1. (20 points) A time series model has been fit and checked with hi...

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1. (20 points) A time series model has been fit and checked with historical data yielding Yt= 50 Suppose at time t = 60 the observation is Y60 = 57. a. Determine forecasts for periods 61, 62, and 63 from origin 60. b. Suppose the observed value of Y61 is 59. What is the absolute percentage error for period 61? Update the forecasts for periods 62 and 63. C. Suppose the estimate for the variance of the error term is s² = 3.2. Compute a 95% prediction interval about the forecast for period 61 (The approximate 95% prediction interval for a stationary series is Y 2s). . 3. (40 points) The data in Accident.dta are the weekly automobile accident counts for the years 2006 and 2007 in Havana County. Determine the appropriate ARIMA model, and forecast the accident rate five weeks ahead from the forecast origin t = 85 (make a line plot comparing the data with your forecast). Compare your forecasts with the actual accident rate using the MAPE (Mean absolute percentage error). How accurate are your forecasts? Forecast the accident rate 10 weeks ahead from the 90th week and make a line plot with the data and forecast. Be sure to check for stationarity with the Dicky-Fuller test, include auto-correlation and partial-autocorrelation figures justifying your best guess for the arima model and results from trying out different alternative models. Please explain why you chose your final model for the forecast (discuss the significance of the coefficients and the independence of the residuals).

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