modwt.vt {WASP}

Variance Transformation Operation - MODWT

Description

Variance Transformation Operation - MODWT

Usage

modwt.vt(
  data,
  wf,
  J,
  boundary,
  cov.opt = "auto",
  flag = "biased",
  detrend = FALSE,
  backward = FALSE,
  verbose = TRUE
)

Arguments

data

A list of response x and dependent variables dp.

wf

Name of the wavelet filter to use in the decomposition.

J

Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2).

boundary

Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

cov.opt

Options of Covariance matrix sign. Use "pos", "neg", or "auto".

flag

Biased or Unbiased variance transformation, c("biased","unbiased").

detrend

Detrend the input time series or just center, default (F).

backward

Detrend the input time series or just center, default (F).

verbose

A logical indicating if some “progress report” should be given.

Value

A list of 8 elements: wf, J, boundary, x (data), dp (data), dp.n (variance transformed dp), and S (covariance matrix).

References

Jiang, Z., Sharma, A., & Johnson, F. (2020). Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling. Water Resources Research, 56(3), e2019WR026962.

Jiang, Z., Rashid, M. M., Johnson, F., & Sharma, A. (2020). A wavelet-based tool to modulate variance in predictors: an application to predicting drought anomalies. Environmental Modelling & Software, 135, 104907.

Examples

### real-world example
data(Ind_AWAP.2.5)
data(obs.mon)
data(SPI.12)
x <- window(SPI.12, start = c(1950, 1), end = c(2009, 12))
dp <- window(obs.mon, start = c(1950, 1), end = c(2009, 12))

op <- par(mfrow = c(ncol(dp), 1), pty = "m", mar = c(1, 4, 1, 2))
for (id in sample(Ind_AWAP.2.5, 1)) {
  data <- list(x = x[, id], dp = dp)
  dwt <- modwt.vt(data, wf = "d4", J = 7, boundary = "periodic", cov.opt = "auto")

  for (i in 1:ncol(dp)) {
    ts.plot(dwt$dp[, i], dwt$dp.n[, i], xlab = NA, col = c("black", "red"), lwd = c(2, 1))
  }
}
par(op)

### synthetic example
# frequency, sampled from a given range
fd <- c(3, 5, 10, 15, 25, 30, 55, 70, 95)

data.SW1 <- data.gen.SW(nobs = 512, fp = 25, fd = fd)
dwt.SW1 <- modwt.vt(data.SW1, wf = "d4", J = 7, boundary = "periodic", cov.opt = "auto")

x.modwt <- waveslim::modwt(dwt.SW1$x, wf = "d4", n.levels = 7, boundary = "periodic")
dp.modwt <- waveslim::modwt(dwt.SW1$dp[, 1], wf = "d4", n.levels = 7, boundary = "periodic")
dp.vt.modwt <- waveslim::modwt(dwt.SW1$dp.n[, 1], wf = "d4", n.levels = 7, boundary = "periodic")

sum(sapply(dp.modwt, var))
var(dwt.SW1$dp[, 1])
sum(sapply(dp.vt.modwt, var))
var(dwt.SW1$dp.n[, 1])

data <- rbind(
  sapply(dp.modwt, var) / sum(sapply(dp.modwt, var)),
  sapply(dp.vt.modwt, var) / sum(sapply(dp.vt.modwt, var))
)

bar <- barplot(data, beside = TRUE, col = c("red", "blue"))
lines(x = bar[2, ], y = sapply(x.modwt, var) / sum(sapply(x.modwt, var)))
points(x = bar[2, ], y = sapply(x.modwt, var) / sum(sapply(x.modwt, var)))