Consider again the first differenced series yt of the weekly crude oil prices from January 3, 1986

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Consider again the first differenced series yt of the weekly crude oil prices from January 3, 1986 to October 6, 2017. Suppose that yt follows the exponential autoregressive model

image text in transcribedwhere ????t is a sequence of iid N(0, σ2 e ).

(a) Put the exponential autoregressive model into a nonlinear Gaussian state space model.

(b) Fit the model using the extended Kalman filter with the first-order Taylor expansion. Write down the parameter estimates.

(c) Check the model using the residuals ̂ ????t = yt − exp( ̂b)yt−1 − exp(̂c +

̂dy2t

−1)yt−8. Are there serial correlations in the residuals? You may use Ljung–Box statistics with 10 lags.

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Nonlinear Time Series Analysis

ISBN: 9781119264057

1st Edition

Authors: Ruey S. Tsay, Rong Chen

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