Problem 1.. In the dataset of “production.txt”, it has

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Problem 1. In the dataset of “production.txt”, it has the monthly industrial production (IP) of US from year1990 to year 2014. The data is retrieved from the Federal Reserve Bank of St. Louis.(a)Plot the time series of IP, ACF and PACF of IP. Test the stationary of the IP.(b)Generate the difference of IP. Plot the time series of differenced IP, ACF and PACF ofthe differenced IP. Test the stationary of the differenced IP. (c)Are there seasonal pattern in the series of IP?(d)Use AIC or BIC to fit an appropriate ARIMA model for the time series. Fit an ARIMAmodel with seasonal lag for the time series. Compare the two models. (e)Use Ljung-Box test to evaluate the serial correlation of residuals.(f)Compute 12-months-ahead forecasts based on the fitted model of your choice.Problem 2. The file “rates.txt” contains the monthly interest rates for eight different terms, including 1-yearrates, 2-year rates, 3-year rates, 4-year rates, 5-year rates, 7-year rates, 10-year rates, 30-yearrates. Use Phillips-Ouliaris Cointegration Test and Johansen-Procedure to analyze the co-integration among the eight time series. (a)Is each time series stationary? (b)Is one-year interest rates co-integrated with the other seven interest rates?(c)Use Johansen-Procedure to find the number of co-integration among the eight time series.Write down the error correction components for the co-integrated time series.1

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