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- Finally, for the remaining contracts, namely, the 6-, 9- and 12-month Eurodollar futures (with a price denoted by edi t), one can directly take the NOte that Gürkaynak et al. (2005) assume unscheduled meetings to be expected as happening with zero probability. daily return as the surprise itself due to their spot settlement nature. Thus, for j = 4, 5, 6 and i = 6, 9, 12 respectively, we have mpj = edi t â edi tâ1. (20) Extracting the target and the path factor.âLet X be a (T Ãn) matrix whose entries correspond to the above-defined monetary policy surprises mpj t
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- for j = 1, ..., n and t = 1, ..., T, that is, the surprise component of the daily change in federal funds futures and Eurodollar futures rates solely associated with FOMC announcements.7 Let us assume X to be generated by the following factor model: X = FÎ + ν, (21) where F is a (T Ã) matrix of ( < n) unobserved factors, Î is a (Ãn) matrix of factor loadings, and ν is a matrix of orthogonal disturbances. Gürkaynak et al. (2005) show that the response of futures prices is sufficiently characterized by two factors (i.e., = 2). We therefore estimate F = {F1t, F2t}t=1,...,T through principal-component analysis.
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- Rotation of the Factors.âGürkaynak et al. (2005) rotate F1 and F2 to obtain Z1 and Z2. Namely, they define Z = FU, (23) where U =    u11 u12 u21 u22    , (24) such that U is a (2 à 2) orthogonal matrix, with Z2 being associated, on average, with no change in the federal funds futures rate for the current month. The orthogonality between Z1 and Z2 requires that: E(Z1Z2) = u11u12 + u21u22 = 0. (25) Then, because: F1 = u22Z1 â u12Z2 u11u22 â u12u21 , (26) F2 = u21Z1 â u11Z2 u12u21 â u11u22 , (27) one can assume that Z2 has no impact on mp1 by imposing the final restriction: λ2u11 â λ1u12 = 0, (28) where λ1 and λ2 are the loadings on mp1 of F1 and F2, respectively. To recover an interpretation as to the magnitude of these factors, one can rescale Z1 (Z2) to match its units with mp1 (mp4 ). Rotation matrix U is obtained by solving the last four equations.
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