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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...

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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, XXXXXXXXXXAnalyze 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):
  • 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.
005_hvmcapo-22lvphra.docx 005_apqcapo-votpuhva.xlsx
Answered Same Day Dec 23, 2021

Solution

David answered on Dec 23 2021
117 Votes
Introduction
Energy is everything in modern world.
Given our technology dependency, which is driven by energy coming from raw resources like coal,
petroleum etc., it’s quite obvious that we are totally dependent on these resources. But, given that
these are natural resources, and the fact that it takes thousands of year for a coal mine or a
petroleum reserve to get formed, this ever increasing dependency is creating a havoc upon the
availability of these resources.
It’s now a known fact that in about hundreds of years all these natural resources will not be
available anymore. So, it is in our prerogative to see how best we can utilize what we have right
now.
We have a monthly dataset containing historical (Jan, 1984 –Dec, 2012). data on volume of
petroleum consumed by the residential sector in the US. If, using this data, we can forecast the
future petroleum consumption, then it will surely help the government policy making, who, armed
with the forecast, can start planning on optimizing the energy resource utilization or maybe even
start planning on moving onto alternative means of energy production to cater to the increasing
demand.
Materials and Methods
The data is shown below as a time series. As we can see, there is a distinct pattern in the data, which
tells us that the variation is not all random noise and we should be able to explain a large portion of
it.
Clearly, the data is periodic, and at least after 2000, follows a downward trend. To compute the
period we take the help of a periodogram (and a smoothed periodogram) which shows that the
period is 12 months, which means that there is an annual cycle in petroleum consumption and it
has peals in year end and start of the year and touched the bottom at around mid-year.
It shows that the petroleum consumption is highest in winters.
This shows that the data can be very well represented in an ARIMA (autoregressive integrated
moving average ) framework which is defined below.
A nonseasonal ARIMA model is classified as an "ARIMA(p,d,q)" model, where:
ï‚· p is the number of autoregressive terms,
ï‚· d is the number of nonseasonal...
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