ai/gateway/knowledge/trading/strategies/stocks/ml-knn.md

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Predicts a stock's future T-day cumulative return using the K-nearest-neighbor algorithm on normalized price and volume features, then trades based on the predicted return signal.	stocks machine-learning knn prediction

Machine Learning — Single-Stock KNN

Section: 3.17 | Asset Class: Stocks | Type: Machine Learning / Prediction

Overview

This single-stock strategy uses the k-nearest-neighbor (KNN) algorithm to predict future cumulative stock returns based on a set of predictor (feature) variables derived from the stock's own price and volume history. For each stock, the model is trained independently using only that stock's data (no cross-sectional information). The predicted return is then used to generate long/short signals.

Construction / Signal

Target variable — cumulative return over the next T trading days:

Y(t) = P(t-T) / P(t) - 1                                  (332)

(t ascending corresponds to going back in time; t=0 is today)

Predictor variables (moving averages of volume and price over varying windows T_1, T_2, T_3, ...):

X_1(t) = (1/T_1) * sum_{s=1}^{T_1} V(t+s)                (333)   [volume MA]
X_2(t) = (1/T_2) * sum_{s=1}^{T_2} P(t+s)                (334)   [price MA 1]
X_3(t) = (1/T_3) * sum_{s=1}^{T_3} P(t+s)                (335)   [price MA 2]
...                                                        (336)

Predictor variables are normalized to [0, 1] using the training period's min/max:

X_tilde_a(t) = (X_a(t) - X_a^-) / (X_a^+ - X_a^-)       (337)

where X_a^+ and X_a^- are the max and min of X_a(t) over the training period.

KNN prediction — for a given t, find the k nearest neighbors of X_tilde_a(t) among training points t' = t+1, t+2, ..., t+T_* using Euclidean distance:

[D(t, t')]^2 = sum_{a=1}^{m} (X_tilde_a(t) - X_tilde_a(t'))^2   (338)

Predicted return (simple average):

Y(t) = (1/k) * sum_{alpha=1}^{k} Y(t'_alpha(t))           (339)

Alternatively, fit a linear model with weights w_alpha and intercept v:

Y(t) = sum_{alpha=1}^{k} Y(t'_alpha(t)) w_alpha + v       (340)

trained by regressing Y(t) on the k neighbor returns over M values of t.

Trading signal (z_1, z_2 are trader-defined thresholds):

Signal = { Establish long position if Y > z_1
          { Liquidate long position if Y <= z_2
          { Establish short position if Y < -z_1
          { Liquidate short position if Y >= -z_2           (341)

Entry / Exit Rules

• Long entry: Predicted cumulative return Y = Y(0) > z_1
• Long exit: Predicted return Y <= z_2 (where z_2 <= z_1)
• Short entry: Predicted return Y < -z_1
• Short exit: Predicted return Y >= -z_2
• All thresholds must be backtested out-of-sample.

Key Parameters

• Number of neighbors k: Typically k = floor(sqrt(T_*)) or k = ceiling(sqrt(T_*)) (T_* = training sample size)
• Training sample size T_*: Number of historical time points used for training
• Prediction horizon T: Number of trading days for the target return
• Feature set m: Number and type of predictor variables (volume MAs, price MAs)
• Thresholds z_1, z_2: Entry and exit thresholds for signals (backtested)
• Train/validation split: E.g., 60% training, 40% cross-validation
• Distance metric: Euclidean (Eq. 338) or Manhattan distance

Variations

• Weighted KNN: Use distance-based weights for the k neighbors instead of uniform averaging (Eq. 340)
• Cross-sectional extension: Compute expected returns Y_i for N stocks and use as inputs to cross-sectional mean-reversion or other multi-stock strategies
• Alternative features: Fundamental data, earnings surprises, sentiment indicators in addition to price/volume

Notes

• This is a single-stock strategy: each stock's model is trained on that stock's own price/volume data only.
• The strategy must be backtested strictly out-of-sample; data leakage is a critical risk.
• Simple uniform KNN (Eq. 339) has no parameters to train; the linear model (Eq. 340) requires cross-validation and is prone to out-of-sample instability.
• k can be optimized via backtesting; common heuristic: k = floor(sqrt(T_*)).
• Typical holding period: T trading days (matching the prediction horizon).
• Training/cross-validation split: e.g., 60%/40%.