# Haar2MA.horiz: Generate 2-D Haar MA process (horizontal direction). In LS2W: Locally stationary two-dimensional wavelet process estimation scheme

## Description

These functions generate an arbitrary number of observations from a Haar MA process of any order with a particular variance. We will focus here on `Haar2MA.horiz` — the routine which generates processes having spectral structure solely in the horizonal decomposition direction.

## Usage

 `1` ```Haar2MA.horiz(n, sd = 1, order = 5) ```

## Arguments

 `n` The dimension of the realisation that you want to create. Note that `n` does NOT have to be a power of two, though it is square (nxn). `sd` The standard deviation of the innovations. `order` The order of the MA process.

## Details

A two-dimensional Haar MA process is a special kind of moving-average (MA) field. A horizontal Haar MA process of order \$k\$ is a MA field of order \$2^k-1\$, the coefficients of the process being given by the filter coefficients of the two-dimensional, discrete Haar wavelet at various scales within the horizontal direction. For example the horizontal Haar MA field of order 1 is an MA process of order 1. It is possible to define such processes for other wavelets as well.

## Value

A matrix containing a realisation of the specified dimension, order and standard deviation.

Idris Eckley

## References

Eckley, I.A., Nason, G.P. and Treloar, R.L. (2010) Locally stationary wavelet fields with application to the modelling and analysis of image texture. Journal of the Royal Statistical Society (Series C), 59, 595 - 616.

Eckley, I.A. and Nason, G.P. (2011). LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R, Journal of Statistical Software, 43(3), 1-23. URL http://www.jstatsoft.org/v43/i03/.

`Haar2MA.diag`,`HaarMontage`
 ```1 2 3 4 5 6 7 8``` ```# # Generate a realisation of a diagonal component 2-D MA field # of order 4. # image1 <- Haar2MA.horiz(n=128, sd=3, order=4) # # # ```