When is a copula constant? A test for changing relationships

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A revisit to the dependence structure between the stock and foreign exchange markets: A dependence-switching copula approach (2013, background): “…argue that a time-invariant copula is not appropriate and hence allow the parameters in a copula function to change over time (Van den Goorbergha et al., 2005; Patton, 2006; Harvey, 2010; Busetti and Harvey, 2011) or allow the copula function to change over time (Okimoto, 2008; Rodriguez, 2007).”
Copula Methods for Forecasting Multivariate Time Series (2013, background): “Locally constant copula models are considered by Giacomini, Härdle and Spokoiny (2009), Guégan and Zhang (2009), Dias and Embrechts (2010), Harvey (2010), Rémillard (2010) and Busetti and Harvey (2011).”
A review of copula models for economic time series (2012, background): “[76], Guégan andZhang [83], Dias and Embrechts [44], Harvey [87], Rémillard [125] as well as in Busetti and Harvey [22].”