% This is the take-home midterm for Stanford Stat 207

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\centerline{\bf{CALIFORNIA STATE UNIVERSITY}}
\centerline{\bf{DEPARTMENT OF STATISTICS}}
\centerline{ }
\centerline{\bf{Statistics 4866/6871: Seminar - Introduction to Times Series Analysis}}
\centerline{\bf{Summer 2005}}
\centerline{ }
\centerline{\bf{Take-home Midterm}}
\centerline{ }
\noindent
{\bf{Instructions:}} This is a take-home exam.  Your are expected to work on the exam
alone.  If you have questions about the exam you may ask the instructor.

\begin{enumerate}
\item (Stat 4866/6871) (Average Air Temperature Racife Brazil, 1953-1962.)  The following problem is to
describe and understand the variation in the temperature data.
\begin{enumerate}
\item Plot the data $\{x_t\}$ and describe its main features.
\item Perform a Classical Decomposition of the data, $X_t = S_t + T_t + I_t$.
\item Are there any unusual years in the data?
\end{enumerate}
\item (Stat 4866/6871) (Yield on short-term British government securities.)  Find a suitable time-series
model and compute forecasts up to 12 months ahead.
\begin{enumerate}
\item Plot the data and describe its main features.  Is there a seasonal pattern?
\item Suggest and apply an appropriate transformation that transforms the data to a
stationary time series.
\item Fit an ARIMA model to this set of data and justify your choice by examining the
appropriate ACF, PACF, and residual plots.
\item Give the estimated model and the value of the AIC.
\item Calculate the formula for the one-step ahead forecast $x_{n+1}^n$.
\item Forecast the time series 12 months ahead.  Comment.
\end{enumerate}
\item (Stat 4866/6871) (Monthly totals of international airline passengers, Jan. 1949 to Dec. 1960.)  Fit an
ARIMA model to the data and produce forecasts up to one year ahead.
\begin{enumerate}
\item Plot the data and describe its main features.
\item Suggest and apply a transformation that stabilizes the variance of the data.
\item Suggest and apply a transformation that transforms the data to a
stationary time series.
\item Identify an appropriate ARIMA model for this set of data and specify any goodness-of-fit
methods used in your selection process.
\end{enumerate}
\item (Stat 6871) Problem 2.19, page 205.
\item (Stat 6871) Determine the best exponential smoothing forecasts for the three time series in the construction data.
\item (Stat 6871) Run the decomposition program for the electricity data and comment on the components of the time series.


\end{enumerate}

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