Gaussian Ensemble
Trading Engine

Applies two Gaussian kernels with different width (fast σ=3, slow σ=6) to the price series. The convolution produces smoothed lines — the fast line reacts quickly, the slow line lags behind.

Crossover logic: When the fast line crosses above the slow, the trend is up (Buy, confidence 0.8). When it crosses below, the trend is down (Sell, 0.8). The relative position also produces a lower-confidence bias signal (0.3) when no crossover has occurred.

Why Gaussian? Unlike simple moving averages, Gaussian convolution gives more weight to the centre bar and smoothly tapers to the edges — producing a cleaner, phase-preserving smooth that doesn't overshoot on sharp moves.

Trains a Gaussian Process on the last InpGPRLookback (default 30) price bars using an RBF (squared-exponential) kernel. The GP produces both a mean prediction and a predictive variance (uncertainty band) for the next bar.

Mean-reversion logic: If the current price is more than InpGPRStdThresh (default 1.5) standard deviations away from the GP mean, the market is considered overextended. A buy signal fires when price is unusually low (below −σ), a sell when unusually high (above +σ).

Implementation: The GP is trained via Cholesky decomposition (O(n³) upfront, O(n²) per prediction). The prediction at x* is: μ = k(x*)ᵀ · α, where α = (K + σ²I)⁻¹ · y. The confidence band shrinks near training points and widens in extrapolation regions.

Fits a 2-component univariate GMM on daily return percentages using the Expectation-Maximisation (EM) algorithm. One component captures the low-volatility regime, the other the high-volatility regime.

Adaptive logic: In the high-vol regime, the strategy looks for momentum continuation — if the latest return exceeds 0.5·σ_HV in the direction of the move, it trades with the trend. In the low-vol regime, it switches to mean reversion — returns beyond 0.3·σ_HV from zero are faded.

EM algorithm: E-step computes responsibility γᵢₖ (probability each point belongs to each component). M-step re-estimates π, μ, σ for each component. Converges in ~10–20 iterations. Components are sorted so component 1 is always the high-vol regime.

Trains a binary Gaussian Naive Bayes classifier on three independent features to predict whether the next bar closes up or down:

• f₀ — Return: (Close[i] − Close[i+1]) / Close[i+1] — captures short-term price change
• f₁ — Volume ratio: log(Volume[i] / Volume[i+1]) — increasing volume often confirms moves
• f₂ — HL spread: (High[i] − Low[i]) / Close[i] — wider ranges indicate uncertainty / volatility

The Naive Bayes assumption (conditional independence of features given the class) allows the joint likelihood to be computed as a product of univariate Gaussians: P(f₀,f₁,f₂ | class) = Πⱼ PDF(fⱼ | μ_class_j, σ_class_j).

Trade logic: If P(up | features) > InpGNBProbThresh (0.60) → Buy. If P(up) < 1 − threshold → Sell. Confidence = |P(up) − 0.5| × 2, mapping the range [0.5, 1.0] → [0, 1.0].

Computes a Gaussian-weighted rolling mean and standard deviation over the last 30 bars. The Gaussian kernel (length 15, σ=4.0) assigns higher weight to recent prices — making the band adaptive to recent market conditions while still retaining statistical stability.

Band logic: When price moves beyond InpVolBandMultiplier (default 2.0) standard deviations from the weighted mean, the market is statistically overextended. A sell signal fires above the upper band, a buy below the lower band. The confidence scales linearly with the distance from the band edge, capped at 1.0.

Why Gaussian-weighted? Unlike a simple rolling window (equal weights), the Gaussian weighting smoothly transitions from recent to older data — avoiding the "cliff edge" effect where a bar suddenly drops out of the window, causing a discontinuous jump in the mean and std.

Calculates the z-score of the current close price relative to the mean and standard deviation of the last period (default 20) bars: z = (Price − μ) / σ. The z-score is a unitless measure of how many standard deviations the current price is from its recent average.

Fade-the-move logic: When |z| > InpZScoreEntry (default 2.0), the price is statistically extreme — large deviations from the mean tend to revert. A buy signal fires at z = −2.0 (oversold), a sell at z = +2.0 (overbought). The confidence scales linearly with |z|, capped at 1.0 at z = 5.0.

Why z-score? The z-score normalises price by recent volatility — it works across different instruments and timeframes without parameter changes. A z-score of 2.0 means the same thing (95th percentile) whether on EUR/USD H1 or XAU/USD D1, making this strategy the most portable of the six.