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

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\centerline{\bf{STANFORD UNIVERSITY}}
\centerline{\bf{STATISTICS DEPARTMENT}}
\centerline{ }
\centerline{\bf{Statistics 207 Introduction to Times Series Analysis}}
\centerline{\bf{Summer 2001}}
\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 (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 (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 (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 Problem 2.19, page 205.
\end{enumerate}

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