Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing
Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing
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DOI：
10.1198/jasa.2011.tm09771
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发表时间：
2011-12-01
影响因子：
3.7
通讯作者：
Snyder, Ralph D.
中科院分区：
文献类型：
--
作者：
De Livera, Alysha M.;Hyndman, Rob J.;Snyder, Ralph D.
介绍了一种新的状态空间建模框架，用于预测复杂的季节性时间序列，例如具有多个季节性周期，高频季节性，非整数季节性和双日历效应的时间序列。新框架结合了Box-Cox变换、时变系数傅立叶表示和阿尔马误差校正。高斯误差假设下的点预测和区间预测的似然估计和解析表达式推导，导致一个简单，全面的方法来预测复杂的季节性时间序列。该框架的一个关键特征是，它依赖于一种新的方法，大大减少了最大似然估计的计算负担。建模框架是有用的广泛的应用，其多功能性被说明在三个实证研究。此外，建议的三角公式作为一种手段分解复杂的季节性时间序列，它表明，这种分解导致识别和提取的季节性成分，否则不明显的时间序列图本身。
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 shown that this decomposition leads to the identification and extraction of seasonal components which are otherwise not apparent in the time series plot itself.