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### Question

Question 1  Consider a simple time series model of the form Xt = a + b t + cXt1 + et; t = 1; 2; : : : ; T; (1) where et  N(0; 1) is a sequence of independent and normally distributed (i.n.d.) random variables. Let X0 = 0, and a, b and c be known constants. Model (1) covers the following commonly used scenarios.  Linear trending model: Xt = a + b t + et; t = 1; 2;  T: (2) What is the probability distribution of Xt ? Provide the necessary detail Random walk model without intercept: Xt = Xt1 + et; t = 1; 2 T: (3) Do you know the probability distribution of Xt ? Provide the necessary detail

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