Holt-Winters Method with Missing Observations

Abstract

The paper presents a simple procedure for interpolating, smoothing, and predicting in seasonal time series with missing observations. The approach suggested by Wright (Wright, D. J. 1986. Forecasting data published at irregular time intervals using extension of Holt's method. Management Sci. 32 499--510.) for the Holt's method with nonseasonal data published at irregular time intervals is extended to the Holt-Winters method in the seasonal case. Numerical examples demonstrate the procedure.missing observations, seasonality, Holt-Winters method

Exponential smoothing for irregular data

“…the ad hoc exponential smoothing method with three smoothing coefficients for local linear trends combined with seasonality) for irregular data suggested by Cipra (see [5]). The additive method is…”

“…Such a situation can include as a special case time series with missing observations (see also [2], [5], [8]). Simple exponential smoothing and Holt's method for irregular data have been suggested by Wright (see [9]).…”

Short-Term Traffic Speed Forecasting Based on Data Recorded at Irregular Intervals

“…In 1986, Wright [3] further developed the simple exponential smoothing method and Holt's method by extending the use of weighted averages for irregularly spaced data. In 1995, Cipra et al [4] expanded on Wright's modification of Holt's method by proposing an extended version of the Holt-Winters method for data taken at irregular time intervals. In 2004, Carmo and Rodrigues [5] compared the methods of Wright and Croston to a neural network method to show how the neural network can be used for filtering and forecasts.…”

Seasonal time series with missing observations

“…Wright [6] proposed to treat the problem of missing observations as irregularly spaced data, and modified in that sense the nonseasonal exponential smoothing methods. Cipra et al [5] suggested an extension of Wright's approach to the (seasonal) Holt-Winters method. Utilizing the fact that exponential smoothing techniques are optimal provided the investigated process follows a certain ARIMA model, Aldrin and Damsleth [3] derived optimal smoothing constants for non seasonal methods for a single gap of missing observations.…”