The sunspot numbers { X t , t = 1 , . . . , 100}, filed as SUNSPOTS. 1 answer below »

The sunspot numbers {Xt, t = 1, . . . , 100}, filed as SUNSPOTS.TSM, have sample auto covariances  width= (0= 1382.2,  width= (1= 1114.4,  width= (2= 591.73, and

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 width= (3= 96.216. Use these values to find the Yule–Walker estimates of φ1φ2, and σ2 in the model

Ytφ1Yt−1 + φ2Yt−2 + Zt , {Zt} ∼ WN(02)for the mean-corrected series YtXt− 46.93, t = 1, . . . , 100. Assuming that the data really are a realization of an AR(2) process, find 95% confidence intervals for φ1 and φ2.

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