# gace-introduction

Introduction to GACE: Generalized Adaptive Capped Estimator

Overview The Generalized Adaptive Capped Estimator (GACE) is a deterministic forecasting framework designed for stable and interpretable projections across weekly, monthly, quarterly, and yearly time series.

Unlike stochastic models, GACE uses a structured set of growth components and volatility-aware caps that ensure consistent behavior, even for noisy business or operational data.

This vignette introduces: • preprocessing and growth extraction, • growth capping, • seasonal factor construction, • recursive forecast generation, • how to use gace_forecast() and plot_gace().

Basic Usage library(GACE)

set.seed(1) y <- ts(rnorm(60, mean = 100, sd = 10), frequency = 12)

fc <- gace_forecast( df = y, periods = 12, freq = “month” )

head(fc)

Plotting the Forecast plot_gace(fc)

How GACE Works

1. Preprocessing GACE optionally cleans the input using: • winsorization of extreme values, • preservation of zeros, • minimal smoothing.

2. Growth Components GACE extracts four growth signals: • Year-over-year • Short-term (lag-1) • Rolling-window movement • Drift / long-run trend

These signals are trimmed, averaged, and dynamically stabilized.

3. Volatility-Aware Caps GACE applies asymmetric caps such as −0.30 to +0.30. Caps adapt when series volatility increases.

4. Seasonal Factors If seasonal = TRUE and frequency > 1, GACE computes smoothed, normalized seasonal loads.

5. Recursive Forecast future = level * (1 + growth_t) * seasonal_factor_t

with decay parameters gamma and beta.

Multi-frequency Support

Weekly → “week” Monthly → “month” Quarterly → “quarter” Yearly → “year”

Conclusion GACE provides a transparent, reproducible, and fast method for forecasting operational time series.