scirs2-series

Production-ready time series analysis for Rust — part of the SciRS2 scientific computing ecosystem.

scirs2-series is a comprehensive time series library covering classical econometric models through state-of-the-art deep learning forecasters. Version 0.3.2 adds neural architecture forecasters (TFT, N-BEATS, N-HiTS, DeepAR), streaming/online algorithms, conformal prediction intervals, long-memory processes, intermittent demand forecasting, and hierarchical reconciliation.

Overview

Time series problems span a wide spectrum: univariate forecasting with uncertainty quantification, multivariate causal modelling, streaming anomaly detection, hierarchical forecasting across organizational hierarchies, regime detection, and functional data analysis. scirs2-series covers all of these in a unified, type-safe API.

Key design goals:

• Breadth: classical (ARIMA, ETS) through neural (TFT, N-BEATS, DeepAR) through streaming (online ARIMA, ADWIN)
• Uncertainty quantification: prediction intervals via conformal prediction and probabilistic models
• Ecosystem coherence: built on scirs2-core abstractions; no C/Fortran dependencies
• Performance: parallel processing with Rayon, SIMD acceleration via scirs2-core

Feature List (v0.3.2)

Decomposition

• STL (Seasonal-Trend decomposition using Loess) with robustness iterations
• TBATS (Trigonometric seasonality, Box-Cox, ARMA errors, Trend, Seasonal)
• SSA (Singular Spectrum Analysis) with grouping and reconstruction
• STR (Seasonal-Trend decomposition with Regression)
• Multi-seasonal decomposition for complex seasonal patterns
• Classical additive and multiplicative decomposition
• Robust variants with outlier handling

Forecasting: Classical & Statistical

• ARIMA / SARIMA with Auto-ARIMA (stepwise and grid search)
• Exponential smoothing: Simple ES, Holt's linear trend, Holt-Winters, ETS framework
• BATS / TBATS for complex multi-seasonal data
• Theta method and Theta-F variants
• Naive, seasonal naive, drift, moving average, and ensemble of simple methods
• Intermittent demand: Croston's method, Syntetos-Boylan Approximation (SBA), TSB (Teunter-Syntetos-Babai)

Forecasting: Neural Architectures

• Temporal Fusion Transformer (TFT): multi-horizon attention-based model with variable selection, gating, and static covariate encoding
• N-BEATS: neural basis expansion for interpretable time series forecasting (trend and seasonality stacks)
• N-HiTS: hierarchical interpolation with multi-rate signal sampling
• DeepAR: autoregressive RNN with probabilistic output (Gaussian, negative binomial) for Amazon-style probabilistic forecasting
• Simple neural forecast API: common interface across all neural models

State-Space Models & Kalman Filtering

• Kalman filter and Rauch-Tung-Striebel smoother
• Extended Kalman filter (EKF) for nonlinear systems
• Unscented Kalman filter (UKF) with sigma-point propagation
• Structural time series (local level, local linear trend, seasonal, cycle)
• Unobserved components models
• Dynamic linear models with time-varying parameters

Volatility & GARCH Models

• GARCH(p,q) and EGARCH (exponential GARCH)
• FIGARCH (fractionally integrated GARCH) for long-memory volatility
• GJR-GARCH (asymmetric leverage effects)
• ARCH-LM test, Ljung-Box test for model diagnostics

Long-Memory Processes

• ARFIMA (Autoregressive Fractionally Integrated Moving Average) estimation and simulation
• Hurst exponent estimation: R/S analysis, detrended fluctuation analysis (DFA), Whittle estimator
• Fractional differencing (fractional-d operator) with memory-preserving transforms

Causality & Cointegration

• Granger causality testing with F-statistics and block-exogeneity
• Transfer entropy with bootstrap significance testing
• Convergent cross mapping (CCM) for nonlinear causality
• Cointegration: Engle-Granger two-step, Johansen trace and max-eigenvalue tests
• Vector Error Correction Models (VECM) with cointegration rank selection

