Question 5 20 Marks Figure 1 Below Shows Quarterly Earnings Per Share For Johnson Johnson J J From The First Quar 1 (73.02 KiB) Viewed 38 times
Question 5 20 Marks Figure 1 Below Shows Quarterly Earnings Per Share For Johnson Johnson J J From The First Quar 2 (40.14 KiB) Viewed 38 times
Question 5 [20 marks]. Figure 1 below shows quarterly earnings per share for Johnson & Johnson (J&J) from the first quarter of 1960 to the last quarter of 1980. (a) The time series in Figure 1 shows an increasing variance. Describe how you would transform the data to solve the problem of increasing variance. [4] 1960 1965 1975 1980 Year Figure 1: Johnson & Johnson quarterly earnings per share in US dollars. First-order differencing and then lag-4 differencing were performed on the transformed J&J data (as detailed in (a)). Figure 2 shows the sample ACF and PACF plots after applying both differencing operators, i.e., V₁V on the transformed J&J data. 12 LAG a 10 12 6 LAG Figure 2: (Top) Sample ACF, (Bottom) Sample PACF of V4V on transformed J&J data. US dollars 1970 www.
(b) State SARIMA model or models indicated by the sample ACF and PACF plots in Figure 2. Explain how you arrived at your conclusion. [8] (c) Suppose that an ARIMA(0, 1, 0) x (2, 1,0)4 model is fitted to the transformed J&J data. Figure 3 below shows the resulting model diagnostics for the standardized residuals. Moreover, performing the Box-Ljung Q test statistic on these residuals yielded Box-Ljung test data: resid (model$fit) X-squared = 42.161, df = 18, p-value = 0.00105 Would you recommend this model to financial analysts working to understand the time dependence of these data? If no, give two suggestions on how to improve this model. Explain your reasoning. Use a = 0.05. [8]
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