<span lang="EN-US">This research presents a methodology for predicting errors of parameters, as the algorithm tries to monitor parameters in order maintain or replace them when needed avoid excessive expenses. The presented implementation mechanism is based on monitoring according specific number batches and each batch consists iterations, which turn are samples. proposed involves designi...

Home Energy Management Systems (HEMSs) are expected to become an inevitable part of the future smart grid technologies. To work effectively, HEMSs require reliable and accurate load forecasts. In this paper, two new modelling methods presented. They both suited for producing multivariate probabilistic forecasts, which consider temporal correlation between forecast horizons. The first method emp...

The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. Baddeley et al. (2005) as an empirical counterpart of the Campbell equilibrium equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs ...

We propose two sequential monitoring schemes for detecting a change in scale. We consider a stable historical period of length m. The goal is to propose test with asymptotically small probability of false alarm and power 1 as the length of the historical period tends to infinity. The distribution under the null hypothesis and also under the alternative hypothesis is shown. A small simulation st...

In this study, the residuals in time series analysis, which were classified in four different classes as ”conditional residuals”, ”unconditional residuals”, ”innovation” and ”normalized residuals”, are calculated by a simulation study for the ARMA model under certain parameter values for different numbers of observation and their conditions in diagnostic checking are examined using the test sta...

Christensen and Lin (2014), henceforth C-L, suggested two lack-of-fit tests to assess the adequacy of a linear model based on partial sums of residuals. In particular, their tests evaluated the adequacy of the mean function. Their tests relied on asymptotic results without requiring small sample normality. We extend this research by proposing additional tests based on partial sums of residuals....