HaarMA | R Documentation |
This function generates an arbitrary number of observations from a Haar MA process of any order with a particular variance.
HaarMA(n, sd=1, order=5)
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. |
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.
A vector containing a realization of a Haar MA process of the specified order, standard deviation and number of observations.
Version 3.9 Copyright Guy Nason 1998
G P Nason
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.
HaarConcat
, ewspec
,
# # 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)
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