Structural Time Series Models
نویسنده
چکیده
1 Trend and Cycle Decomposition y t = t + t where y t is an n 1 vector and t and t represent trend and cycle components respectively. This decomposition into components is not unique. Beveridge and Nelson (1981) and Stock and Watson (1988) derive the following decomposition: y t = C(L)" t = C(1)" t + (1 L)C (L)" t Integrating up gives: y t = C(1) 1 X i=0 " ti | {z } + C (L)" t | {z } trend cycle NB: (1) The 'cycle'here could be white noise or a …rst order AR process y t = y t1 + t (2) Innovations in trend and cycle are perfectly correlated.
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