8.8 The data in Table 8-8 are the daily scores achieved by a schizophrenic patient on a test of…

8.8  The data in Table 8-8 are the daily scores achieved by a schizophrenic patient on a test of perceptual speed. The pa- tient began receiving a powerful tranquilizer (chlorpromazine) on the sixty-first day and continued receiving the drug for the rest of the sample period. It is expected that this drug would reduce  perceptual speed.

(a)    Produce a time plot of the data showing where the intervention  occurred.

(b)    Fit an intervention model with a step function interven- tion to the series. Write out the model including the ARIMA model for the errors.

(c)    What does the model say about the effect of the drug?

(d)    Fit a new intervention model with a delayed response to the drug. Which model fits the data better? Are the forecasts from the two models very different?

(e)    Construct an ARIMA model ignoring the intervention and compare the forecasts with those obtained from your preferred intervention model. How much does the intervention affect the forecasts?

(f)     If the level of drug given varied from day-to-day, how could you modify your model to allow for this?