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Unformatted text preview: Matlab Solutions Time Series (2DD23) Week 12 Exercise 10.2 The special case of the linear growth model is described by the following equations: X t = t + n t (1) t = t- 1 + t- 1 (2) t = t- 1 + w t (3) Please notice that there is a small difference with the regular linear growth model: there is no noise term in equation 2. We want to rewrite these equations into a state-space form: X t = h T t t + n t t = G t t- 1 + w t This means that we need to find expressions for h t , t and G t . Besides the noise terms n t and w t , we have parameters t and t , so the state of the system is described by t = t t . From equation 1 we find that h t = 1 . Using equations 2 and 3 we find: t = t t = t- 1 + t- 1 t- 1 + w t = 1 1 1 t- 1 t- 1 + w t So G t = 1 1 1 . In this case w t = w t . Now we will use equation 10.17 on page 213 to compute m ,( m = 2 ) . This means that we have to find matrix M , which follows from the equation above equation 10.17:, which follows from the equation above equation 10....
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