`RollingLinearRegression`#

Description#

Rolling OLS fit of y ≈ slope · x + intercept + ε, returning four outputs per step:

Output	Formula
`slope`	\((n S_{xy} - S_x S_y) / (n S_{xx} - S_x^2)\)
`intercept`	\((S_y - \text{slope} \cdot S_x) / n\)
`r_squared`	\((n S_{xy} - S_x S_y)^2 / [(n S_{xx} - S_x^2)(n S_{yy} - S_y^2)]\)
`stderr`	\(\sqrt{\text{SSE} / (n-2)}\) - RMSE of residuals

Note on stderr: this is the standard error of the estimate (RMSE of the fit), not the standard error of the slope coefficient. Multiply by 1/sqrt(Σ(x - mean_x)²) to get slope confidence.

2-input, 4-output (FunctorBase<_, 2, 4>). Inputs (y, x); outputs (slope, intercept, r_squared, stderr). First valid output at sample index window_size - 1. First 2→4 consumer of the Plan E N→M dispatcher.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import RollingLinearRegression

np.random.seed(0)
x = np.random.normal(0.0004, 0.012, size=300)
y = 0.8 * x + np.random.normal(0.0003, 0.007, size=300)
out = RollingLinearRegression(window_size=63)(y, x)   # columns: slope, intercept, r_squared, stderr
slope = out[:, 0]

fig = make_subplots(rows=2, cols=1, shared_xaxes=True,
                    row_heights=[0.55, 0.45], vertical_spacing=0.08)
fig.add_trace(go.Scatter(y=y, mode="lines", name="y returns"), row=1, col=1)
fig.add_trace(go.Scatter(y=x, mode="lines", name="x returns"), row=1, col=1)
fig.add_trace(go.Scatter(y=slope, mode="lines", name="slope",
                         line=dict(color="red")), row=2, col=1)
fig.update_layout(title="Rolling OLS slope of y on x over 63 bars (RollingLinearRegression)",
                  margin=dict(l=20, r=20, t=60, b=20),
                  legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1))
fig.update_yaxes(title_text="returns", row=1, col=1)
fig.update_yaxes(title_text="slope", row=2, col=1)
fig.show()