During Session Expansion:** As institutional volume drives price away from the anchored mean, AK-Score measures whether the momentum is a healthy intra-session expansion ($+1.0\sigma \dots +1.5\sigma$) or has stretched into an unsustainable statistical climax ($> +2.0\sigma \dots +2.5\sigma$).
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* **During Post-Session Hours:** When used with `ANCHOR_PERIOD_CUSTOM_SESSION`, the indicator cleanly disconnects during off-hours, ensuring that only valid institutional trading windows are evaluated.
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ AK-SCORE DISPERSION MODEL │
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├────────────────────────────────────────────────────────────────────────┤
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│ AK-Score(t) = [ Price(t) - AKAMA(t) ] / IntraSession_StdDev(t) │
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│ Expressed in session-relative Standard Deviation multiples (σ) │
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└────────────────────────────────────────────────────────────────────────┘
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```
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---
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## 2. Mathematical Foundations & Kinetic Dynamics
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```text
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+2.5σ (Extreme Session Climax)
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───────────────────────────────────────────────────────────── DeepSkyBlue (Bull Climax)
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+1.5σ (Bullish Flow Threshold)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - LightSkyBlue (Bull Flow)
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0.0σ (Session Anchor / AKAMA Baseline)
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───────────────────────────────────────────────────────────── Gray (Noise / Equilibrium)
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-1.5σ (Bearish Flow Threshold)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Coral (Bear Flow)
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-2.5σ (Extreme Session Climax)
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───────────────────────────────────────────────────────────── OrangeRed (Bear Climax)
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```
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### 2.1. Anchor Reset & Intra-Session Lookback Expansion
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At each session boundary bar ($t = \text{Anchor Bar}$), AKAMA initializes directly from the opening price:
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$$\text{AKAMA}_{\text{anchor}} = P_{\text{anchor}}$$
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For any subsequent bar 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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$$\text{ER}_t = \frac{\text{Direction}_t}{\text{Volatility}_t}$$
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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 ($\sigma_{\text{session}, t}$)
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Standard deviation is calculated by accumulating the squared deviations of price relative to the evolving 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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$$\sigma_{\text{session}, t} = \sqrt{\text{Variance}_t}$$
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### 2.3. Standardized AK-Score Formulation
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$$AK\text{Score}_t = \begin{cases} \frac{P_t - \text{AKAMA}_t}{\sigma_{\text{session}, t}}, & \text{if } \sigma_{\text{session}, t} > 10^{-9} \\ 0.0, & \text{at anchor bar } (k_t = 0) \end{cases}$$
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---
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### 2.4. Swapped Thermal 5-Zone Color Palette
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| State Index | Color | Classification | Sigma Level Trigger | Contextual Action |
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| :---: | :---: | :--- | :--- | :--- |
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| **0.0** | `clrGray` | **Neutral / Equilibrium** | $\|AK\text{Score}\| \le 1.5\sigma$ | Normal distribution around AKAMA; trend in balance. |
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| **1.0** | `clrLightSkyBlue` | **Bullish Flow** | $+1.5\sigma < AK\text{Score} \le +2.0\sigma$ | Healthy intra-session upward impulse expansion. |
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| **2.0** | `clrDeepSkyBlue` | **Bullish Climax** | $AK\text{Score} > +2.0\sigma$ | Parabolic intra-session exhaustion; prepare scale-out. |
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| **3.0** | `clrCoral` | **Bearish Flow** | $-2.0\sigma \le AK\text{Score} < -1.5\sigma$ | Healthy intra-session downward impulse expansion. |
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| **4.0** | `clrOrangeRed` | **Bearish Climax** | $AK\text{Score} < -2.0\sigma$ | Panic intra-session exhaustion; prepare short-covering. |
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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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│ KScore_Anchored_Calculator.mqh │
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│ (Core Engine: Encapsulated CKamaAnchoredCalculator) │
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs Standardized AK-Score in O(1)
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▼
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┌────────────────────────────────────────────────────────┐
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│ KScore_Anchored_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Buffer Layer (3) │ Centralized Framework │
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│ • BufferAKScore (DATA) │ • DataSync_Tools.mqh │
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│ • BufferColors (INDEX) │ • MovingAverage_Engine │
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│ • BufferSignal (DATA) │ • Dynamic Sigma Levels │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **Defensive Memory & Auto-Resizing Engine:** `CKScoreAnchoredCalculator` implements auto-resizing safety guards for all internal dynamic arrays (`m_kama_odd`, `m_kama_even`, `m_price`, `out_akscore`), guaranteeing 100% crash-proof execution.
