Estimation And Prediction For Holt-Winters Time Series Models

For the theoretical part, this paper mainly introduces the additive Holt-Winters time series model with seasonal terms in single-error state space. When the error terms of the model are uncorrelated and obey a homoscedastic and normal distribution, the joint distribution of the data vector is a multivariate normal distribution by an iterative formulation. Then, on the basis of the feasible generalized least squares method of the linear models, we provide a maximum likelihood estimate method for both the unknown smoothing parameters and seed values, and then obtain the several-step ahead prediction of the model. For the case of missing data, we apply a EM method for the model to get the maximum likelihood estimators, and we also prove the convergence of the EM algorithm.For the data analysis part, we conduct the Monte-Carlo simulations to assess the effectiveness of the proposed estimation method. We use the complete generation data that the parameters and the seed values are assigned to estimate the parameters of the original unknown model with the help of the software " Mathematica". Finally, we analyze the reason of the error between the estimates and the true values.