Tim Olson
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86 lines
4.3 KiB
Markdown
86 lines
4.3 KiB
Markdown
---
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description: "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."
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tags: [stocks, machine-learning, knn, prediction]
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---
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# Machine Learning — Single-Stock KNN
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**Section**: 3.17 | **Asset Class**: Stocks | **Type**: Machine Learning / Prediction
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## Overview
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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.
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## Construction / Signal
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**Target variable** — cumulative return over the next T trading days:
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```
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Y(t) = P(t-T) / P(t) - 1 (332)
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```
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(t ascending corresponds to going back in time; t=0 is today)
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**Predictor variables** (moving averages of volume and price over varying windows T_1, T_2, T_3, ...):
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```
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X_1(t) = (1/T_1) * sum_{s=1}^{T_1} V(t+s) (333) [volume MA]
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X_2(t) = (1/T_2) * sum_{s=1}^{T_2} P(t+s) (334) [price MA 1]
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X_3(t) = (1/T_3) * sum_{s=1}^{T_3} P(t+s) (335) [price MA 2]
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... (336)
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```
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Predictor variables are normalized to [0, 1] using the training period's min/max:
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```
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X_tilde_a(t) = (X_a(t) - X_a^-) / (X_a^+ - X_a^-) (337)
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```
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where `X_a^+` and `X_a^-` are the max and min of `X_a(t)` over the training period.
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**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:
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```
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[D(t, t')]^2 = sum_{a=1}^{m} (X_tilde_a(t) - X_tilde_a(t'))^2 (338)
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```
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**Predicted return** (simple average):
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```
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Y(t) = (1/k) * sum_{alpha=1}^{k} Y(t'_alpha(t)) (339)
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```
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Alternatively, fit a linear model with weights w_alpha and intercept v:
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```
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Y(t) = sum_{alpha=1}^{k} Y(t'_alpha(t)) w_alpha + v (340)
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```
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trained by regressing Y(t) on the k neighbor returns over M values of t.
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**Trading signal** (z_1, z_2 are trader-defined thresholds):
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```
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Signal = { Establish long position if Y > z_1
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{ Liquidate long position if Y <= z_2
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{ Establish short position if Y < -z_1
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{ Liquidate short position if Y >= -z_2 (341)
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```
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## Entry / Exit Rules
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- **Long entry**: Predicted cumulative return `Y = Y(0) > z_1`
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- **Long exit**: Predicted return `Y <= z_2` (where z_2 <= z_1)
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- **Short entry**: Predicted return `Y < -z_1`
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- **Short exit**: Predicted return `Y >= -z_2`
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- All thresholds must be backtested out-of-sample.
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## Key Parameters
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- **Number of neighbors k**: Typically `k = floor(sqrt(T_*))` or `k = ceiling(sqrt(T_*))` (T_* = training sample size)
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- **Training sample size T_***: Number of historical time points used for training
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- **Prediction horizon T**: Number of trading days for the target return
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- **Feature set m**: Number and type of predictor variables (volume MAs, price MAs)
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- **Thresholds z_1, z_2**: Entry and exit thresholds for signals (backtested)
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- **Train/validation split**: E.g., 60% training, 40% cross-validation
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- **Distance metric**: Euclidean (Eq. 338) or Manhattan distance
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## Variations
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- **Weighted KNN**: Use distance-based weights for the k neighbors instead of uniform averaging (Eq. 340)
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- **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
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- **Alternative features**: Fundamental data, earnings surprises, sentiment indicators in addition to price/volume
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## Notes
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- This is a single-stock strategy: each stock's model is trained on that stock's own price/volume data only.
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- The strategy must be backtested strictly out-of-sample; data leakage is a critical risk.
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- 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.
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- k can be optimized via backtesting; common heuristic: `k = floor(sqrt(T_*))`.
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- Typical holding period: T trading days (matching the prediction horizon).
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- Training/cross-validation split: e.g., 60%/40%.
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