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(a) Under what conditions two I (1) time-series variables will not involve the so-called spurious regression? (b) Consider two I (1) time-series variables: Price ( P,) and Quantity demanded (0, ). Assume the following linear relationship between P, and 0, : OQ, =pB + PBF +e, What properties of & will lead to the conclusion that £ and ©, are co-integrated? (c) Consider the following two estimated error correction models: the first model is estimated for a group credit-constrained consumers and the second model is estimated for group of wealthy consumers. APCE, = 246.09 +0.189APDI, — 0.036u, , +¢, APCE, =145.06 + 0.389APDI, — 0.09%4u, , +&, Here APCE is the first difference of personal consumption expenditure, APDI is the first difference of personal disposable income, and ¥; is the series of residual from the regression of PCE on PDI . Is it consistent that the coefficient of #,_; for a credit-constrained consumer is greater that of a wealthy consumer? Explain your answers. Explain the purpose of estimating an error correction model, and the reason you would include the %;.; term. Problem 3: Suppose, a forecaster estimated the following AR (7) model using the monthly exchange rate data from January 1995 to November 2009. S$; =0.009+0.189S,, +0.036S, , +0.007S, , (a) Using the Box-Jenkins methodology explain the steps that the researcher followed to select and estimate this model for the exchange rate. (b) Explain why is it likely that the researcher used this AR(7) model to forecast the exchange rate (i.e. discuss the pattern of the ACF and PACF graphs.) (c) What is the forecasted exchange rate for December 2009? (d) Briefly explain a diagnostic test to understand whether the researcher has picked the right model. Problem 4: In class we discussed the Dickey Fuller Test and the Augmented Dickey Fuller. Dickey and Fuller (1979) actually considered three different regression equations that can be used to test the presence of a unit root: 1. Ay, =p, +6, 2. Ay, =a,+pw,, +6, 3. Ay, =a,+w,_ +at+e, How do we call each regression model and what are the components of each model? If we were to test for a unit root using the Dickey Fuller Test, what would be the parameter of interest in models 1., 2., and 3.? How would you formulate the null and alternative hypothesis for this test? Write the t-statistic associated with this test, and comment whether we should use the critical values from a standard normal distribution? In what case would you use the Augmented Dickey Fuller Test and how would you modify models 1., 2., and 3.? If we found evidence of a unit root, how would pictures of models 1. and 2. look like?