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Midterm 2 for STAT 4363

1. (15 points) Consider the eggs time series from the fma package in R. The series has prices of dozen eggs 1900 to 1993.

a. Is there an underlying seasonal period in this time series? Comment.

b. Build an appropriate ARIMA(p, d, q) model for this time series. Explain your selection.

c. Provide 5 steps ahead forecasts for this time series based on the model you built in part b.

2. (15 points) Consider the crimes time series from the cityA-crimes.RData data object. This time series records monthly crime index in city of Anvey from 2000 to 2009.

a. Plot the series, its ACF and PACF as a panel plot. Suggest ARMA(p, q) model orders using these plots.

b. Perform AR model order selections using AIC and BIC and report the results. Use the ar() and SelectModel() functions in R. Comment on the differences between the two selection methods.

c. Forecast this time series for the next 12 months. Use the AR model order selected by BIC.

3. (15 points) Consider fdeaths time series from the datasets package in R. This series Xt has monthly deaths of females due to lung diseases from 1949 to 1979.

a. Identify the seasonal period s of this series and comment on the seasonal behavior of this series during the various months of the year.

b. Apply seasonal differencing to this series and suggest a mixed seasonal ARMA(p, q)×(P, Q)s model. Explain your selection.

4. (10 points) Consider the uspop from the datasets package in R. This series Xt has the population of the United States (in millions) for the period 1790–1970. Suggest a transformation of this series that results in a stationary time series.

5. (15 points) A time series Xt is given by a seasonal ARIMA model denoted by ARIMA(p, d, q)×(P, D, Q)s. Write down the model equation for the following specifications.

a. ARIMA(p = 0, d = 0, q = 0) × (P = 1, D = 0, Q = 1)4

b. ARIMA(p = 0, d = 1, q = 1) × (P = 0, D = 0, Q = 2)12

c. ARIMA(p = 1, d = 1, q = 1) × (P = 1, D = 1, Q = 1)16