In this paper we present a copula-based model for a binary and a continuous variable in a time series setup. Within this modeling framework both marginals can be equipped with their own dynamics whereas the contemporaneous dependence between both processes can be flexibly captured via a copula function. We propose a method for testing the goodness-of-fit of such a time series model using probability integral transforms (PIT). This verification procedure allows not only a verification of the goodness-of-fit of the estimated marginal distribution for a continuous variable but also the conditional distribution of a continuous variable given the outcome of its binary counterpart (i.e. the adequacy of the copula choice). We test the model on an empirical example: investigating the relationship between trading volume and the indicators of arbitrarily ’large’ price movements on the interbank EUR/PLN spot market.

The paper considers the modeling and estimation of the stochastic frontier model where the error components are assumed to be correlated and the inefficiency error is assumed to be autocorrelated. The multivariate Farlie-Gumble-Morgenstern (FGM) and normal copula are used to capture both the contemporaneous and the temporal dependence between, and among, the noise and the inefficiency components. The intractable multiple integrals that appear in the likelihood function of the model are evaluated using the Halton sequence based Monte Carlo (MC) simulation technique. The consistency and the asymptotic efficiency of the resulting simulated maximum likelihood (SML) estimators of the present model parameters are established. Finally, the application of model using the SML method to the real life US airline data shows significant noise-inefficiency dependence and temporal dependence of inefficiency.

In the paper, we document how conditional dependencies observed in the FOREX market change during a trading day. The analysis is performed for the pairs (GBP/EUR, USD/EUR) and (GBP/USD, EUR/USD) of exchange rates. We consider daily returns calculated using the exchange rates quoted at different hours of a day. The dynamics of the dependencies is modeled by means of 3-regime Markov regime switching copula models, and the strength of the linkages is described using dynamic Spearman’s rho and the dynamic coefficients of tail dependence. The established approach allows us to monitor the changes in the dependence structure.

The aim of the study is to formally compare the explanatory power of Copula-GARCH and MGARCH models. The models are estimated for logarithmic daily rates of return of two exchange rates: EUR/PLN, USD/PLN and stock market indices: SP500, BUX. The analysis is performed within the Bayesian framework. The posterior model probabilities point to AR(1)-tSBEKK(1,1) for the exchange rates and VAR(1)-tCopula-GARCH(1,1) for the stock market indices, as the superior specifications. If the marginal sampling distributions are different in terms of tail thickness, the Copula-GARCH models have higher explanatory power than the MGARCH models.

Against the background of increasing installed capacity of wind power in the power generation system, high-precision ultra-short-term wind power prediction is significant for safe and reliable operation of the power generation system. We present a method for ultra-short-term wind power prediction based on a copula function, bivariate empirical mode decomposition (BEMD) algorithm and gated recurrent unit (GRU) neural network. First we use the copula function to analyze the nonlinear correlation between wind power and external factors to extract the key factors influencing wind power generation. Then the joint data composed of the key factors and wind power are decomposed into a series of stationary subsequence data by a BEMD algorithm which can decompose the bivariate data jointly. Finally, the prediction model based on a GRU network uses the decomposed data as the input to predict the power output in the next four hours. The experimental results show that the proposed method can effectively improve the accuracy of ultra-short-term wind power prediction.

In this study, an energy-based spectrum sensing method combined with copula theory is proposed for cognitive radio systems. In the proposed spectrum sensing model, cognitive radio users first make their own local spectrum decision with energy-based spectrum sensing. Then, they forward their decision to the fusion center. In the fusion center, this decision is compared with the threshold value determined by copula theory and global spectrum decision is made. The test statistic at the fusion center were obtained with the Neyman Pearson approach. Thus, the fusion rule was created for the fusion center and necessary simulation studies were performed. According to the results of the simulation studies, the proposed detection method showed better results than the traditional energy based detection method.