Hi,
Having been through Chapter 17 on Copulas, have three basic questions on the coefficient of upper&lower tail dependence:
Question 1 - The definitions of the coefficient of upper and lower tail dependence include that: (i) the coefficient of the upper tail is the limiting value as we move further into the upper tail (from below) and (ii) the coefficient of the lower tail is the limiting value as we move further into the lower tail (from above). Why is it important to know if we're approaching the limit from above or below -surely the main thing that matters is the limit itself (which is 1 for upper tail and 0 for lower tail)?
Q2: Page 38 (2019 version of notes) includes several questions (a to g) asking to identify an appropriate copula for seven different types of data.
What are the factors that can help identify the appropriate copula - only the coefficients of the upper and lower tail dependence and the general purpose of the copula (ie. the 'independence' copula is obv suitable for data showing independence
)?
Q3: Do the solutions (on the same page as the questions about identifying appropriate copulas) contain the exhaustive list of possible answers or only a sample of answers (and other correct answers exist but just aren't written here). [If the former, why isn't the Co-monotonic copula a good option for (question g) data with both upper and lower tail dependence?]
Thanks in advance
Having been through Chapter 17 on Copulas, have three basic questions on the coefficient of upper&lower tail dependence:
Question 1 - The definitions of the coefficient of upper and lower tail dependence include that: (i) the coefficient of the upper tail is the limiting value as we move further into the upper tail (from below) and (ii) the coefficient of the lower tail is the limiting value as we move further into the lower tail (from above). Why is it important to know if we're approaching the limit from above or below -surely the main thing that matters is the limit itself (which is 1 for upper tail and 0 for lower tail)?
Q2: Page 38 (2019 version of notes) includes several questions (a to g) asking to identify an appropriate copula for seven different types of data.
What are the factors that can help identify the appropriate copula - only the coefficients of the upper and lower tail dependence and the general purpose of the copula (ie. the 'independence' copula is obv suitable for data showing independence
Q3: Do the solutions (on the same page as the questions about identifying appropriate copulas) contain the exhaustive list of possible answers or only a sample of answers (and other correct answers exist but just aren't written here). [If the former, why isn't the Co-monotonic copula a good option for (question g) data with both upper and lower tail dependence?]
Thanks in advance