randomstatsmodels 4.0.7

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

Advanced Ensembles

Model	Description
AutoStacked	Meta-learner stacking — ridge regression on base model predictions
AutoBagged	Block-bootstrap bagging — median of models trained on resampled series
AutoDynamic	Horizon-adaptive weighting — model weights change per forecast step

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Benchmarks

22 models evaluated on 20 real-world time series (10 from FRED with 300-600 points, 10 classic hardcoded) using speed="slow" grids. Ranked by RMSE per dataset. Includes 5 statsforecast baselines. AutoRIFT and AutoHybridForecaster excluded from fast benchmark (>30s fit time per dataset).

Overall Rankings

Rank	Model	Type	Avg Rank	#1st	#Top3	#Top7	Median MAE	Median RMSE	Median MAPE	Median sMAPE
1	SF_AutoTBATS	statsforecast	7.30	1	5	10	18.28	23.53	7.66%	7.77%
2	SF_AutoARIMA	statsforecast	8.00	1	3	10	18.03	23.29	7.14%	7.65%
3	AutoNEO	randomstatsmodels	8.94	2	4	8	25.86	36.51	7.38%	7.59%
4	AutoMELD	randomstatsmodels	8.95	2	4	7	20.80	27.83	7.79%	7.84%
5	SF_AutoETS	statsforecast	9.35	0	0	9	33.65	38.18	11.53%	12.08%
6	SF_AutoCES	statsforecast	9.80	5	6	9	18.96	23.27	10.70%	10.71%
7	AutoNaive	randomstatsmodels	10.05	1	1	7	24.43	30.87	12.94%	13.68%
8	AutoKoopman	randomstatsmodels	10.75	0	5	5	31.60	40.47	12.63%	12.59%
9	AutoPolymath	randomstatsmodels	10.84	0	4	6	22.65	29.33	9.48%	9.00%
10	SF_AutoTheta	statsforecast	11.00	0	3	7	20.07	25.67	8.97%	9.27%
11	AutoPALF	randomstatsmodels	11.00	2	2	7	42.30	49.53	12.77%	13.84%
12	AutoKNN	randomstatsmodels	11.05	1	2	8	35.92	43.24	12.71%	13.89%
13	AutoPDEField	randomstatsmodels	11.25	0	2	5	36.12	41.58	11.16%	11.66%
14	AutoSSA	randomstatsmodels	11.75	0	3	6	31.47	38.00	12.24%	13.28%
15	AutoThetaAR	randomstatsmodels	11.80	0	1	5	38.03	43.81	15.11%	16.76%
16	AutoHoltWinters	randomstatsmodels	12.20	2	2	7	49.16	60.66	14.24%	14.63%
17	AutoGreensKernel	randomstatsmodels	12.60	1	3	6	40.53	48.61	15.87%	16.51%
18	AutoVariationalPath	randomstatsmodels	12.80	0	3	5	57.52	67.07	13.10%	13.52%
19	AutoSpectralGradient	randomstatsmodels	13.25	1	3	4	54.54	64.10	15.53%	15.02%
20	AutoFourier	randomstatsmodels	14.15	1	3	4	69.65	83.66	22.71%	22.45%
21	AutoLocalLinear	randomstatsmodels	15.10	0	1	5	56.44	63.38	20.47%	25.01%
22	AutoFracDiff	randomstatsmodels	18.60	0	0	0	110.80	113.95	30.43%	36.00%

Speed Presets

Every Auto* model accepts a speed parameter controlling grid search thoroughness:

from randomstatsmodels import AutoKoopman

model = AutoKoopman(speed="super_fast")   # ~1 combo, seconds
model = AutoKoopman(speed="fast")         # ~6 combos
model = AutoKoopman(speed="normal")       # default grids
model = AutoKoopman(speed="slow")         # ~864 combos
model = AutoKoopman(speed="super_slow")   # ~2640 combos

Datasets

20 real-world datasets (10 from FRED with 300-600 points, 10 classic):

Source	Datasets
FRED (300-600 pts)	USUnemployment, USConsumerPrices, USIndProdIndex, USHousingStarts, USMoneySupply, FedFundsRate, USRetailSales, USElectricity, SP500, US10YrTreasury
Classic (89-168 pts)	MilkProduction, GoldPrice, NileMinLevel, AirPassengers, CO2, GlobalTemp, IntlAirline, Lynx, Nile, Sunspots

Key Findings

• SF_AutoTBATS is #1 by RMSE — strong on seasonal FRED data
• SF_AutoARIMA is #2 — most consistent across dataset types
• AutoNEO is the best randomstatsmodels model (#3) — polynomial AR features
• AutoMELD is #4 — multiscale embedding excels on longer series
• AutoKoopman (#8) — DMD eigenvalue propagation, 5 top-3 finishes
• No single model dominates — model selection matters for your data type

