2017/12/28 by Moreno Bevilacqua, Bevilacqua, Moreno, Tarik Faouzi +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Environmental Science · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Hydrological Forecasting Using AI #Methodology (stat.ME) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.1712.09957
openalex publication_date 2017/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study estimation and prediction of Gaussian processes with covariance\nmodel belonging to the generalized Cauchy (GC) family, under fixed domain\nasymptotics. Gaussian processes with this kind of covariance function provide\nseparate characterization of fractal dimension and long range dependence, an\nappealing feature in many physical, biological or geological systems. The\nresults of the paper are classified into three parts. In the first part, we\ncharacterize the equivalence of two Gaussian measures with GC covariance\nfunction. Then we provide sufficient conditions for the equivalence of two\nGaussian measures with Mat 'ern (MT) and GC covariance functions and two\nGaussian measures with Generalized Wendland (GW) and GC covariance functions.\nIn the second part, we establish strong consistency and asymptotic distribution\nof the maximum likelihood estimator of the microergodic parameter associated to\nGC covariance model, under fixed domain asymptotics. The last part focuses on\noptimal prediction with GC model and specifically, we give conditions for\nasymptotic efficiency prediction and asymptotically correct estimation of mean\nsquare error using a misspecified GC, MT or GW model, under fixed domain\nasymptotics. Our findings are illustrated through a simulation study: the first\ncompares the finite sample behavior of the maximum likelihood estimation of the\nmicroergodic parameter of the GC model with the given asymptotic distribution.\nWe then compare the finite-sample behavior of the prediction and its associated\nmean square error when the true model is GC and the prediction is performed\nusing the true model and a misspecified GW model.\n