Vector Autoregressive (VAR) Models

• VAR(p) fitting with OLS and information criterion lag selection (AIC, BIC, HQIC)
• Impulse response functions (IRF) with bootstrap confidence bands
• Forecast error variance decomposition (FEVD)
• Granger causality block-exogeneity Wald test
• VECM for cointegrated systems

Functional Data Analysis (FDA)

• Functional PCA (FPCA) with PACE algorithm for sparse/irregular data
• B-spline and Fourier basis expansions for functional data representation
• Functional linear model (scalar-on-function regression)
• Functional clustering (k-centres, hierarchical functional)
• Dynamic time warping barycenter averaging (DBA)

Hierarchical Forecasting & Reconciliation

• Bottom-up, top-down (average historical proportions, PHA, TDA), and middle-out aggregation
• Optimal reconciliation: MinT (trace minimisation), WLS (weighted least squares), OLS
• Cross-temporal reconciliation for multi-frequency hierarchies
• Evaluation with hierarchical MASE and weighted MAPE

Conformal Prediction for Time Series

• Split conformal prediction intervals (exchangeable and time-series-adapted variants)
• Adaptive conformal inference (ACI) for online coverage guarantees
• Mondrian conformal prediction for conditional coverage
• Calibration diagnostics and coverage plots

Online / Streaming Algorithms

• ADWIN (Adaptive Windowing) concept drift detector
• Online ARIMA with recursive least squares parameter tracking
• Streaming mean, variance, quantile estimation (P² algorithm, KLL sketch)
• Online anomaly detection: CUSUM, EWMA control charts, streaming isolation forest
• Reservoir sampling and sliding window statistics

Change Detection

• PELT (Pruned Exact Linear Time) for multiple change point detection
• Binary segmentation (greedy and exact variants)
• CUSUM (cumulative sum) control charts
• Bayesian online change point detection (BOCPD)
• Kernel-based change detection (MMD statistics)

Anomaly Detection

• Statistical process control (SPC): Shewhart, CUSUM, EWMA charts
• Z-score and modified Z-score methods
• IQR-based detection
• Isolation forest adapted for time series
• Prediction-error-based and reconstruction-based anomaly scores
• Distance-based approaches (matrix profile, LOF)

Pattern Analysis

• Autocorrelation (ACF) and partial autocorrelation (PACF) with confidence bands
• Cross-correlation with bootstrap confidence intervals
• Dynamic time warping (DTW) with Sakoe-Chiba and Itakura constraints
• Motif discovery and discord detection via matrix profile
• Symbolic Aggregate approXimation (SAX), APCA, PLA
• Time-frequency analysis: STFT, CWT (Morlet), coherence analysis

Feature Engineering (60+ features)

• Statistical: mean, variance, skewness, kurtosis, entropy, crossing rate, linearity
• Frequency domain: spectral entropy, spectral centroid, dominant frequency, bandwidth
• Complexity: approximate entropy, sample entropy, permutation entropy, Lyapunov exponent estimate
• Trend: linear trend slope, Hurst exponent, CUSUM range, range/IQR ratio
• Lag-based: ACF at specified lags, PACF, partial correlation coefficients
• Automated selection: filter, wrapper (forward/backward), embedded (LASSO, tree importance)

Regression Models for Time Series

• Distributed lag (DL) models with flexible lag structures
• Autoregressive distributed lag (ARDL) with automatic lag selection
• Error correction models (ECM) for cointegrated series
• Regression with ARIMA errors (ARIMAX / REGARIMA)

Clustering & Classification

• Time series k-means, k-medoids (PAM), hierarchical clustering
• DBSCAN and HDBSCAN with DTW distance
• k-NN classification with DTW, Euclidean, correlation-based distances
• Shapelet discovery and shapelet transform classification
• Functional data clustering (k-centres functional)

Ensemble & Probabilistic Forecasting

• Ensemble forecasting: simple average, weighted average, stacking
• Prediction interval methods: bootstrap, conformal, quantile regression forests
• Probabilistic forecast evaluation: CRPS, log score, reliability diagrams, PIT histograms

