randomstatsmodels 4.5.0

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

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	48402.79	83881.03	32.56%	41.87	51.48	20.43%	0.00	100
fast	46825.06	82219.58	31.01%	39.12	47.55	19.36%	0.00	100
normal	55665.87	82470.84	29.79%	27.33	33.06	17.35%	0.00	100
slow	55665.62	82470.65	29.85%	33.33	40.96	16.32%	0.00	100
super_slow	55666.08	82471.08	29.84%	33.33	40.96	16.32%	0.00	100

AutoThetaAR

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	66231.58	105091.88	28.39%	38.03	43.80	15.98%	0.01	100
fast	66231.58	105091.88	28.39%	38.03	43.80	15.98%	0.01	100
normal	66231.58	105091.88	28.39%	38.03	43.80	15.98%	0.01	100
slow	66231.58	105091.88	28.39%	38.03	43.80	15.98%	0.01	100
super_slow	66231.58	105091.88	28.39%	38.03	43.80	15.98%	0.01	100

AutoKNN

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	45495.17	81223.33	30.94%	37.34	43.61	17.77%	0.01	100
fast	46081.70	81754.65	32.17%	39.10	45.58	19.54%	0.04	100
normal	44846.01	80618.64	32.61%	38.31	47.24	19.55%	0.06	100
slow	45077.83	81224.90	31.70%	40.49	51.34	18.16%	0.19	99
super_slow	45711.61	81671.07	30.70%	40.49	51.34	18.02%	0.60	99

AutoPDEField

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	71364.72	113802.04	34.27%	46.73	54.63	16.75%	0.00	100
fast	62836.93	100782.31	34.26%	46.73	54.63	16.66%	0.01	100
normal	61394.96	98643.02	32.35%	30.15	36.51	15.19%	0.14	100
slow	59601.86	96607.74	32.43%	30.10	36.19	14.63%	0.22	100
super_slow	59880.46	96029.28	31.13%	30.90	36.42	14.23%	3.22	100

AutoFourier

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	55563.07	80172.78	33.44%	57.76	68.20	22.97%	0.00	100
fast	51677.30	76308.97	36.55%	57.76	68.20	23.72%	0.00	100
normal	52139.33	79995.06	35.59%	61.08	66.96	23.36%	0.00	100
slow	49132.03	77423.79	35.22%	61.08	66.96	23.36%	0.01	100
super_slow	48872.80	77122.95	33.60%	61.08	66.96	23.36%	0.02	100

AutoGreensKernel

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	72348.83	99254.58	51.74%	111.93	126.21	35.64%	0.01	100
fast	70411.59	96782.30	50.11%	104.02	112.41	34.89%	0.03	100
normal	50902.81	77641.40	34.90%	47.15	56.76	22.73%	0.21	100
slow	49221.30	76075.91	34.15%	45.95	55.78	21.83%	0.61	100
super_slow	49778.84	78193.66	33.07%	44.38	54.47	20.69%	6.14	100

AutoSpectralGradient

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	52722.21	84979.30	33.96%	58.04	67.81	19.47%	0.00	100
fast	44047.84	74975.53	33.86%	51.63	63.20	19.38%	0.01	100
normal	51565.84	80725.74	33.57%	49.33	60.86	18.60%	0.32	100
slow	59388.87	86750.79	35.76%	53.36	64.10	21.49%	0.92	100
super_slow	59750.35	86300.03	36.95%	52.61	58.78	21.71%	13.32	100

AutoFracDiff

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	135625.12	165178.89	85.97%	501.87	571.23	86.19%	0.01	100
fast	130154.81	157580.15	81.32%	455.90	483.54	81.51%	0.02	100
normal	95424.54	126662.35	56.29%	254.84	256.02	51.90%	0.30	100
slow	85441.64	119020.80	38.24%	111.51	115.23	31.00%	1.13	100
super_slow	87305.06	121693.81	36.59%	94.22	98.15	27.19%	7.01	100

AutoKoopman

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	45411.65	72908.35	33.11%	35.13	43.04	19.67%	0.00	100
fast	44888.15	72263.73	33.14%	34.39	41.02	21.42%	0.01	100
normal	52062.77	81243.92	29.71%	29.11	34.77	18.06%	0.77	100
slow	52822.65	82219.21	30.71%	28.06	34.25	18.18%	3.75	100
super_slow	50844.52	79799.29	28.94%	35.61	44.43	17.06%	28.62	100

AutoLocalLinear

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	80495.97	113829.66	35.81%	33.08	40.21	15.17%	0.01	100
fast	45131.52	70541.57	32.41%	28.64	35.57	15.60%	0.01	100
normal	75742.64	104015.39	39.67%	31.57	37.60	15.31%	0.03	100
slow	124413.16	151654.08	48.26%	31.57	37.60	18.08%	0.06	100
super_slow	168910.25	206433.85	49.40%	46.44	52.03	25.45%	0.12	100

AutoPolymath

Speed	Mean MAE	Mean RMSE	Mean sMAPE	Median MAE	Median RMSE	Median sMAPE	Median Fit (s)	OK
super_fast	49431.52	81177.78	26.29%	33.47	38.35	11.78%	0.00	100
fast	67358.56	102976.44	27.13%	27.62	32.61	11.43%	0.05	95
normal	83892.45	139210.80	27.52%	24.51	32.43	12.03%	2.97	88
slow	84919.11	137332.12	29.43%	24.29	32.35	12.59%	6.15	90
super_slow	188379.08	377591.15	29.79%	34.81	41.63	13.12%	31.60	84

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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