\HeaderA{HaarMA}{Generate Haar MA processes.}{HaarMA}
\keyword{manip}{HaarMA}
\begin{Description}\relax
This function generates an arbitrary number of observations from a Haar MA process of any order with a particular variance.
\end{Description}
\begin{Usage}
\begin{verbatim}
HaarMA(n, sd=1, order=5)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{n}] The number of observations in the realization that you want to create. Note that n does NOT have to be a power of two.
\item[\code{sd}] The standard deviation of the innovations.
\item[\code{order}] The order of the Haar MA process.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
A Haar MA process is a special kind of time series moving-average (MA) process. A Haar MA process of order k is a MA process of order 2^k. The coefficients of the Haar MA process are given by the filter coefficients of the discrete Haar wavelet at different scales. 

For example: the Haar MA process of order 1 is an MA process of order 2. The coefficients are 1/sqrt(2) and -1/sqrt(2). The Haar MA process of order 2 is an MA process of order 4. The coefficients are 1/2, 1/2, -1/2, -1/2 and so on. It is possible to define other processes for other wavelets as well. 

Any Haar MA process is a good example of a (stationary) LSW process because it is sparsely representable by the locally-stationary wavelet machinery defined in Nason, von Sachs and Kroisandt.
\end{Details}
\begin{Value}
A vector containing a realization of a Haar MA process of the specified order, standard deviation and number of observations.
\end{Value}
\begin{Section}{RELEASE}
Version 3.9 Copyright Guy Nason 1998
\end{Section}
\begin{References}\relax
Nason, G.P., von Sachs, R. and Kroisandt, G. (1998). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. \emph{Technical Report}, Department of Mathematics University of Bristol/ Fachbereich Mathematik, Kaiserslautern.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{HaarConcat}{HaarConcat}}, \code{\LinkA{ewspec}{ewspec}},
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
#
# Generate a Haar MA process of order 1 (high frequency series)
#
#MyHaarMA <- HaarMA(n=151, sd=2, order=1)
#
# Plot it
#
#ts.plot(MyHaarMA)
#
# Generate another Haar MA process of order 3 (lower frequency), but of
# smaller variance
#
#MyHaarMA2 <- HaarMA(n=151, sd=1, order=3)
#
# Plot it
#
#ts.plot(MyHaarMA2)
#
# Let's plot them next to each other so that you can really see the
# differences.
# 
# Plot a vertical dotted line which indicates where the processes are
# joined
#
#ts.plot(c(MyHaarMA, MyHaarMA2))
#abline(v=152, lty=2)
\end{ExampleCode}
\end{Examples}

