Mathematical Genesis of the Spatio-Temporal Covariance Functions

Obtaining new and flexible classes of nonseparable spatio-temporal covariances have resulted in a key point of research in the last years within the context of spatiotemporal Geostatistics. Approach: In general, the literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Results: By exploring mathematical properties of positive definite functions and their close connection to covariance functions we are able to develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Conclusion/Recommendations: The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.Spatial anisotropy, bernstein and complete monotone functions, spatio-temporal geostatistics, positive definite functions, space-time modeling, spatio-temporal data

Mathematical Genesis of the Spatio-Temporal Covariance Functions

Obtaining new and flexible classes of nonseparable spatio-temporal covariances have resulted in a key point of research in the last years within the context of spatiotemporal Geostatistics. Approach: In general, the literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Results: By exploring mathematical properties of positive definite functions and their close connection to covariance functions we are able to develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Conclusion/Recommendations: The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability

Inference and testing breaks in large dynamic panels with strong cross sectional dependence

In this paper we provide a new Central Limit Theorem for estimators of the slope papers in large dynamic panel data models (where both n and T increase without bound) in the presence of, possibly, strong cross-sectional dependence. We proceed by providing two related tests for breaks/homogeneity in the time dimension. The first test is based on the CUSUM principle; the second test is based on a Hausman–Durbin–Wu approach. Some of the key features of the tests are that they have nontrivial power when the number of individuals, for which the slope parameters may differ, is a “negligible” fraction or when the break happens to be towards the end of the sample, and do not suffer from the incidental parameter problem. We provide a simple bootstrap algorithm to obtain (asymptotic) valid critical values for our statistics. An important feature of the bootstrap is that there is no need to know the underlying model of the cross-sectional dependence. A Monte-Carlo simulation analysis sheds some light on the small sample behaviour of the tests and their bootstrap analogues. We implement our test to some real economic data

Geostatistical spatiotemporal modelling with application to the western king prawn of the Shark Bay managed prawn fishery

Geostatistical methodology has been employed in the modelling of spatiotemporal data from various scientific fields by viewing the data as realisations of space-time random functions. Traditional geostatistics aims to model the spatial variability of a process so, in order to incorporate a time dimension into a geostatistical model, the fundamental differences between the space and time dimensions must be acknowledged and addressed. The main conceptual viewpoint of geostatistical spatiotemporal modelling identified within the literature views the process as a single random function model utilising a joint space-time covariance function to model the spatiotemporal continuity. Geostatistical space-time modelling has been primarily data driven, resulting in models that are suited to the data under investigation, usually survey data involving fixed locations. Space-time geostatistical modelling of fish stocks within the fishing season is limited as the collection of fishery-independent survey data for the spatiotemporal sampling design is often costly or impractical. However, fishery-dependent commercial catch and effort data, throughout each season, are available for many fisheries as part of the ongoing monitoring program to support their stock assessment and fishery management. An example of such data is prawn catch and effort data from the Shark Bay managed prawn fishery in Western Australia. The data are densely informed in both the spatial and temporal dimensions and cover a range of locations at each time instant. Both catch and effort variables display an obvious spatiotemporal continuity across the fishing region and throughout the season. There is detailed spatial and temporal resolution as skippers record their daily fishing shots with associated latitudinal and longitudinal positions. In order to facilitate the ongoing management of the fishery, an understanding of the spatiotemporal dynamics of various prawn species within season is necessary. A suitable spatiotemporal model is required in order to effectively capture the joint space-time dependence of the prawn data. An exhaustive literature search suggests that this is the first application of geostatistical space-time modelling to commercial fishery data, with the development and evaluation of an integrated space-time geostatistical model that caters for the commercial logbook prawn catch and effort data for the Shark Bay fishery. The model developed in this study utilises the global temporal trend observed in the data to standardise the catch rates. Geostatistical spatiotemporal variogram modelling was shown to accurately represent the spatiotemporal continuity of the catch data, and was used to predict and simulate catch rates at unsampled locations and future time instants in a season. In addition, fishery-independent survey data were used to help improve the performance of catch rate estimates