Monitoring test for stability of copula parameter in time series

Abstract

a b s t r a c tIn this paper, we consider a monitoring procedure to detect changes of the copula parameter of strong mixing processes. We propose two monitoring procedures based on the cumulative sums of scores evaluated at consistent copula parameter estimates and their fluctuations. We investigate the asymptotic properties of our monitoring procedures under both the null of no change in the copula parameter and its alternative. We also illustrate a simulation study and a real data analysis.

Monitoring Test for Stability of Dependence Structure in Multivariate Data Based on Copula

“…This assumption is in line with other precedent studies on testing for structural breaks in copula (see, e.g., Harvey [10], Busetti and Harvey [11], Bouzebda [26], Bücher and Ruppert [14] and Na et al [12,21]). Furthermore, this assumption is very crucial in real practice since one can encounter the situation that the monitoring test detects a change in copula function although the change actually occurs in marginal distributions.…”

“…Consequently, our test has better power properties for early change points. Similar findings were reported in Na et al [21] and Lee et al [22]. This result indicates that it is desirable to renew the historical data appropriately to escalate the power when the null hypothesis appears to be true for a certain period time.…”

“…In particular, our test is compared with the monitoring test proposed by Na et al [21]. Recall that Na et al [21]'s test can be applied to detect a copula parameter change when the copula family does not change.…”

“…Recall that Na et al [21]'s test can be applied to detect a copula parameter change when the copula family does not change. Na et al [21] proposed the detector in (2) based on the difference between estimates of the copula parameter:…”

“…Recently, Na et al [21] developed a monitoring procedure to detect a change of the copula parameter. However, one major drawback of this test is that the test statistic is derived under the assumption that the copula family does not change.…”