international banking finance -- 2

i) returns on a cryptocurrency (R_i), ii) returns on the cryptocurrency market (R_m), iii) trading volume (Vol), iv) cross-sectional absolute deviation, CSAD (see, e.g., Equation 3 in Christie and Huang 1995). Please note that CSAD measuresthe dispersion of returns. EViews will be used for estimations and tests. Assume, where relevant the significance level of 5%. Variable definitions: ??,? = 100 ∙ ?? ( ??,? ??,?−1 ), where ??,? is the price of a cryptocurrency ? at time ?. The return on cryptocurrency is measured in daily percentage. ??,? = ∑ ??,? ?? ?=1 ??,? is the market return (in daily percentage), calculated as a weighted average of returns on ?? cryptocurrencies at time ?. The weight is calculated as the market share of cryptocurrency ? at time ?. ????,? is the trading volume of cryptocurrency ? at time ? (in millions of USD). ?????,? = ∑ |??,?−??,? | ?? ?=1 ?? is the cross-sectional absolute deviation, which measures the dispersion of returns on cryptocurrencies. (a) Plot the series Ri and discuss if there is evidence of volatility clustering in the data. Comment on the result. (b) Calculate the squared Ri and depict graphically the correlation and partial correlation functions of the squared Ri. Comment on the result. (c) With respect to the series Ri, test for the presence of conditional heteroscedasticity in residuals of the conditional mean model, formulated as an autoregressive process of order 1, ??,? = ?0 + ?1??,?−1 + ??,? . (Please use this specification in the following parts of this question.) Perform the LMARCH test for lag orders 1 and 7. Comment on the results. Is there evidence of conditional heteroscedasticity in the data? (d) If you are confident that there is significant evidence of conditional heteroscedasticity, proceed to estimate the ARCH(1) and ARCH(7) models. Discuss the results. (e) Now estimate the conditional variance using GARCH(1,1) and TGARCH(1,1) models. (The conditional mean model is as in (b). You may choose either the T-student or the General Error Distribution.) Discuss the results. Which of the two models provides the best fit? (f) Now estimate a GARCH(1,1)-M model, in which the conditional mean model is formulated as ??,? = ?0 + ?1??,?−1 + Λ??,?−1 2 + ??,? . Comment on the results. (g) Now estimate Equation (4) in BenSaïda (2017). Describe the statisical significance of the coefficients ? and ?. Are the results qualitatively similar to BenSaïda (2017)? (h) In relation to (f), Lamoureux and Lastrapes (1990) interpret Vol as measuring the arrival of new information. They hypothesise that ? > 0, ?1 = ?1 = 0. Discuss if these hypotheses are supported by the data.