torsh-series

Time series analysis and forecasting components for ToRSh - powered by SciRS2.

Overview

This crate provides comprehensive time series analysis, forecasting, and modeling capabilities with PyTorch-compatible neural network integration. It leverages scirs2-series for classical time series methods while enabling deep learning approaches through ToRSh's neural network modules.

Features

• Forecasting Models: ARIMA, SARIMA, Prophet, Exponential Smoothing
• Neural Forecasting: LSTM, GRU, Temporal CNNs, Transformers, N-BEATS, DeepAR
• Decomposition: STL, seasonal decomposition, trend extraction
• Anomaly Detection: Isolation forests, statistical methods, autoencoders
• State Space Models: Kalman filters, particle filters, Hidden Markov Models
• Feature Engineering: Lag features, rolling statistics, fourier features
• Changepoint Detection: PELT, Binary segmentation, Bayesian methods
• Frequency Analysis: FFT, spectral analysis, wavelets
• Utilities: Differencing, transformations, stationarity tests
• GPU Acceleration: Neural forecasting models on CUDA

Usage

Basic Time Series Operations

use torsh_series::prelude::*;
use torsh_tensor::prelude::*;

// Create time series data
let data = tensor![1.0, 2.0, 3.0, 5.0, 8.0, 13.0, 21.0, 34.0];
let timestamps = tensor![0, 1, 2, 3, 4, 5, 6, 7];

// Create TimeSeries object
let ts = TimeSeries::new(data, Some(timestamps), None)?;

println!("Length: {}", ts.len());
println!("Start: {:?}, End: {:?}", ts.start(), ts.end());

// Basic statistics
println!("Mean: {:.4}", ts.mean()?);
println!("Std: {:.4}", ts.std()?);

Time Series Decomposition

STL Decomposition (Seasonal-Trend decomposition using Loess)

use torsh_series::decomposition::*;

let data = generate_seasonal_data(365 * 2, 12, 0.1)?;  // 2 years of monthly data

// Perform STL decomposition
let stl = STL::new()
    .seasonal_window(13)
    .trend_window(51)
    .seasonal_degree(1)
    .trend_degree(1);

let result = stl.fit(&data)?;

let trend = result.trend();
let seasonal = result.seasonal();
let residual = result.residual();

println!("Seasonal strength: {:.4}", result.seasonal_strength()?);
println!("Trend strength: {:.4}", result.trend_strength()?);

// Plot components
plot_decomposition(&result)?;

Classical Decomposition

use torsh_series::decomposition::*;

let data = load_ts("airline_passengers.csv")?;

// Additive decomposition: data = trend + seasonal + residual
let decomp_add = seasonal_decompose(&data, 12, "additive")?;

// Multiplicative decomposition: data = trend * seasonal * residual
let decomp_mul = seasonal_decompose(&data, 12, "multiplicative")?;

let trend = decomp_add.trend();
let seasonal = decomp_add.seasonal();
let residual = decomp_add.residual();

ARIMA Models

use torsh_series::forecast::*;

let data = load_ts("co2_levels.csv")?;

// Auto ARIMA - automatically selects best (p,d,q) parameters
let auto_model = AutoARIMA::new()
    .seasonal(true)
    .m(12)  // Seasonal period
    .max_p(5)
    .max_q(5)
    .max_d(2)
    .information_criterion("aic");

let model = auto_model.fit(&data)?;
println!("Selected model: ARIMA{:?}", model.order());

// Forecast next 24 steps
let forecast = model.predict(24, None)?;
let conf_int = model.predict_interval(24, 0.95)?;  // 95% confidence interval

// Manual ARIMA(2,1,1)
let arima = ARIMA::new(2, 1, 1)?;
arima.fit(&data)?;

let forecast = arima.predict(12, None)?;

SARIMA (Seasonal ARIMA)

use torsh_series::forecast::*;

let data = load_ts("monthly_sales.csv")?;

// SARIMA(1,1,1)(1,1,1,12)
// (p,d,q) = non-seasonal parameters
// (P,D,Q,m) = seasonal parameters (m=12 for monthly data)
let sarima = SARIMA::new(1, 1, 1, 1, 1, 1, 12)?;

sarima.fit(&data)?;

// Forecast with confidence intervals
let forecast = sarima.predict(24, None)?;
let (lower, upper) = sarima.predict_interval(24, 0.95)?;

// Model diagnostics
let residuals = sarima.residuals()?;
let aic = sarima.aic()?;
let bic = sarima.bic()?;

println!("AIC: {:.4}, BIC: {:.4}", aic, bic);

// Check residuals for white noise
let ljung_box = ljung_box_test(&residuals, 10)?;
println!("Ljung-Box p-value: {:.4}", ljung_box.p_value);

