# The OCR every 100 days, according to the Reserve Bank of NZ data...

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# The OCR every 100 days, according to the Reserve Bank of NZ data <- structure (list (y = c(4.5, 4.5, 5.25, 6.5, 6.5, 6, 5.75, 4.75, 5.75, 5.75, 5.75, 5, 5.25, 5.75, 6.5, 6.75, 6.75, 7.25, 7.25, 7.25, 7.5, 8.25, 8.25, 8.25, 6.5, 3, 2.5, 2.5, 2.75, 3, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5), N= 37L), Names = c("y", "N")) (a) [2 mark(s)] Plot the data with the axes appropriately labelled. (b) [2 mark(s)] Apply the AR(1) time series model to the data, and find the posterior predic- tive distribution for the interest rate 10 times units beyond the end of the data. Plot that distribution. (c) [5 mark(s)] Perform a posterior predictive check by (i) modifying the JAGS code appropriately, and (ii) plotting ten simulated datasets on the same set of axes. What is one property of the real data that the simulated datasets do not share? # The OCR every 100 days, according to the Reserve Bank of NZ data <- structure (list (y = c(4.5, 4.5, 5.25, 6.5, 6.5, 6, 5.75, 4.75, 5.75, 5.75, 5.75, 5, 5.25, 5.75, 6.5, 6.75, 6.75, 7.25, 7.25, 7.25, 7.5, 8.25, 8.25, 8.25, 6.5, 3, 2.5, 2.5, 2.75, 3, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5), N= 37L), Names = c("y", "N")) (a) [2 mark(s)] Plot the data with the axes appropriately labelled. (b) [2 mark(s)] Apply the AR(1) time series model to the data, and find the posterior predic- tive distribution for the interest rate 10 times units beyond the end of the data. Plot that distribution. (c) [5 mark(s)] Perform a posterior predictive check by (i) modifying the JAGS code appropriately, and (ii) plotting ten simulated datasets on the same set of axes. What is one property of the real data that the simulated datasets do not share?

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