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For example, where the ADF tests use a parametric autoregression to approximate the ARMA structure of the errors in the test regression, the PP test ignore any serial correlation in the test regression.
The outputs of the training part are K SVM models for the spot forecast, K SBL models for the error distribution forecast, and one copula-based DCCMR model describing the temporal-spatial interdependence structure of the errors.
The method also provides maximum likelihood (ML) estimates of the Hurst exponent (which can be readily translated to the fractal dimension or spectral exponent) characterizing the correlational structure of the errors, and the error variance.
With this method, the regression model is estimated using ordinary least squares, but the standard errors are estimated without imposing a constraint (either assumed or modelled) on the structure of the errors.
The correlation structure of the errors, using the ARMA (p,q) process, was provided as a model input based on steps 1 and 2. Model acceptance was based on behaviour of model residuals.
The funnel shape of the Bland Altman plots showed that the three interpolation techniques tended to overestimate the air pollution concentrations compared with the building matching, particularly for higher values, supporting a multiplicative structure of the errors.
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However, this procedure requires additional assumptions on the structure of the error model.
A detailed accuracy test is performed, revealing the structure of the error and the effect of how the convective terms are discretized near the boundary.
To this aim first the structure of the error on point measurements and its propagation on the space travelled are investigated.
Where, D t is a vector of deterministic term (constant, trend etc)., n for lagged difference term, ∆x t − i term for ARMA structure of the error and ε t is for white nose (error term).
The structure of the error matrix thus contains mainly zeros except in its upper right submatrix, which itself is a diagonal matrix whose diagonal is composed of the elements, with (16).
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