https://www.robjhyndman.com/papers/ijf25.pdf

25 years of time series forecasting

This paper is a critical review of exponential smoothing since the original work by Brown and Holt in the 1950s. Exponential smoothing is based on a pragmatic approach to forecasting which is shared in this review. The aim is to develop state-of-the-art guidelines for application of the exponential smoothing methodology. The first part of the paper discusses the class of relatively simple models which rely on the Holt-Winters procedure for seasonal adjustment of the data. Next, we review general exponential smoothing (GES), which uses Fourier functions of time to model seasonality. The research is reviewed according to the following questions. What are the useful properties of these models? What parameters should be used? How should the models be initialized? After the review of model-building, we turn to problems in the maintenance of forecasting systems based on exponential smoothing. Topics in the maintenance area include the use of quality control models to detect bias in the forecast errors, adaptive parameters to improve the response to structural changes in the time series, and two-stage forecasting, whereby we use a model of the errors or some other model of the data to improve our initial forecasts. Some of the major conclusions: the parameter ranges and starting values typically used in practice are arbitrary and may detract from accuracy. The empirical evidence favours Holt's model for trends over that of Brown. A linear trend should be damped at long horizons. The empirical evidence favours the Holt-Winters approach to seasonal data over GES. It is difficult to justify GES in standard form–the equivalent ARIMA model is simpler and more efficient. The cumulative sum of the errors appears to be the most practical forecast monitoring device. There is no evidence that adaptive parameters improve forecast accuracy. In fact, the reverse may be true.

Exponential smoothing: The state of the art

An innovations state space modeling framework is introduced for forecasting complex seasonal time series such as those with multiple seasonal periods, high-frequency seasonality, non-integer seasonality, and dual-calendar effects. The new framework incorporates Box–Cox transformations, Fourier representations with time varying coefficients, and ARMA error correction. Likelihood evaluation and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensive approach to forecasting complex seasonal time series. A key feature of the framework is that it relies on a new method that greatly reduces the computational burden in the maximum likelihood estimation. The modeling framework is useful for a broad range of applications, its versatility being illustrated in three empirical studies. In addition, the proposed trigonometric formulation is presented as a means of decomposing complex seasonal time series, and it is show...

/pdf/forecasting-time-series-with-complex-seasonal-patterns-using-559fdkmheo.pdf

Forecasting time series with complex seasonal patterns using exponential smoothing

https://www.bauer.uh.edu/gardner/docs/pdf/Exponential-Smoothing.pdf

Exponential smoothing: the state of the art, part ii

The Holt-Winters forecasting procedure is a variant of exponential smoothing which is simple, yet generally works well in practice, and is particularly suitable for producing short-term forecasts for sales or demand time-series data. Some practical problems in implementing the method are discussed, including the normalisation of seasonal indices, the choice of starting values and the choice of smoothing parameters. There is an important distinction between an automatic and a nonautomatic approach to forecasting and detailed suggestions are made for implementing Holt-Winters in both ways. The question as to what underlying model, if any, is assumed by the method is also addressed. Some possible areas for future research are then outlined.

Holt-Winters Forecasting: Some Practical Issues

This paper is concerned with the formulation of short-term forecasting models, and introduces a range of models of considerable importance. These are defined in terms of predictions and sensible updating mechanisms for estimates of quantities such as level, growth, and seasonality, and constitute generalizations of familiar linear exponential smoothing predictors. They are shown to be equivalent to particular ARIMA models, and generally these do not lie within that subset of the ARIMA class which forms the basis of the Box-Jenkins modelling approach. It is argued that the models of this paper have a reasoned structure, and are to be preferred to the Box-Jenkins models for most socio-economic applications.

https://www.jstor.org/stable/pdfplus/2631264.pdf

A General Class of Holt-Winters Type Forecasting Models

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A General Class of Holt-Winters Type Forecasting Models