HaarMA: Generate Haar MA processes.

In wavethresh: Wavelets Statistics and Transforms

Generate Haar MA processes.

Description

This function generates an arbitrary number of observations from a Haar MA process of any order with a particular variance.

Usage

HaarMA(n, sd=1, order=5)

Arguments

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.
sd	The standard deviation of the innovations.
order	The order of the Haar MA process.

Details

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 examples: 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 examples of a (stationary) LSW process because it is sparsely representable by the locally-stationary wavelet machinery defined in Nason, von Sachs and Kroisandt.

Value

A vector containing a realization of a Haar MA process of the specified order, standard deviation and number of observations.

RELEASE

Version 3.9 Copyright Guy Nason 1998

Author(s)

G P Nason

References

Nason, G.P., von Sachs, R. and Kroisandt, G. (1998). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Technical Report, Department of Mathematics University of Bristol/ Fachbereich Mathematik, Kaiserslautern.

See Also

HaarConcat, ewspec,

Examples

#
# Generate a Haar MA process of order 1 (high frequency series)
#
MyHaarMA <- HaarMA(n=151, sd=2, order=1)
#
# Plot it
#
## Not run: 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
#
## Not run: 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
#
## Not run: ts.plot(c(MyHaarMA, MyHaarMA2))
## Not run: abline(v=152, lty=2)

wavethresh documentation built on Sept. 11, 2024, 9:33 p.m.