Probabilistic Forecasting

Nixtla StatsForecast

• High-performance statistical forecasting
• Native probabilistic interval generation
• Models: AutoARIMA, AutoETS, AutoTheta, MSTL
• Conformal prediction for calibrated intervals

Implementation Patterns

TimesFM Zero-Shot Forecasting

import timesfm

# Initialize the model
tfm = timesfm.TimesFm(
    context_len=512,
    horizon_len=128,
    input_patch_len=32,
    output_patch_len=128,
    num_layers=20,
    model_dims=1280,
)
tfm.load_from_checkpoint(repo_id="google/timesfm-1.0-200m")

# Generate forecasts with confidence intervals
point_forecast, quantile_forecast = tfm.forecast(
    inputs=historical_data,
    freq=[0],  # 0 for high-frequency data
)

Nixtla StatsForecast with Intervals

from statsforecast import StatsForecast
from statsforecast.models import AutoARIMA, AutoETS

# Initialize with multiple models
sf = StatsForecast(
    models=[
        AutoARIMA(season_length=24),
        AutoETS(season_length=24)
    ],
    freq='H',  # Hourly data
    n_jobs=-1
)

# Fit and predict with confidence intervals
sf.fit(historical_df)
forecasts = sf.predict(
    h=24,  # 24-hour horizon
    level=[90, 95]  # 90% and 95% confidence intervals
)

# Result columns: AutoARIMA, AutoARIMA-lo-90, AutoARIMA-hi-90, etc.

FastAPI Integration Pattern

from fastapi import APIRouter
from typing import List

router = APIRouter()

@router.post("/forecast/air-quality")
async def forecast_air_quality(
    station_id: str,
    parameter: str,
    horizon_hours: int,
    confidence_levels: List[float] = [0.90, 0.95]
):
    # Fetch historical data from ClickHouse
    historical_data = await get_station_history(station_id, parameter)
    
    # Generate probabilistic forecast
    forecast = generate_probabilistic_forecast(
        data=historical_data,
        horizon=horizon_hours,
        levels=confidence_levels
    )
    
    return {
        "point_forecast": forecast.mean.tolist(),
        "confidence_intervals": {
            f"{int(level*100)}%": {
                "lower": forecast[f'lo-{int(level*100)}'].tolist(),
                "upper": forecast[f'hi-{int(level*100)}'].tolist()
            }
            for level in confidence_levels
        }
    }

Environmental Forecasting Considerations

Parameter-Specific Models

• PM2.5/PM10: High variability, use ensemble methods
• AQI: Composite index, forecast components separately
• Water Quality (WQI): Slower dynamics, longer horizons viable
• Noise (Lden): Strong temporal patterns, use MSTL

Seasonality Handling

# Multi-seasonal decomposition for environmental data
from statsforecast.models import MSTL

model = MSTL(
    season_length=[24, 168],  # Daily and weekly patterns
    trend_forecaster=AutoARIMA()
)

Model Performance Metrics

• CRPS (Continuous Ranked Probability Score): Primary metric for probabilistic forecasts
• Coverage: Percentage of actuals within confidence intervals
• Interval Width: Narrower is better if coverage maintained

Best Practices

1. Use at least 2-3 weeks of hourly data for training
2. Always validate coverage rates on holdout data
3. Account for seasonal patterns (daily, weekly, annual)
4. Use ensemble of models for robust predictions
5. Cache model artifacts for fast inference during demos

References

• TimesFM: https://github.com/google-research/timesfm
• Nixtla StatsForecast: https://nixtlaverse.nixtla.io/statsforecast/
• Probabilistic Forecasting Tutorial: https://nixtlaverse.nixtla.io/statsforecast/docs/tutorials/uncertaintyintervals.html