Application of non-Gaussian multidimensional autoregressive model for climate data prediction

Abstract

From the point of view of agriculture, ecology, or environmental engineering, the capability of forecasting meteorological variables in the long and short term is crucial. Short-term forecasts enabling the planning of field work in agriculture, management of mass events, or tourism are important, while long-term forecasts related to advancing climate change are also very interesting. In the literature, there are known many approaches that can be used to forecast climate time series. The most common is based on the statistical modelling of the corresponding data, and the prediction is made on the fitted model. There are known one-dimensional approaches, where single variables are modeled separately; however, in the last decade, there appears a new trend which assumes the importance of the relationship between different time series. This is the approach considered in this paper. We propose to examine the climate data (temperature and precipitation) using the multidimensional vector autoregressive model (VAR). However, because in the time series we observe non-Gaussian behaviour, the classical VAR model can not be applied and the multidimensional Gaussian noise is replaced by the $$\alpha -$$ α - stable one. This model was previously analyzed by the authors in the context of financial data description where also non-Gaussian characteristics are observed. The main goal of this paper is to answer the question whether there are reasons to go from the Gaussian model to the generalized models, like $$\alpha -$$ α - stable based. The second purpose is to link total precipitation data with temperature time series. In the classical approach, precipitation was treated as a variable not correlated with temperature, which, as we will show in the paper, is inconsistent with reality. We hope the presented in this paper results open new areas of interest related to climate data modelling and prediction.

Estimating stratospheric polar vortex strength using ambient ocean‐generated infrasound and stochastics‐based machine learning

“…It is established in the literature that dynamical systems of weather variables are well represented by statistical linear autoregressive models (e.g., Benth et al ., 2008; Benth & Benth, 2010; Broszkiewicz‐Suwaj & Wyłomańska, 2021; Campbell & Diebold, 2005; Eggen, 2022; Eggen et al ., 2022). Overviews and implementations of such models are provided in Brockwell and Davis (2016) and Gómez (2019).…”

Alpha-Stable Autoregressive Modeling of Chua's Circuit in the Presence of Heavy-Tailed Noise

“…Some examples that might have heavy-tailed behavior include tracking highly maneuvering objects (Gan and Godsill 2020;Gan et al 2021), interference in IoT networks (Clavier et al 2021), financial data (McCulloch 1996Maleki et al 2020;Janczura et al 2011;Wesselhöfft 2021), chaotic systems (Savaci and Yilmaz 2015;Contreras-Reyes 2021), frequency fluctuations in the power grid (Schäfer et al 2018;Anvari et al 2020), the dose distributions for proton breast treatment (Van den Heuvel et al 2015), proton pencil beams for cancer therapy (Van den Heuvel et al 2018), climate dynamics (Ditlevsen 1999;Broszkiewicz-Suwaj and Wyłoma ńska 2021). Therefore, alpha-stable (α-stable) distributions are more suitable for modeling such impulsive behavior (Nolan 2003).…”