Estimasi parameter robust holt-winters smoothing dengan robustified maximum likelihood

Abstract

Time series data is a collection of data with certain time intervals. Time series data processing models include Moving Average (MA), Autoregressive, and smoothing. Forecasting time series data with trends and seasonal popular using Holt-Winters smoothing. Holt-Winters exponential smoothing is good at predicting data patterns with simultaneous trend and seasonal effects. Holt-Winters smoothing gives weighting to the data with certain criteria. However, the Holt-Winters smoothing model is not robust for outliers. Data containing outliers affect parameters and forecasts. The method used to overcome outliers is robust. Robust Holt-Winters model with cleaned using the Huber function on outlier data weighting. Parameter estimation in the data contains popular trend and seasonality using likelihood parameter estimation. However, the likelihood estimation is not robust to the data series with outliers. Estimator τ used in the data model with outliers. Weighting is done on the data containing outliers with the ρ function. The purpose of this article is to estimate the parameters of the Holt-Winters smoothing using maximum likelihood with τ estimator. The research method is carried out by studying literature from articles, books, and journals. The results obtained are the robust Holt-Winters smoothing model with the estimated parameters robustified maximum likelihood. The robustified maximum likelihood form replaces the square of the error with τ estimator.