Exponential Smoothing

use torsh_series::forecast::*;

let data = load_ts("demand.csv")?;

// Simple Exponential Smoothing
let ses = SimpleExpSmoothing::new(0.3)?;  // alpha=0.3
ses.fit(&data)?;
let forecast = ses.predict(12)?;

// Holt's Linear Trend
let holt = Holt::new(0.8, 0.2)?;  // alpha=0.8, beta=0.2
holt.fit(&data)?;
let forecast = holt.predict(12)?;

// Holt-Winters (Triple Exponential Smoothing)
let hw = HoltWinters::new()
    .seasonal_periods(12)
    .trend("add")
    .seasonal("add")
    .alpha(0.8)
    .beta(0.2)
    .gamma(0.3);

hw.fit(&data)?;
let forecast = hw.predict(24)?;

// Auto ETS - automatically selects Error-Trend-Seasonal components
let auto_ets = AutoETS::new()
    .information_criterion("aic")
    .allow_multiplicative_trend(true);

let model = auto_ets.fit(&data)?;
println!("Selected model: {}", model.name());

Neural Forecasting Models

LSTM for Time Series

use torsh_series::forecast::neural::*;
use torsh_nn::prelude::*;

let data = load_ts("stock_prices.csv")?;

// Prepare sequences for LSTM
let (X, y) = create_sequences(&data, window_size=20, horizon=1)?;

// Define LSTM model
let lstm = LSTMForecaster::new()
    .input_size(1)
    .hidden_size(64)
    .num_layers(2)
    .output_size(1)
    .dropout(0.2)
    .bidirectional(false);

// Train model
lstm.fit(&X, &y, epochs=100, batch_size=32, lr=0.001)?;

// Forecast
let forecast = lstm.predict(&data, horizon=10)?;

// Multi-step forecasting
let multi_step_forecast = lstm.predict_multi_step(&data, horizon=30)?;

Temporal Convolutional Network (TCN)

use torsh_series::forecast::neural::*;

let tcn = TCN::new()
    .input_channels(1)
    .output_size(1)
    .num_channels(vec![32, 32, 32, 32])
    .kernel_size(3)
    .dropout(0.2);

tcn.fit(&X, &y, epochs=50, batch_size=64)?;
let forecast = tcn.predict(&data, horizon=20)?;

Transformer for Time Series

use torsh_series::forecast::neural::*;

let transformer = TimeSeriesTransformer::new()
    .d_model(64)
    .nhead(8)
    .num_encoder_layers(3)
    .num_decoder_layers(3)
    .dim_feedforward(256)
    .dropout(0.1)
    .sequence_length(50)
    .forecast_horizon(10);

transformer.fit(&data, epochs=100, batch_size=32)?;
let forecast = transformer.predict(&data, horizon=10)?;

N-BEATS (Neural Basis Expansion Analysis)

use torsh_series::forecast::neural::*;

// N-BEATS: interpretable and accurate forecasting
let nbeats = NBEATS::new()
    .stack_types(vec!["trend", "seasonality", "generic"])
    .num_blocks_per_stack(3)
    .forecast_length(24)
    .backcast_length(96)
    .hidden_layer_units(256)
    .share_weights_in_stack(true);

nbeats.fit(&data, epochs=100)?;
let forecast = nbeats.predict(&data, horizon=24)?;

// Get interpretable components
let (trend, seasonality) = nbeats.decompose(&data)?;

DeepAR (Probabilistic Forecasting)

use torsh_series::forecast::neural::*;

// DeepAR provides probabilistic forecasts
let deepar = DeepAR::new()
    .input_size(1)
    .hidden_size(40)
    .num_layers(2)
    .dropout(0.1)
    .context_length(30)
    .prediction_length=10;

deepar.fit(&data, epochs=50)?;

// Get probabilistic forecast with quantiles
let median_forecast = deepar.predict(&data, quantile=0.5)?;
let lower_bound = deepar.predict(&data, quantile=0.1)?;
let upper_bound = deepar.predict(&data, quantile=0.9)?;

// Sample from predictive distribution
let samples = deepar.sample(&data, num_samples=100)?;

Anomaly Detection

use torsh_series::anomaly::*;

let data = load_ts("sensor_data.csv")?;

// Statistical anomaly detection
let detector = StatisticalAnomalyDetector::new()
    .method("zscore")
    .threshold(3.0)
    .window_size(None);

let anomalies = detector.detect(&data)?;
println!("Found {} anomalies", anomalies.sum()?);

// Isolation Forest
let iforest = IsolationForest::new()
    .n_estimators(100)
    .contamination(0.1)
    .max_samples("auto");

iforest.fit(&data)?;
let anomaly_scores = iforest.score(&data)?;
let anomalies = iforest.predict(&data)?;  // -1 for anomalies, 1 for normal

