fastWavelets

Compute Maximal Overlap Discrete Wavelet Transform (DWT) and A Trous DWT

https://github.com/johnswyou/fastwavelets

Repository

Compute Maximal Overlap Discrete Wavelet Transform (DWT) and A Trous DWT

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# fastWavelets 




A lightweight R package for computing the Maximal Overlap Discrete Wavelet Transform (MODWT) and À Trous DWT. This package was originally developed to aid forecasting research in water resources (streamflow forecasting, urban water demand forecasting, etc.)

## Installation

You can install the latest version of fastWavelets with

```r
install.packages("fastWavelets")
```

You can also install the development version of fastWavelets from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("johnswyou/fastWavelets")
```

## Example

Here we decompose a white noise series using MODWT:

```{r example}
library(fastWavelets)

set.seed(839)                       # make this example reproducible

N <- 1e4                            # number of time series points
J <- 9                              # decomposition level
my.filter <- 'coif1'                # filter
X <- matrix(rnorm(N),N,1)           # white noise
modwt.X <- mo_dwt(X,my.filter,J,remove_boundary_coefs=FALSE)
colnames(modwt.X) <- c(paste0("W", 1:J), paste0("V", J))
nbc <- n_boundary_coefs(my.filter, J) # number of boundary affected coefficients

# Visualizations
plot.ts(X, main = "White noise series", ylab="")
plot.ts(modwt.X, nc=1, main="MODWT coefficients")
abline(v=nbc, lwd=2, col="blue", lty=2)
```

In the context of forecasting, everything to the left of the vertical dashed blue line would be removed prior to training a forecasting model using the MODWT coefficients. It is often useful to view wavelet decomposition methods such as the MODWT as a "feature generation" or "feature engineering" method.

Here's how to remove the boundary coefficients:

```{r}
modwt.X <- mo_dwt(X,"coif1",J,remove_boundary_coefs=TRUE)
```

## Available filters

The set of possible values for the argument `filter` (see functions `mo_dwt()` and `atrous_dwt()`):

```r
c('bl7', 'bl9', 'bl10',
'beyl',
'coif1', 'coif2', 'coif3', 'coif4', 'coif5',
'db1', 'db2', 'db3', 'db4', 'db5', 'db6', 'db7', 'db8', 'db9', 'db10', 'db11', 'db12',
'db13', 'db14', 'db15', 'db16', 'db17', 'db18', 'db19', 'db20', 'db21', 'db22', 'db23',
'db24', 'db25', 'db26', 'db27', 'db28', 'db29', 'db30', 'db31', 'db32', 'db33',
'db34', 'db35', 'db36', 'db37', 'db38', 'db39', 'db40', 'db41', 'db42', 'db43', 'db44', 'db45',
'fk4', 'fk6', 'fk8', 'fk14', 'fk18', 'fk22',
'han2_3', 'han3_3', 'han4_5', 'han5_5',
'dmey',
'mb4_2', 'mb8_2', 'mb8_3', 'mb8_4', 'mb10_3', 'mb12_3', 'mb14_3', 'mb16_3', 'mb18_3', 'mb24_3', 'mb32_3',
'sym2', 'sym3', 'sym4', 'sym5', 'sym6', 'sym7', 'sym8', 'sym9', 'sym10', 'sym11', 'sym12', 'sym13', 'sym14',
'sym15', 'sym16', 'sym17', 'sym18', 'sym19', 'sym20', 'sym21', 'sym22', 'sym23', 'sym24', 'sym25', 'sym26', 'sym27',
'sym28', 'sym29', 'sym30', 'sym31', 'sym32', 'sym33', 'sym34', 'sym35', 'sym36', 'sym37', 'sym38', 'sym39', 'sym40',
'sym41', 'sym42', 'sym43', 'sym44', 'sym45',
'vaid',
'la8', 'la10', 'la12', 'la14', 'la16', 'la18', 'la20')
```

## References

Quilty, J., & Adamowski, J. (2018). Addressing the incorrect usage of wavelet-based hydrological and water resources forecasting models for real-world applications with best practices and a new forecasting framework. Journal of Hydrology, 563, 336–353. https://doi.org/10.1016/j.jhydrol.2018.05.003

Bašta, M. (2014). Additive decomposition and boundary conditions in wavelet-based forecasting approaches. Acta Oeconomica Pragensia, 22(2), 48–70. https://doi.org/10.18267/j.aop.431 

Benaouda, D., Murtagh, F., Starck, J.-L., & Renaud, O. (2006). Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting. Neurocomputing, 70(1-3), 139–154. https://doi.org/10.1016/j.neucom.2006.04.005 

Maheswaran, R., & Khosa, R. (2012). Comparative study of different wavelets for hydrologic forecasting. Computers & Geosciences, 46, 284–295. https://doi.org/10.1016/j.cageo.2011.12.015 

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