Answer the following related questions

The graph below shows the plot of the log prices for SPOT denoted by LSPOT and FUTURES denoted by LFUTURES. 7.4 7.3 7.2 7.1 7.0 LSPOT 6.9 6.8 6.7 - LFUTURES 11 III IV In I IV In I IV II III IV II III IV 2002 2003 2004 2005 2006 2007 (a) Is the statement "LFUTURES leads LSPOT" true or false? Explain. [1] (b) A student runs the following regression to determine the relationship between LFUTURES and LSPOT: LFUTURES = a + BLSPOT + u Is this the correct regression to run? Explain based on your answer in (a). [2] The results of the Augmented Dickey Fuller test for both series are shown below. Unit Root Test for LSPOT Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=10) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -4.515486 0.0031 Test critical values: 1% level -4.107947 5% level -3.481595 10% level -3.168695 *Mackinnon (1996) one-sided p-values. Unit Root Test for LFUTURES Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on SIC, maxlag=10) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.284052 0.0780 Test critical values: 1% level -4.105534 5% level -3.480463 10% level -3.168039 *Mackinnon (1996) one-sided p-values. (c) Explain the difference between the Augmented Dickey Fuller (ADF) test and the Dickey Fuller (DF) test. Why does one perform an ADF test in the presence of autocorrelation? [2] (d) Stat the null and alternative hypotheses for the ADF test. Using the unit root test results, what do you conclude about the stationarity property of LSPOT and LFUTURES at the 5% significance level. [2, 2] (e) Provide two different and alternative terminologies for a series that has a unit root. [2] (f) State and explain two problems associated with using LSPOT and LFUTURES in regression analysis? [2] The table below shows the results of the Engle and Granger test. The test is performed with LSPOT as the dependent variable followed by LFUTURES as the dependent variable. Series: LSPOT LFUTURES Sample: 2002M02 2007M07 Included observations: 66 Cointegrating equation deterministics: C @TREND Automatic lags specification based on Schwarz criterion (maxlag=10) Dependent tau-statistic Prob.* z-statistic Prob.* LSPOT -8.101528 0.0000 -66.98674 0.0000 LFUTURES -7.928076 0.0000 -65.65357 0.0000 *Mackinnon (1996) p-values. (g) What can you conclude about the nature of long run relationship (or cointegration) between LSPOT and LFUTURES based on the Engle and Granger test results? Explain. [2]