// LSTM Autoencoder for anomaly detection
let ae = LSTMAutoencoder::new()
    .encoding_dim(16)
    .sequence_length(50)
    .threshold_percentile(95);

ae.fit(&data, epochs=50)?;
let reconstruction_errors = ae.reconstruction_error(&data)?;
let anomalies = ae.detect_anomalies(&data)?;

// Seasonal Hybrid ESD (S-H-ESD) for seasonal data
let shesd = SeasonalESD::new()
    .max_anomalies(10)
    .alpha(0.05)
    .periodicity(24);

let anomalies = shesd.detect(&data)?;

Changepoint Detection

use torsh_series::changepoint::*;

let data = load_ts("regime_changes.csv")?;

// PELT (Pruned Exact Linear Time)
let pelt = PELT::new()
    .model("rbf")
    .min_size(2)
    .jump(1)
    .penalty(Some(3.0));

let changepoints = pelt.detect(&data)?;
println!("Detected changepoints at: {:?}", changepoints);

// Binary Segmentation
let binseg = BinarySegmentation::new()
    .n_changepoints(5)
    .model("l2");

let changepoints = binseg.detect(&data)?;

// Bayesian Online Changepoint Detection
let bocd = BayesianOnlineChangepointDetection::new()
    .hazard_rate(1.0 / 100.0)
    .delay(15);

let changepoint_probs = bocd.detect_online(&data)?;

// Cumulative Sum (CUSUM)
let cusum = CUSUM::new()
    .threshold(5.0)
    .drift(1.0);

let changepoints = cusum.detect(&data)?;

State Space Models

Kalman Filter

use torsh_series::state_space::*;

// Linear Kalman Filter
let kf = KalmanFilter::new()
    .state_transition(transition_matrix)
    .observation_matrix(observation_matrix)
    .process_noise(process_cov)
    .observation_noise(obs_cov)
    .initial_state(initial_state)
    .initial_covariance(initial_cov);

// Filter (estimate current state)
let filtered_states = kf.filter(&observations)?;

// Smooth (estimate all states given all observations)
let smoothed_states = kf.smooth(&observations)?;

// Predict future states
let predictions = kf.predict(horizon=10)?;

Particle Filter

use torsh_series::state_space::*;

// Particle Filter for nonlinear/non-Gaussian systems
let pf = ParticleFilter::new()
    .num_particles(1000)
    .state_transition_fn(transition_fn)
    .observation_fn(observation_fn)
    .resampling_strategy("systematic");

let estimated_states = pf.filter(&observations)?;

Hidden Markov Model (HMM)

use torsh_series::state_space::*;

// Discrete HMM
let hmm = HMM::new()
    .n_states(3)
    .n_observations(10);

hmm.fit(&observation_sequences)?;

// Viterbi algorithm - find most likely state sequence
let state_sequence = hmm.viterbi(&observations)?;

// Forward-backward algorithm - compute state probabilities
let state_probs = hmm.forward_backward(&observations)?;

// Predict next observations
let predictions = hmm.predict(&observations, horizon=5)?;

Frequency Domain Analysis

use torsh_series::frequency::*;

let data = load_ts("signal.csv")?;

// Fast Fourier Transform
let fft_result = fft(&data)?;
let power_spectrum = fft_result.abs()?.pow(2)?;

// Find dominant frequencies
let dominant_freqs = find_dominant_frequencies(&data, top_k=5)?;
println!("Dominant frequencies: {:?}", dominant_freqs);

// Periodogram
let (freqs, psd) = periodogram(&data, window="hann")?;

// Welch's method for power spectral density
let (freqs, psd) = welch(&data, nperseg=256, overlap=128)?;

// Wavelet transform
let wavelet = WaveletTransform::new("morlet");
let coeffs = wavelet.transform(&data, scales)?;

// Spectrogram
let (times, freqs, spec) = spectrogram(&data, window_size=256, overlap=128)?;

Feature Engineering

use torsh_series::features::*;

let data = load_ts("sales.csv")?;

// Create lag features
let lag_features = create_lags(&data, lags=vec![1, 7, 30])?;

// Rolling statistics
let rolling_mean = rolling_mean(&data, window=7)?;
let rolling_std = rolling_std(&data, window=7)?;
let rolling_min = rolling_min(&data, window=7)?;
let rolling_max = rolling_max(&data, window=7)?;

// Expanding statistics
let expanding_mean = expanding_mean(&data)?;
let expanding_std = expanding_std(&data)?;

