

    \filetitle{arf}{Run autoregressive function on a tseries object}{tseries/arf}

	\paragraph{Syntax}
 
 \begin{verbatim}
 X = arf(X,A,Z,RANGE,...)
 \end{verbatim}
 \paragraph{Input arguments}
 
 \begin{itemize}
 \item
   \texttt{X} {[} tseries {]} - Input data from which initial condition
   will be taken.
 \item
   \texttt{A} {[} numeric {]} - Vector of coefficients of the
   autoregressive polynomial.
 \item
   \texttt{Z} {[} numeric \textbar{} tseries {]} - Exogenous input or
   constantn in the autoregressive process.
 \item
   \texttt{RANGE} {[} numeric \textbar{} Inf {]} - Date range on which
   the new time series observations will be computed; \texttt{RANGE} does
   not include pre-sample initial condition. \texttt{Inf} means the
   entire possible range will be used (taking into account the length of
   pre-sample initial condition needed).
 \end{itemize}
 \paragraph{Output arguments}
 
 \begin{itemize}
 \item
   \texttt{X} {[} tseries {]} - Output data with new observations created
   by running an autoregressive process described by \texttt{A} and
   \texttt{Z}.
 \end{itemize}
 \paragraph{Description}
 
 The autoregressive process has one of the following forms:
 
 \begin{verbatim}
 a1*x + a2*x(-1) + ... + an*x(-n) = z,
 \end{verbatim}
 or
 
 \begin{verbatim}
 a1*x + a2*x(+1) + ... + an*x(+n) = z,
 \end{verbatim}
 depending on whether the range is increasing (running forward in time),
 or decreasing (running backward in time). The coefficients
 \texttt{a1},\ldots{}\texttt{an} are gathered in the \texttt{A} vector,
 
 \begin{verbatim}
 A = [a1,a2,...,an].
 \end{verbatim}
 \paragraph{Example}
 
 The following two lines create an autoregressive process constructed
 from normally distributed residuals,
 
 \[ x_t = \rho x_{t-1} + \epsilon_t \]
 
 \begin{verbatim}
 rho = 0.8;
 X = tseries(1:20,@randn);
 X = arf(X,[1,-rho],X,2:20);
 \end{verbatim}


