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Homework answers / question archive / Time Series Assignment   Books used for this class: - Introductory Time Series with R, Paul S

Time Series Assignment   Books used for this class: - Introductory Time Series with R, Paul S

Statistics

Time Series Assignment

 

Books used for this class:

- Introductory Time Series with R, Paul S.P. Cowpertwait, Andrew V. Metcalfe
- Applied Econometric Time Series, Fourth Edition, Walter Enders

 

Requirements:

- All required datasets are attached

- Each plot should have a meaningful title

- Each plot should have labeled axes (show unit of measurement)

- An explanation/analysis is required for every single plot (around 4-5 lines) 

- A screenshot of each code/plot must be used in a Word Doc, with explanations for each plot.

- Word Doc and R file are required for submission

 

Please make sure to answer each part of the question with clear description and detailed discussion. This is a take-home exam and is not only graded based on an accurate R-code, but also on the interpretation and theoretical justification of the code/plots/questions.

Problem 1. Identify the following specific ARIMA(p, d, q) models. That is, what are p, d, and q and what are the values of the parameters (the O's and 0's)? Also discuss in detail the assumptions of each model parameter estimation (e.g. stationarity and invertibility). 
(a) Yi = Yt-i - 0.25Yt-2 + Et — 0.1Et_i (b) Yt = 2Yt-i - Yt-2 + Et (c) Y = 0.5Yt-1 — 0.5Yt-2 + et - 0.5et_i + 0.25et-2 
Problem 2. The file named gold contains the daily price of gold (in dollars per troy ounce) for the 252 trading days of year 2005. The data series `gold.dat' can be accessed from the zip-file provided in blackboard. (a) Display the time series plot of these data. Interpret the plot. (b) Display the time series plot of the differences of the logarithms of these data. Interpret this plot. (c) Calculate and display the sample ACF for the differences of the logarithms of these data and argue that the logarithms appear to follow a random walk model. (d) Display the differences of logs in a histogram and interpret. (e) Display the differences of logs in a quantile-quantile normal plot and interpret. 
Problem 3. Quarterly earnings per share for the Johnson & Johnson Company are given in the data file named JJ. The data cover the years from 1960 through 1980. The data series `JJ.dat' can be accessed from the zip-file provided in blackboard. 
(a) Display a time series plot of the data. Interpret the interesting features in the plot. (b) Transform the series using logarithms, plot the series again and discuss any changes with respect to part (a). (c) Display a time series plot of the transformed values. Does this plot suggest that a stationary model might be appropriate? Provide all appropriate theoretical and practical evidence and discussions to substantiate your answer. (d) Display a time series plot of the differences of the transformed values. Does this plot suggest that a stationary model might be appropriate for the differences? Provide all appropriate theoretical and practical evidence and discussions to substantiate your answer. 
(e) Conduct ADF, Phillips-Perron and KPSS tests of the transformed series. Does it support your conclusions from part (d) & (e)? 
 

(f) Estimate an ARMA or ARIMA model as it's appropriate and supported by the evidence from the previous sections. (g) Find the best specification for your model. Discuss all the steps and information you have used to arrive to this conclusion. Make sure you also provide a discussion and evidence that your model is well-specified. 
(h) Use your model to forecast 8 quarters earnings ahead. 
Problem 4. Use the dataset `unitroot.xls' (see blackboard) and conduct a unit root test for all the 'exchange rate variables.' Please note that the exchange rate variables in this file end with 'EX' (e.g.,the variable `CANEX' is the exchange rate between the Canadian dollar and the U.S. dollar). You should conduct at least two unit-root tests for each series. That is, one using a test with a unit-root null hypothesis (e.g., ADF or PP) and a reverse null unit root test (stationarity as the null hypothesis) such as the KPSS test. You must justify all your steps and assumptions when conducting these tests using all the tools presented to you (e.g., economic theory, graphical analysis and statistical properties of the series). Also, you have to determine the order of integration for each and one of the series. 
Problem 5. The data file `SP.dat' (see zip-file in Blackboard) contains quarterly Standard & Poor's Composite Index stock price values from the first quarter of 1936 through the fourth quarter of 1977. (a) Display and interpret the time series plot for these data. (b) Now take natural logarithms of the quarterly values and display and the time series plot of the transformed values. Describe the effect of the logarithms on the behavior of the series. (c) Calculate the (fractional) relative changes, (Yt — Yt_i)/Yt_i, and compare them to the differences of (natural) logarithms, Alog(Yt). How do they compare for smaller values and for larger values? (d) Use the Box-Jenkins procedure to model this series. Document all your steps and justify aproopriartly your model selection. 
 

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