// Exponentially weighted statistics
let ewm_mean = ewm_mean(&data, alpha=0.3)?;
let ewm_std = ewm_std(&data, alpha=0.3)?;

// Time-based features
let ts_features = TimeSeriesFeatures::new()
    .add_hour_of_day()
    .add_day_of_week()
    .add_day_of_month()
    .add_month_of_year()
    .add_quarter()
    .add_is_weekend()
    .add_is_holiday(holidays);

let features = ts_features.transform(&timestamps)?;

// Fourier features for seasonality
let fourier = fourier_features(&timestamps, period=365.25, order=10)?;

// Calendar features
let calendar = calendar_features(&dates, country="US")?;

Stationarity and Transformations

use torsh_series::utils::*;

let data = load_ts("non_stationary.csv")?;

// Test for stationarity
let adf_result = augmented_dickey_fuller(&data, regression="c", lags=None)?;
println!("ADF statistic: {:.4}, p-value: {:.4}", adf_result.statistic, adf_result.p_value);

if adf_result.p_value > 0.05 {
    println!("Series is non-stationary");
}

// KPSS test
let kpss_result = kpss_test(&data, regression="c", lags=None)?;

// Differencing
let diff1 = difference(&data, periods=1)?;
let diff2 = difference(&data, periods=2)?;  // Second-order differencing

// Seasonal differencing
let seasonal_diff = seasonal_difference(&data, period=12)?;

// Log transformation
let log_data = data.log()?;

// Box-Cox transformation
let (transformed, lambda) = boxcox(&data)?;
println!("Optimal lambda: {:.4}", lambda);

// Inverse transform
let original = inv_boxcox(&transformed, lambda)?;

// Detrending
let detrended = detrend(&data, method="linear")?;

Model Selection and Validation

use torsh_series::validation::*;

let data = load_ts("training_data.csv")?;

// Train-test split
let split = 0.8;
let (train, test) = train_test_split(&data, split)?;

// Time series cross-validation
let tscv = TimeSeriesSplit::new(n_splits=5, gap=0);

for (train_idx, val_idx) in tscv.split(&data) {
    let train_fold = data.index_select(0, &train_idx)?;
    let val_fold = data.index_select(0, &val_idx)?;

    // Train and validate model
    model.fit(&train_fold)?;
    let predictions = model.predict(val_fold.len(), None)?;
    let score = mae(&val_fold, &predictions)?;
}

// Expanding window cross-validation
let expanding_cv = ExpandingWindowSplit::new(
    initial_train_size=100,
    forecast_horizon=10,
    step=10,
);

// Grid search for hyperparameters
let param_grid = vec![
    ("p", vec![0, 1, 2]),
    ("d", vec![0, 1]),
    ("q", vec![0, 1, 2]),
];

let best_params = grid_search_arima(&data, &param_grid, metric="aic")?;
println!("Best parameters: {:?}", best_params);

Evaluation Metrics

use torsh_series::metrics::*;

let y_true = test_data;
let y_pred = forecasts;

// Mean Absolute Error
let mae = mean_absolute_error(&y_true, &y_pred)?;

// Root Mean Squared Error
let rmse = root_mean_squared_error(&y_true, &y_pred)?;

// Mean Absolute Percentage Error
let mape = mean_absolute_percentage_error(&y_true, &y_pred)?;

// Symmetric MAPE
let smape = symmetric_mape(&y_true, &y_pred)?;

// Mean Absolute Scaled Error
let mase = mean_absolute_scaled_error(&y_true, &y_pred, &y_train, seasonality=1)?;

// Forecast bias
let bias = forecast_bias(&y_true, &y_pred)?;

// Tracking signal
let tracking_signal = tracking_signal(&y_true, &y_pred)?;

Integration with SciRS2

This crate leverages the SciRS2 ecosystem for:

• Classical time series methods through scirs2-series
• Signal processing via scirs2-signal
• Statistical functions from scirs2-stats
• Neural network components via ToRSh modules
• Optimized tensor operations through scirs2-core

All implementations follow the SciRS2 POLICY for consistent APIs and optimal performance.

Examples

See the examples/ directory for detailed examples:

• arima_forecasting.rs - ARIMA/SARIMA modeling
• lstm_forecasting.rs - Neural forecasting with LSTM
• anomaly_detection.rs - Time series anomaly detection
• decomposition.rs - STL and seasonal decomposition
• changepoint_detection.rs - Detecting regime changes
• kalman_filter.rs - State space modeling

Performance Tips

1. Use GPU acceleration for neural forecasting models
2. Apply differencing to make series stationary before ARIMA
3. Normalize data before training neural networks
4. Use parallel processing for cross-validation
5. Cache decomposition results when used multiple times

License

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE)
• MIT license (LICENSE-MIT)

at your option.