\documentstyle[11pt,fullpage,psfig]{article}

\input info.tex

\frenchspacing

\begin{document}

\begin{center}\bf
Finger Exercises --- Due Thursday, April 21, 1998
\end{center}

\begin{quote}\em
Please prepare answers for these exercises, to be turned in.  Your
grade will be based on how many questions you made a reasonably strong
effort to answer, {\bf not} how many questions you get right or
partially right.  There is no partial credit, but the grader may give
you additional written feedback on each question you attempt.

Feel free to discuss these exercises with each other and with me.  You
will get the most benefit from the grader's remarks, however, if the
work you turn in is your own.

\rm

This hw, like most material for this course, is posted on the World
Wide Web at URL \www{}; you can cut and paste data directly out of the
\TeX{} file if you wish.  Look for something under week13.

\em

\end{quote}

{\em Guess the model.} All but one of the time series below was
simulated from a fairly simple ARIMA$(p,d,q)$ model; the one that was
not simulated from an ARIMA model was simulated as a sinusoid plus
white noise.  Use methods (graphical, exploratory or modeling fitting)
from class to determine, for each data set
\begin{itemize}
\item whether it was generated from the sinusoidal model
\item if it is not what kind of ARIMA model was it generated from:
  pure AR, pure MA, ARMA, or ARIMA.
\end{itemize}
and finally use appropriate model-fitting methods to estimate the
ARIMA parameters of the three ARIMA models and the appropriate
parameters of the one sinusoidal model.
\begin{enumerate}

\item {\tt ts1.s} %  tsplot(tsx _ rnorm(250) + sin(2*pi*(1:250)/10)) 

\item {\tt ts2.s} %  tsplot(ts2 _ arima.sim(list(ar=.9),n=250))

\item {\tt ts3.s} %  tsplot(ts3 _ arima.sim(list(ma=1),n=250))

\item {\tt ts4.s} %  tsplot(ts4 _ arima.sim(list(ar=.5, ma=.5,ndiff=1),n=250))

\end{enumerate}

Note: If you say 
\begin{verbatim}
402 > source("ts1.s") 
\end{verbatim}
this will create an {\tt rts} object named {\tt ts1} that contains the
observations in {\tt ts1.s}.  Similarly for the other three files.

\end{document}
