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**Approaches for multi-step density forecasts with application to aggregated wind power.**
*(English)*
Zbl 1202.62129

Ann. Appl. Stat. 4, No. 3, 1311-1341 (2010); correction ibid. 4, No. 4, 2205 (2010).

Summary: The generation of multi-step density forecasts for non-Gaussian data mostly relies on Monte Carlo simulations which are computationally intensive. Using aggregated wind power in Ireland, we study two approaches of multi-step density forecasts which can be obtained from simple iterations so that intensive computations are avoided. In the first approach, we apply a logistic transformation to normalize the data approximately and describe the transformed data using ARIMA-GARCH models so that multi-step forecasts can be iterated easily. In the second approach, we describe the forecast densities by truncated normal distributions which are governed by two parameters, namely, the conditional mean and conditional variance. We apply exponential smoothing methods to forecast the two parameters simultaneously. Since the underlying model of exponential smoothing is Gaussian, we are able to obtain multi-step forecasts of the parameters by simple iterations and thus generate forecast densities as truncated normal distributions. We generate forecasts for wind power from 15 minutes to 24 hours ahead. Results show that the first approach generates superior forecasts and slightly outperforms the second approach under various proper scores. Nevertheless, the second approach is computationally more efficient and gives more robust results under different lengths of training data. It also provides an attractive alternative approach since one is allowed to choose a particular parametric density for the forecasts, and is valuable when there are no obvious transformations to normalize the data.

### MSC:

62M20 | Inference from stochastic processes and prediction |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62P12 | Applications of statistics to environmental and related topics |

65C05 | Monte Carlo methods |

### Keywords:

non-Gaussian time series; logistic transformation; exponential smoothing; truncated normal distribution; ARIMA-GARCH model; continuous ranked probability score
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\textit{A. Lau} and \textit{P. McSharry}, Ann. Appl. Stat. 4, No. 3, 1311--1341 (2010; Zbl 1202.62129)

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