Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing

Abstract

A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.

Cyclical Patterns in Risk Indicators Based on Financial Market Infrastructure Transaction Data

“…The dummy variables we include in the ARIMA models relate to the day of the week, months and decision by the Governing Council (with respect to the reserve maintenance period). The state space models are introduced by De Livera et al (2011) and Hyndman and Athanasopoulos (2013). They study forecasting time series with complex seasonal patterns using exponen-1 These time series are the basis of the risk indicator development by Berndsen and Heijmans (2017).…”

Predicting the Evolution of CO2 Emissions in Bahrain with Automated Forecasting Methods

“…Additionally, see Chatfield [15] for a more in-depth overview of the Holt-Winters Model. The BATS and TBATS models, which are in the exponential-smoothing framework and are capable of handling multiple seasonalities as well as complex seasonalities were proposed by De Livera, Hyndman and Snyder (2011) [17]. Here, we fit a BATS/TBATS model applied to the time series of carbon dioxide emissions in Bahrain through the forecast package in R. Parallel processing is used by default to speed up the computations.…”

http://www.growingscience.com/msl/Vol5/msl_2015_43.pdf

“…A good earnings forecast helps investors make better investment decisions and build a portfolio with better performance (De Livera et al, 2011). It also helps reduce stock price fluctuation and investors do not have to worry about the day to day stock market events (Kasznik, 1996).…”