### 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.The time series of the IP is shown below.ACF of IP is shown below.1

PACF of the IP series is shown below.In order to test the stationarity of the time series, Augmented-Dickey-Fuller test is used. Thealternate hypothesis is that the time series is stationary. As can be seen from the figure below thep value is greater than 0.05 So the time series is not stationary.(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.The time series of the differenced IP is shown below.2

The ACF of the differenced time series is shown below.The PACF of the differenced time series is shown below.The test for the stationarity is shown below. The Differenced Time Series is found to bestationary.(c)Are there seasonal pattern in the series of IP?In order to detect the seasonal pattern in the series, the Fourier Transform Technique is used. Thespike in the graphs shows the presence of seasonality with different frequency.3

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