The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Recently, new statistical models have been proposed to provide stochastic simulations of high-resolution data to downscale and forecast solar irradiance measurements. Most of the existing models are linear and highly depend on normality assumptions. However, solar irradiance shows strong nonlinearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive model to quantify the variability of the daily irradiance time series. We establish the sufficient conditions for our model to be stationary, and we develop an inferential procedure to estimate the model parameters. When we apply our model to study the statistical properties of observed irradiance data in Guadeloupe island group, a French overseas region located in the Southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear-sky and non-clear sky regimes. Using our model, we are able to simulate irradiance series that behave similarly to the real data in mean and variability, and more accurate forecasts compared to linear models.

中文翻译：

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使用阈值时间序列模型的多日太阳辐照度统计分析

太阳辐照度分析在预测太阳能发电厂的太阳能生产方面具有重要应用。尽管太阳每天提供的能量比我们需要的要多，但环境条件引起的变化会影响电力生产。最近，已经提出了新的统计模型来提供高分辨率数据的随机模拟，以缩小和预测太阳辐照度测量值。大多数现有模型是线性的，并且高度依赖于正态假设。然而，太阳辐照度表现出很强的非线性，并且只在白天进行测量。因此，我们提出了一种新的多日阈值自回归模型来量化每日辐照度时间序列的可变性。我们建立了模型静止的充分条件，我们开发了一个推理程序来估计模型参数。当我们应用我们的模型研究位于南加勒比海的法国海外地区瓜德罗普岛群观测到的辐照度数据的统计特性时，我们能够表征辐照度系列的两个状态。这些状态代表晴空和非晴空状态。使用我们的模型，我们能够模拟在均值和变异性方面与真实数据表现相似的辐照度序列，并且与线性模型相比，预测更准确。这些状态代表晴空和非晴空状态。使用我们的模型，我们能够模拟在均值和变异性方面与真实数据表现相似的辐照度序列，并且与线性模型相比，预测更准确。这些状态代表晴空和非晴空状态。使用我们的模型，我们能够模拟在均值和变异性方面与真实数据表现相似的辐照度序列，并且与线性模型相比，预测更准确。