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2. **Stateless Session Tracking:** Compares bar timestamps deterministically, ensuring that real-time tick recalculations never corrupt historical session registers.
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3. **2026 MTF Framework (`DataSync_Tools.mqh`):** Higher-timeframe AK-Score histograms map into synchronized steps on lower-timeframe execution charts with zero step-warping.
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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 operates 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 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 strong directional efficiency.
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* `InpSlowEmaPeriod` (*default: `30`*): Slowest smoothing period ($S$) during consolidation.
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* `InpSourcePrice` (*default: `PRICE_CLOSE_STD`*): Applied price series (Standard OHLC or Synthetic Heikin Ashi).
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### Signal Line Settings
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* `InpShowSignal` (*default: `true`*): Toggle visibility of the Signal Moving Average line.
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* `InpSignalPeriod` (*default: `5`*): Lookback period for the signal line.
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* `InpSignalType` (*default: `EMA`*): Smoothing algorithm (`SMA`, `EMA`, `SMMA`, `LWMA`, `TMA`, `DEMA`, `TEMA`, `VWMA`).
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* `InpColorSignal` (*default: `clrFireBrick`*): Color applied to the signal line plot.
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### Indicator Levels (Sigma Units)
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* `InpLevelFlowHigh` (*default: `1.5`*): Bullish Flow warning boundary.
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* `InpLevelFlowLow` (*default: `-1.5`*): Bearish Flow warning boundary.
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* `InpLevelClimaxHigh` (*default: `2.0`*): Bullish Climax threshold (`DeepSkyBlue`).
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* `InpLevelClimaxLow` (*default: `-2.0`*): Bearish Climax threshold (`OrangeRed`).
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* `InpLevelExtremeHigh` (*default: `2.5`*): Extreme statistical exhaustion level.
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* `InpLevelExtremeLow` (*default: `-2.5`*): Extreme statistical capitulation level.
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* `InpLevelColor` (*default: `clrSilver`*): Color of horizontal level lines.
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* `InpLevelStyle` (*default: `STYLE_DOT`*): Line style of horizontal level lines.
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---
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## 5. Institutional Trading Playbooks (The Custom Session Advantage)
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ INSTITUTIONAL CUSTOM SESSION PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. LSE Breakout Filter: Confirm London opening breakout when AK-Score │
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│ crosses +1.5σ with Signal MA confirmation. │
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│ 2. Session Climax Fade: When AK-Score hits +2.5σ in late session, │
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│ prepare to fade back to the AKAMA mean. │
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│ 3. Squeeze Invalidation: In tight session ranges, spikes into ±2.0σ │
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│ identify liquidity sweeps (false breakouts). │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The London Opening Session Momentum Trigger (LSE Open)
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* **Configuration:** `InpResetPeriod = ANCHOR_PERIOD_CUSTOM_SESSION`, `InpCustomStart = "08:00"`, `InpCustomEnd = "16:30"`.
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* **Execution:** At the 08:00 London bell, AK-Score starts at $0.0\sigma$. If European institutional order flow drives price aggressively:
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* A cross above `+1.5σ (LightSkyBlue)` confirmed by the Signal MA line validates that institutional capital is actively expanding the session range $\rightarrow$ Enter Long.
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* A cross below `-1.5σ (Coral)` confirmed by the Signal MA validates downward expansion $\rightarrow$ Enter Short.
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### 5.2. Session Climax & Late-Day Mean Reversion
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* If AK-Score spikes above `+2.0σ` or `+2.5σ (DeepSkyBlue)` during midday or late session and then crosses **below** the Signal MA line:
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* **Action:** Close trend-following long positions or enter mean-reversion counter-trades targeting the session AKAMA baseline ($0.0\sigma$).
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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** | `BufferAKScore` | `INDICATOR_DATA` | Standardized AK-Score Values in Session Sigma Multiples ($\sigma$) |
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| **1** | `BufferColors` | `INDICATOR_COLOR_INDEX` | Swapped Thermal 5-Zone Palette Index ($0.0 \dots 4.0$) |
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| **2** | `BufferSignal` | `INDICATOR_DATA` | Smoothed Signal Moving Average Plot |
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring instant compatibility with MetaTrader 5 Expert Advisors via `iCustom()`.*
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