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Multiscale correlation using the maximal overlap discrete wavelet transform

`wcorr = modwtcorr(w1,w2)`

`wcorr = modwtcorr(w1,w2,wav)`

```
[wcorr,wcorrci]
= modwtcorr(___)
```

```
[wcorr,wcorrci]
= modwtcorr(___,conflevel)
```

```
[wcorr,wcorrci,pval]
= modwtcorr(___)
```

```
[wcorr,wcorrci,pval,nj]
= modwtcorr(___)
```

`wcorrtable = modwtcorr(___,'table')`

`[___] = modwt(___,'reflection')`

`modwtcorr(___)`

returns
the wavelet correlation by scale for the maximal overlap discrete
wavelet transforms (MODWTs) specified in `wcorr`

= modwtcorr(`w1`

,`w2`

)`w1`

and `w2`

. `wcorr`

is
an *M*-by-1 vector of correlation coefficients, where *M* is
the number of levels with nonboundary wavelet coefficients. If the
final level has enough nonboundary coefficients, `modwtcorr`

returns
the scaling correlation in the final row of `wcorr`

.

returns
an `wcorrtable`

= modwtcorr(___,'table')*M*-by-6 table with the correlation, confidence
bounds, p-value, and adjusted p-value. The table also lists the number
of nonboundary coefficients by level. The row names of the table `wcorrtable`

designate
the type and level of each estimate. For example, `D1`

designates
that the row corresponds to a wavelet or detail estimate at level
1 and `S6`

designates that the row corresponds to
the scaling estimate at level 6. The scaling correlation is only computed
for the final level of the MODWT and only when there are nonboundary
scaling coefficients. You can specify the `'table'`

flag
anywhere after the input transforms `w1`

and `w2`

.
You must enter the entire character vector `'table'`

.
If you specify `'table'`

, `modwtcorr`

only
outputs one argument.

`[___] = modwt(___,'reflection')`

reduces
the number of wavelet and scaling coefficients at each scale by half
before computing the correlation. Use this option only when you obtain
the MODWT of `w1`

and `w2`

were
obtained using the `'reflection' `

boundary condition.
You must enter the entire character vector `'reflection'`

.
If you added a wavelet named 'reflection' using the wavelet manager,
you must rename that wavelet prior to using this option.

`modwtcorr`

supports only unbiased estimates
of the wavelet correlation. For these estimates, the algorithm must
removed the extra coefficients obtained using the `'reflection'`

boundary
condition. Specifying the `'reflection'`

option in `modwtcorr`

is
identical to first obtaining the MODWT of `w1`

and `w2`

using
the default `'periodic' `

boundary handling and then
computing the wavelet correlation estimates.

`modwtcorr(___)`

with no output
arguments plots the wavelet correlations by scale with lower and upper
confidence bounds. By default, the coverage probability is 0.95. Scales
with NaNs for the confidence bounds and the scaling correlation are
excluded.

[1] Percival, D. B., and Walden, A. T. *Wavelet
Methods for Time Series Analysis*. Cambridge, U.K: Cambridge
University Press, 2000.

[2] Whitcher, B., P. Guttorp, and D. B. Percival. "Wavelet
analysis of covariance with application to atmospheric time series." *Journal
of Geophysical Research*, Vol. 105, 2000, pp. 14941–14962.

`imodwt`

| `modwt`

| `modwtmra`

| `modwtvar`

| `modwtxcorr`

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