Forecasting

Time-series forecasting predicts future values from observed history. In an operational context — infrastructure monitoring, capacity planning, SLA management — forecasts drive automated….

Time-series forecasting predicts future values from observed history. In an operational context — infrastructure monitoring, capacity planning, SLA management — forecasts drive automated decisions: scale-out triggers, anomaly baselines, budget projections.

Taxonomy of Methods

Chronix implements classical statistical forecasters. The table below places each method in the broader forecasting landscape:

Family	Method	Trend	Seasonality	Complexity
Exponential Smoothing	Simple (SES)	✗	✗	O(n)
	Holt	✓	✗	O(n)
	Holt-Winters	✓	✓	O(n)
Autoregressive	ARIMA	✓	✗	O(n·p²)
	SARIMA	✓	✓	O(n·(p+P·s)²)

When to Use What

                     Seasonality?
                     ╱          ╲
                  Yes            No
                  ╱                ╲
            Strong trend?      Strong trend?
            ╱       ╲          ╱       ╲
          Yes       No       Yes       No
           │         │        │         │
       Holt-     Seasonal   Holt      SES
       Winters   ARIMA      or
       or                   ARIMA
       SARIMA

Rules of thumb:

SES — flat series, short horizons, no seasonal pattern
Holt — trended series without seasonality
Holt-Winters — trended series with clear periodic seasonality
ARIMA — auto-correlated residuals, non-seasonal
SARIMA — auto-correlated residuals with seasonal component

Or skip the chart: auto_forecast fits every eligible candidate and picks by out-of-sample error at the horizon you asked for, and tells you what it tried (see Model Selection).

use chronix_analytics::forecast::{auto_forecast, AutoForecastOptions};

let chosen = auto_forecast(&timestamps, &values, 24, &AutoForecastOptions::default())?;
println!("{} — {} {:.3}", chosen.selection.label, chosen.selection.metric, chosen.selection.score);

Forecast Horizon

The forecast horizon h is the number of future time steps to predict. All Chronix forecasters produce h point estimates plus optional prediction intervals (see Prediction Intervals).

Forecast accuracy degrades with increasing h. A common heuristic is to keep h ≤ n/3 where n is the training history length.

Stationarity

Many methods assume stationarity — the statistical properties (mean, variance, autocorrelation) do not change over time. Non-stationary series are made stationary through differencing:

$$ y't = y_t - y{t-1} $$

Second-order differencing removes quadratic trends:

$$ y''t = y't - y'{t-1} = y_t - 2y{t-1} + y_{t-2} $$

ARIMA automates this through its d parameter. Exponential smoothing methods handle non-stationarity implicitly through level and trend components.

Integration with Chronix

Forecasters are registered through the Model Lifecycle system, which handles versioning, training, and retraining. The query engine exposes forecasting through the FORECAST SQL extension:

SELECT forecast(value, _time, 24) FROM metrics
WHERE metric_name = 'cpu'
  AND _time > now() - INTERVAL '7 days';

Deep dives into each method family follow in the sub-sections.