Time Series Report,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,… 1 answer below »

PROJECT II and Take-home Final
(Due on Wednesday, June 12)
Statistics 137
Spring Quarter, 2013
Please note that the take-home part is 20% of the final examination. You may work in a group (max group size=3) of registered students in the course. Only one report per group needs to be submitted. Please write down the names of the students in the group on submitted work.
Please find attached a data set on petroleum consumed by the residential sector in the US (Jan, 1984 –Dec, 2012). Analyze the data using time series methods. You are free to use any number of methods that we have covered in this course. You may consider the following points in your analysis (with appropriate comments/explanations):

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  • Explain the data, why it is a time series, why it is important to analyze it.
  • Use graphical techniques to understand the nature of variation in the data.
  • Determine if the series is stationary or not. You may need to transform, estimate the trend and seasonal in order to carry out the analysis.
  • Obtain the appropriate ACF, PACF plots and periodogram (and its smoothed version), and use these to make a preliminary identification of a time series model.
  • Fit an ARIMA model obtained via preliminary identification and, examine the residuals and their properties.
  • Select the final models using a model selection criterion such as AICC. [If you fit ARIMA(p,d,q), it is enough to consider the 25 models with p=0,…,10 and q=0,…,10, where p is the AR order and q is the MA order. The R function auto.arima can be used.]
  • Plot the spectral density of the final model as well as the smoothed periodogram.
  • Perform a residual analysis on the final model: obtain the ACF and PACF plots of the residuals as well as smoothed periodogram.
  • Write down the final model, the estimated parameters and the standard errors.
  • Refit the final model (i.e., use AR and MA orders of the final model, but not the parameter estimates) using all the data except for the year 2012 and use this model to forecast petroleum consumption for the 12 months in 2012. Plot the observed and the forecasted values against time. [If you need to extrapolate the trend, often a linear extrapolation is reasonable.]
  • Summarize your findings from the analysis and explain your conclusion. If you feel the analysis done by you can be improved, please provide a brief explanation.

Your report may include the following Sections:

  • Introduction: Statement of the problem.
  • Materials and Methods: Description of the data and the methods used in the analysis.
  • Results: Explanation of the results of your analyses. You can cut and paste the relevant parts of your computer outputs and refer to them in explaining your results.
  • Conclusion and Discussion: Highlight the main points and discuss them.

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