randomstatsmodels 2.0.0

Lightweight univariate time-series forecasting with auto-tuned models — NumPy only.

randomstatsmodels

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Lightweight univariate time-series forecasting with auto-tuned models — NumPy only, no heavy dependencies.

19 forecasting models with a unified .fit(y) / .predict(h) API. Each Auto* wrapper grid-searches hyperparameters on a validation split and refits the best configuration on the full series.

Installation

pip install randomstatsmodels

Requires: Python 3.9+ and NumPy.

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Quick Start

from randomstatsmodels import AutoKoopman, AutoPolymath, AutoSSA
import numpy as np

rng = np.random.default_rng(42)
t = np.arange(200)
y = 10 + 0.05 * t + np.sin(2 * np.pi * t / 24) + 0.1 * rng.normal(size=t.size)

h = 12  # forecast horizon

model = AutoKoopman().fit(y)
yhat = model.predict(h)
print("Forecast:", yhat[:5])
print("Best config:", model.best_)

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Models

19 models organised by approach. Every Auto* class accepts a parameter grid, fits/evaluates candidates, and exposes .fit(y) and .predict(h).

Classical

Model	Description
AutoNaive	Baselines: last value, seasonal, drift, mean
AutoHoltWinters	Triple exponential smoothing (level + trend + seasonal)
AutoThetaAR	Theta method with AR(1) residual correction
AutoFourier	Harmonic regression with optional linear trend

Regression-Based

Model	Description
AutoNEO	Nonlinear Evolution Operator — polynomial AR features
AutoPolymath	Polynomial + Fourier basis + ridge regression
AutoLocalLinear	Weighted local regression with exponential decay
AutoPALF	Proximal Aggregation Lag Forecaster — penalised lag weighting

Decomposition / Spectral

Model	Description
AutoSSA	Singular Spectrum Analysis — SVD on trajectory matrix
AutoKoopman	Dynamic Mode Decomposition / Koopman operator via delay embedding
AutoSpectralGradient	Spectral derivative flow — extrapolates Fourier mode dynamics

Advanced / Calculus-Based

Model	Description
AutoFracDiff	Fractional calculus — Grunwald-Letnikov fractional differencing + AR
AutoGreensKernel	Integral equation — Green's function convolution kernel
AutoPDEField	Partial differential equations — advection-diffusion on time-scale field
AutoVariationalPath	Calculus of variations — Euler-Lagrange optimal path

Hybrid / Meta

Model	Description
AutoHybridForecaster	Linear (Fourier + trend + AR) + GRU residual network
AutoMELD	Multiscale embedding with Random Fourier Features + kNN
AutoRIFT	Recursive Information Flow Tensor — information-channel dynamics
AutoEnsemble	Combines multiple base forecasters with learned weights

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Benchmarks

All 19 models evaluated on 36 real-world time series (20% holdout), ranked by MAE.

Overall Rankings

Rank	Model	Avg Rank	#1st	#Top3	Mdn sMAPE
1	AutoHybridForecaster	5.56	3	12	8.92%
2	AutoPolymath	6.14	5	12	9.54%
3	AutoNEO	6.56	2	12	13.57%
4	AutoKoopman	6.81	4	9	13.00%
5	AutoSSA	8.03	3	11	10.80%
6	AutoKNN	8.68	4	9	11.74%
7	AutoNaive	8.75	2	6	12.56%
8	AutoLocalLinear	8.94	2	6	13.30%
9	AutoFourier	9.67	2	6	18.93%
10	AutoMELD	9.85	0	6	12.79%
11	AutoGreensKernel	9.89	4	4	17.46%
12	AutoPALF	10.42	2	2	13.89%
13	AutoThetaAR	10.56	1	4	24.03%
14	AutoSpectralGradient	11.50	0	1	16.28%
15	AutoPDEField	11.58	1	3	23.29%
16	AutoHoltWinters	12.31	1	2	23.47%
17	AutoVariationalPath	12.78	0	1	18.16%
18	AutoRIFT	13.29	0	1	29.67%
19	AutoFracDiff	16.78	0	1	88.03%

Dataset Coverage

36 real-world datasets across 11 challenge categories:

Category	Datasets
Trend + Seasonality	AirPassengers, MilkProduction, JohnsonJohnson, AusBeer, CO2, WineSales
Pure Seasonality	Nottem, USAccDeaths, UKGas, MelbourneTemp
Trend-Dominant	Shampoo, USGDPGrowth, WorldPopulation
Cyclical	Sunspots, Lynx, SOI
Level Shift	Nile, UKDriverDeaths, LakeHuron
Volatile / Financial	GoldPrice, USIndProduction
Short Series	TornadoDeaths, WheatYield, Discoveries, USStrikes
Long Memory	NileMinLevel, GlobalTemp
Count / Intermittent	VolcanicEruptions, IntlAirline, LondonRain
Nonlinear	SingaporeHumidity, FedFundsRate, ChampagneSales
Additional	PigSlaughter, HousingStarts, WikiPageviews

Key Findings

• AutoHybridForecaster leads overall — linear decomposition + GRU residuals, but slowest to fit
• AutoPolymath is the best fast model — polynomial + Fourier features with ridge regression
• AutoKoopman (new) is #4 overall — Koopman/DMD eigenvalue propagation, extremely fast
• AutoGreensKernel (new) gets the most 1st-place wins (4) among calculus-based models
• No single model dominates — model selection matters for your data type

Benchmarking Your Own Data

from randomstatsmodels.benchmarking.datasets import load_datasets
from randomstatsmodels.benchmarking.evaluation import evaluate_all, print_summary
from randomstatsmodels import AutoKoopman, AutoPolymath, AutoSSA

datasets = load_datasets()
results = evaluate_all([AutoKoopman, AutoPolymath, AutoSSA], datasets)
print_summary(results["summary"])

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Metrics

from randomstatsmodels.metrics import mae, mse, rmse, mape, smape

The evaluation framework also provides MASE, MSSE, and Median Absolute Error.

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License

MIT