Per-Model Speed Benchmarks (100 real-world datasets)

AutoNaive

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	48355.60	83837.06	32.57%	41.87	51.48	20.43%	0.00	100
fast	48268.56	83741.53	30.11%	39.12	46.52	19.94%	0.01	100
normal	49620.68	85113.47	28.95%	26.38	31.77	16.16%	0.04	100
slow	49620.69	85114.67	28.87%	26.38	31.77	15.10%	0.04	100
super_slow	49620.68	85114.66	28.83%	26.38	31.77	15.10%	0.05	100

AutoThetaAR

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	66109.39	105001.45	27.89%	38.03	43.81	15.97%	0.02	100
fast	66109.39	105001.45	27.89%	38.03	43.81	15.97%	0.02	100
normal	66109.39	105001.45	27.89%	38.03	43.81	15.97%	0.02	100
slow	66109.39	105001.45	27.89%	38.03	43.81	15.97%	0.02	100
super_slow	66109.39	105001.45	27.89%	38.03	43.81	15.97%	0.02	100

AutoKNN

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	45452.00	81194.06	31.06%	37.34	43.61	17.88%	0.01	100
fast	45304.15	81091.92	31.31%	40.02	48.08	18.00%	0.03	100
normal	45697.77	81570.68	31.60%	39.12	47.55	17.76%	0.07	100
slow	46640.29	82929.84	29.64%	40.49	51.34	18.34%	0.20	99
super_slow	48880.39	85178.97	29.65%	40.49	51.34	19.27%	0.70	97

AutoGreensKernel

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	72373.74	99252.08	51.75%	111.93	126.21	35.64%	0.01	100
fast	70434.24	96781.19	50.12%	104.02	112.41	34.89%	0.04	100
normal	50920.74	77641.34	34.90%	47.15	56.76	22.88%	0.28	100
slow	49235.24	76074.76	34.16%	45.95	55.78	21.83%	0.74	100
super_slow	49763.01	78210.19	33.07%	44.38	54.47	20.69%	6.94	100

AutoSpectralGradient

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	53316.38	85569.53	34.03%	58.04	67.81	19.47%	0.01	100
fast	44542.17	75589.66	33.71%	51.63	63.20	19.38%	0.01	100
normal	46075.34	80332.99	33.34%	49.33	60.86	18.60%	0.36	100
slow	56011.19	91226.06	36.50%	53.36	64.10	21.49%	1.07	100
super_slow	95136.50	117307.84	39.52%	52.61	58.78	23.13%	15.15	100

AutoKoopman

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	45069.80	72627.75	33.09%	35.13	43.04	19.67%	0.00	100
fast	44554.91	71975.49	33.14%	34.39	41.02	21.42%	0.01	100
normal	51366.06	80560.52	29.90%	29.11	34.77	18.22%	0.57	100
slow	52145.81	81563.80	30.73%	28.06	34.25	18.02%	3.85	100
super_slow	50192.31	79077.97	29.19%	35.61	44.43	17.71%	26.99	100

AutoFracDiff

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	137729.69	166397.10	182.14%	501.87	571.23	183.72%	0.01	100
fast	129876.60	156541.33	171.14%	455.90	483.54	170.10%	0.02	100
normal	95469.19	126705.61	84.24%	254.84	256.02	78.84%	0.34	100
slow	85507.34	119072.89	46.03%	111.51	115.23	34.62%	1.22	100
super_slow	87346.14	121727.84	40.56%	94.22	98.15	27.94%	7.72	100

AutoFourier

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	56973.62	80744.33	36.51%	57.76	68.20	22.85%	0.04	100
fast	51807.32	83105.96	35.91%	57.76	70.78	25.32%	0.08	100
normal	49107.44	82548.25	36.48%	57.76	70.78	22.27%	0.42	100
slow	47379.61	78767.00	38.15%	67.92	85.39	24.42%	0.60	100
super_slow	48264.45	79597.11	36.16%	58.70	76.04	21.99%	1.57	100

AutoPDEField

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	71307.70	113766.45	34.29%	46.73	54.63	16.75%	0.00	100
fast	62768.35	100745.97	34.28%	46.73	54.63	16.66%	0.01	100
normal	61327.62	98601.13	32.37%	30.15	36.51	15.19%	0.10	100
slow	59534.52	96565.85	32.45%	30.10	36.19	14.63%	0.16	100
super_slow	59790.17	95980.60	31.14%	30.90	36.42	14.23%	3.52	100

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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