A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities, since March 8, 2020 until May 13, 2020. An empirical comparative study with Machine Learning (ML) regression, based on random
k
-fold cross-validation, and bootstrapping confidence interval and probability density estimation, is carried out. This empirical analysis also investigates the performance of ML regression models in a hard- and soft-data frameworks. The results could be extrapolated to other counts, countries, and posterior COVID-19 waves.
Supplementary Information
The online version contains supplementary material available at 10.1007/s00477-021-02021-0.
This paper presents a multivariate functional data statistical approach, for spatiotemporal prediction of COVID-19 mortality counts. Specifically, spatial heterogeneous nonlinear parametric functional regression trend model fitting is first implemented. Classical and Bayesian infinite-dimensional log-Gaussian linear residual correlation analysis is then applied. The nonlinear regression predictor of the mortality risk is combined with the plug-in predictor of the multiplicative error term. An empirical model ranking, based on random K-fold validation, is established for COVID-19 mortality risk forecasting and assessment, involving Machine Learning (ML) models, and the adopted Classical and Bayesian semilinear estimation approach. This empirical analysis also determines the ML models favored by the spatial multivariate Functional Data Analysis (FDA) framework. The results could be extrapolated to other countries.
A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive 2 -valued processes (SAR 2 processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality.
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