Over the last three decades, accurate modeling and forecasting of electricity prices has become a key issue in competitive electricity markets. As electricity price series usually exhibit several complex features, such as high volatility, seasonality, calendar effect, non-stationarity, non-linearity and mean reversion, price forecasting is not a trivial task. However, participants of electricity market need price forecast to make decisions in their daily activity in the market, such as trading, risk management or future planning. In this study we consider linear and nonlinear models for one-day-ahead forecast of electricity prices using components estimation techniques. This approach requires to filter out the structural, deterministic components from the original time series and to model the residual component by means of some stochastic process. The final forecast is obtained by combining the predictions of both these components. In this work, linear and non-linear models are applied to both, deterministic and stochastic, components. In the case of stochastic component, AutoRegressive, Nonparametric AutoRegressive, Functional AutoRegressive, and Nonparametric Functional AutoRegressive have been considered. Furthermore, two naïve benchmarks are applied directly to the price time series and their results are compared with our proposed models. An application of the proposed methodology is presented for the Italian electricity market (IPEX). Our analysis suggests that, in terms of Mean Absolute Error, Mean Absolute Percentage Error, and Pearson correlation coefficient, best results are obtained when deterministic component is estimated by using parametric approach. Further, Functional AutoRegressive model performs relatively better than the rest while Nonparametric AutoRegressive is highly competitive. INDEX TERMS Electricity prices forecasting, Parametric and nonparametric models, Univariate and multivariate time series, Modeling and forecasting, IPEX

Time Between Events (TBE) charts have advantages over the traditional control charts when monitoring high quality processes with very low defect rates. This article introduces a new discrete TBE control chart following discrete Weibull distribution. The design of the proposed chart is derived analytically and discussed numerically. Moreover, the performance is assessed by using the Average Run Length (ARL) and the Coefficient of Variation of Run Length (CVRL). Besides simulation studies, the proposed scheme is also illustrated using four real data examples. INDEX TERMS Average run length, discrete Weibull distribution, coefficient of variation, process monitoring.

Control charts are a popular statistical process control (SPC) technique for monitoring to detect the unusual variations in different processes. Contrary to the classical charts, control charts have also been modified to include covariates using regression approaches. is study assesses the performance of risk-adjusted control charts under the complexity of estimation error by considering logistic and negative binomial regression models. To be more precise, risk-adjusted Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are used to evaluate the impact of the estimation error. To compute the average run length (ARL), Markov Chain Monte Carlo simulations are conducted. Furthermore, a bootstrap method is also used to compute the ARL assuming different Phase-I data sets to minimize the effect of estimation error on risk-adjusted control charts. e results for cardiac surgery and respiratory disease data sets show that the modified control charts improve the performance in detecting small shifts.

A control chart named as the hybrid double exponentially weighted moving average (HDEWMA) to monitor the mean of Weibull distribution in the presence of type-I censored data is proposed in this study. In particular, the focus of this study is to use the conditional median (CM) for the imputation of censored observations. The control chart performance is assessed by the average run length (ARL). A comparison between CM-DEWMA control chart and CM-based HDEWMA control chart is also presented in this article. Assuming different shift sizes and censoring rates, it is observed that the proposed control chart outperforms the CM-DEWMA chart. The effect of estimation, particularly the scale parameter estimation, on ARL is also a part of this study. Finally, a practical example is provided to understand the application and to investigate the performance of the proposal in practical scenarios.

To study the high quality processes, Time-between-events (TBE) control charts have several advantages over the ordinary control charts. However, the existing TBE charts are based on the exponential distribution, which limit the application of these charts to monitor rare events. Therefore, to generalize existing exponential TBE charts, recently two new TBE charts assuming Weibull and generalized exponential distributions for the inter-arrival times of the renewal process, have been proposed in the literature. The main aim of this study is to present a detailed comparison of these charts. We use the expected quadratic loss (EQL), relative average run length (RARL), continuous rank probability score (CRPS) and closeness measure to assess the performance of the Weibull and the generalized exponential charts. We also discuss four real data examples in this article. INDEX TERMS Average run length, continuous rank probability score, Expected quadratic loss, Generalized exponential distribution, High quality process, Relative average run length, Weibull distribution.