Domain-Specific Extensions

• Financial: GARCH volatility, 15+ technical indicators (CCI, MFI, OBV, Parabolic SAR, RSI, MACD, Bollinger Bands, ATR)
• Environmental: heat wave detection, SPI drought index, growing degree days, SOI/NAO climate indices
• Biomedical: ECG R-peak detection, HRV analysis, EEG frequency band decomposition, EMG onset detection
• IoT sensors: environmental sensor fusion, GPS activity recognition, predictive maintenance scoring

Transformations

• Box-Cox transformation with automatic lambda estimation
• Differencing (regular and seasonal), fractional differencing
• Normalization: Z-score, Min-Max, robust (median/IQR)
• Stationarity transformation pipeline with ADF/KPSS guidance

Regime-Switching Models

• Markov-switching autoregression (MS-AR) with Hamilton filter
• Threshold autoregressive (TAR) and SETAR models
• Smooth transition autoregressive (STAR) models
• Structural break detection (Bai-Perron multiple break test)

Quick Start

[dependencies]
scirs2-series = "0.3.2"

ARIMA Forecasting

use scirs2_series::arima_models::AutoArima;
use scirs2_core::ndarray::Array1;

let data: Array1<f64> = Array1::from(vec![
    110.0, 115.0, 118.0, 122.0, 120.0, 125.0, 130.0, 128.0,
    132.0, 135.0, 140.0, 138.0, 145.0, 148.0, 152.0, 155.0,
]);

let model = AutoArima::fit(&data, None).unwrap();
let forecast = model.predict(5).unwrap();
println!("5-step forecast: {:?}", forecast.values);
println!("95% intervals:   {:?}", forecast.intervals_95);

Temporal Fusion Transformer

use scirs2_series::neural_forecast::{TFT, TFTConfig};

let config = TFTConfig {
    hidden_size: 64,
    num_heads: 4,
    num_encoder_steps: 24,
    forecast_horizon: 12,
    ..Default::default()
};

let mut model = TFT::new(config);
model.fit(&train_data, &covariates, 100).unwrap();
let forecasts = model.predict(&test_context, &future_covariates).unwrap();

Granger Causality Test

use scirs2_series::causality::granger_causality;
use scirs2_core::ndarray::array;

let x = array![1.0f64, 1.5, 2.0, 2.5, 3.0, 3.2, 2.8, 3.5, 4.0, 3.7];
let y = array![0.5f64, 0.8, 1.2, 1.8, 2.2, 2.6, 2.4, 2.9, 3.3, 3.1];

let result = granger_causality(&x.view(), &y.view(), 2).unwrap();
println!("F-statistic: {:.4}, p-value: {:.4}", result.f_stat, result.p_value);
println!("Does x Granger-cause y? {}", result.p_value < 0.05);

ADWIN Concept Drift Detection

use scirs2_series::streaming::adwin::ADWIN;

let mut detector = ADWIN::new(0.002);  // delta parameter

for &obs in &stream_of_values {
    if detector.update(obs) {
        println!("Concept drift detected at this point!");
    }
}

Hierarchical Reconciliation

use scirs2_series::reconciliation::{MinTReconciler, HierarchyMatrix};

let hierarchy = HierarchyMatrix::from_summing_matrix(&s_matrix);
let reconciler = MinTReconciler::sample_covariance(hierarchy);

let reconciled = reconciler.reconcile(&base_forecasts, &residual_matrix).unwrap();

Conformal Prediction Intervals

use scirs2_series::conformal::SplitConformalForecaster;

let mut cp = SplitConformalForecaster::new(0.90);  // 90% coverage target
cp.calibrate(&calibration_residuals);

let interval = cp.predict_interval(&point_forecast);
println!("[{:.2}, {:.2}]", interval.lower, interval.upper);

API Overview

Feature Flags

Links

• SciRS2 project
• docs.rs
• crates.io
• TODO.md

License

Apache License 2.0. See LICENSE for details.

Authors

COOLJAPAN OU (Team KitaSan)