Time Series Analysis

The assignment consists of three problems. Problem 1 involves analyzing the monthly industrial production (IP) dataset from 1990 to 2014, including plotting time series, testing for stationarity, and fitting an ARIMA model. Problem 2 deals with the file 'rates.txt', which contains interest rates for eight different terms, using Phillips-Ouliaris Cointegration Test and Johansen-Procedure to analyze co-integration among the time series. Problem 3 involves studying how house owner preferences are affected by house features using a logit model on the 'HousePrices.csv' dataset.

Problem 1.
In the dataset of “production.txt”, it has the monthly industrial production (IP) of US from year
1990 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 of
the 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 ARIMA
model 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-year
rates, 2-year rates, 3-year rates, 4-year rates, 5-year rates, 7-year rates, 10-year rates, 30-year
rates. 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.
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Problem 3.
Using the dataset “HousePrices.csv”, we study how the preference of house owner is affected by
the features of a house such as price, lot size, number of bathroom, and so on. If the house is
preferred, the variable, “prefer” is a binary variable, taking the values of yes or no. Use a logit
model to the data and study the probability of a house preferred by a home owner. The dependent
variable is “prefer” and all the other variables are independent variables.
(a) Fit the data by a full model and use stepwise the select an optimal model. Display
summary of the model estimations. Compare the full model and the selected model.
Justify the selected model by the AIC criteria.
(b) In the selected model, calculate the odd of preference to non-preference if there is a
driveway given that all the other variables have no change. Calculate the probability of
preference by the home owner if all continuous variables take the mean value and dummy
variables take the value of one.
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