Dynamic dependence structure between energy markets and the Italian stock index


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The dependence structure between the main energy markets (such as crude oil, natural gas, and coal) and the main stock index plays a crucial role in the economy of a given country. As the dependence structure between these series is dramatically complex and it appears to change over time, time-varying dependence structure given by a class of dynamic copulas is taken into account.
To this end, each pair of time series returns with a dynamic t-Student copula is modelled, which takes as input the time-varying correlation. The correlation evolves with the DCC(1,1) equation developed by Engle.
The model is tested through a simulation by employing empirical data issued from the Italian Stock Market and the main connected energy markets. The author considers empirical distributions for each marginal series returns in order to focus on the dependence structure. The model’s parameters are estimated by maximization of the log-likelihood. Also evidence is found that the proposed model fits correctly, for each pair of series, the left tail dependence coefficient and it is then compared with a static copula dependence structure which clearly underperforms the number of joint extreme values at a given confidence level.

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    • Figure 1. Scatter plot for each pair of returns
    • Figure 2. Linear correlation coefficients between each pair of returns variables: MIB (1), oil (2), gas (3) and coal (4)
    • Figure 3. Dynamic correlation between each pair of variables (following DCC equation)
    • Table 1. Descriptive statistics: MIB, oil, gas, coal and associated returns
    • Table 2. Correlation matrix between MIB, oil, gas and coal returns, %
    • Table 3. Left tail parameter estimation for each pair of variables (number of cases between parentheses) at 95% level
    • Table 4. T-copula and DCC parameters for each pair of returns series
    • Table 5. Left tail parameter estimation and correlation for some pairs of simulated variables (number of cases between parentheses)