HaarMA {wavethresh} | R Documentation

## 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 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.

### 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

### 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
    #
    #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)

[Package wavethresh version 4.0-2 Index]