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

The sunspot numbers {*X _{t}, t *= 1

*, . . . ,*100}, filed as SUNSPOTS.TSM, have sample auto covariances

*(*0

*)*= 1382

*.*2,

*(*1

*)*= 1114

*.*4,

*(*2

*)*= 591

*.*73, and

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

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* (*3*) *= 96*.*216. Use these values to find the Yule–Walker estimates of *φ*_{1}, *φ*_{2}, and *σ*^{2} in the model

*Y _{t}*=

*φ*

_{1}

*Y*

_{t}_{−1}+

*φ*

_{2}

*Y*

_{t}_{−2}+

*Z*{

_{t},*Z*} ∼ WN(0

_{t}*,σ*

^{2})

*,*for the mean-corrected series

*Y*=

_{t}*X*− 46

_{t}*.*93

*, t*= 1

*, . . . ,*100. Assuming that the data really are a realization of an AR(2) process, find 95% confidence intervals for

*φ*

_{1}and

*φ*

_{2}.