sketch_holt.nx

sketch_holt.nx -- Holt's linear method (double exponential smoothing). Time-series forecasting primitive that extends EWMA with a TREND component. Two recurrences: level_t = alpha * y_t + (1 - alpha) * (level_{t-1} + trend_{t-1}) trend_t = beta * (level_t - level_{t-1}) + (1 - beta) * trend_{t-1} forecast(h) = level_t + h * trend_t (h steps ahead) alpha controls level smoothing; beta controls trend smoothing. Both in PPM [1, 1_000_000]. COMPLEMENTS EWMA (single-component): - EWMA: smoothed level only; bad for trending data - Holt: level + trend; tracks linear trajectories - (Holt-Winters with seasonality is the natural v2) USE CASES: - revenue / user-count forecasting - SRE: capacity planning given growth trends - sensor calibration drift detection INTEGER FIXED-POINT IMPLEMENTATION (no f64): level, trend stored as i64. Updates via PPM arithmetic. Overflow budget: |y| < 2^32 to keep alpha * y in i64. LOSSLESS-LANGUAGE DISCIPLINE: Production tier; envelope NX_ENV_ABS with param_a = 1 (quantization error per step) and conf 1e9.