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Unformatted text preview: φ + θ ) / (1 + θ 2 + φθ ) ρ k = φρ ( k-1) ,k = 2 , 3 ,... 6. For the model (1-B )(1-. 2 B ) X t = (1-. 5 B ) ± t : (a) Classify the model as an ARIMA(p,d,q) process (i.e. ﬁnd p,d,q) (b) Determine whether the process is stationary 7. Show that the AR(2) process X t = X t-1 + cX t-2 + ± t is stationary provided-1 < c < 0. 1 (a) Find the autocorrelation function when c =-3 / 16. (b) Show that the AR(3) process X t = X t-1 + cX t-2-cX t-3 + ± t is non-stationary for all values of c . 8. Consider X t to follow a SARIMA (seasonal ARIMA) model of order (1 , , 0) × (0 , 1 , 1) 12 . (a) Write out the model in B notation (b) Expand this equation, and write the model in terms of X t and ± t . 2...
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- Spring '09
- Autocorrelation, Stationary process, ACF, Xt