stepwise.VT {WASP}

Calculate stepwise high order VT in calibration

Description

Calculate stepwise high order VT in calibration

Usage

stepwise.VT(
  data,
  alpha = 0.1,
  nvarmax = 4,
  mode = c("MRA", "MODWT", "AT"),
  wf,
  J,
  method = "dwt",
  pad = "zero",
  boundary = "periodic",
  cov.opt = "auto",
  flag = "biased",
  detrend = FALSE
)

Arguments

data

A list of data, including response and predictors

alpha

The significance level used to judge whether the sample estimate is significant. A default alpha value is 0.1.

nvarmax

The maximum number of variables to be selected.

mode

A mode of variance transformation, i.e., MRA, MODWT, or AT

wf

Wavelet family

J

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

method

Either "dwt" or "modwt" of MRA.

pad

The method used for extend data to dyadic size. Use "per", "zero", or "sym".

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.

detrend

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

Value

A list of 2 elements: the column numbers of the meaningful predictors (cpy), and partial informational correlation (cpyPIC).

References

Sharma, A., Mehrotra, R., 2014. An information theoretic alternative to model a natural system using observational information alone. Water Resources Research, 50(1): 650-660.

Jiang, Z., Sharma, A., & Johnson, F. (2021). Variable transformations in the spectral domain – Implications for hydrologic forecasting. Journal of Hydrology, 126816.

Examples

### Real-world example
data("rain.mon")
data("obs.mon")
mode <- switch(1,
  "MRA",
  "MODWT",
  "AT"
)
wf <- "d4"
station.id <- 5 # station to investigate
#SPI.12 <- SPEI::spi(rain.mon, scale = 12)$fitted
SPI.12 <- SPI.calc(window(rain.mon, start=c(1949,1), end=c(2009,12)),sc=12)
lab.names <- colnames(obs.mon)
# plot.ts(SPI.12[,1:10])

x <- window(SPI.12[, station.id], start = c(1950, 1), end = c(1979, 12))
dp <- window(obs.mon[, lab.names], start = c(1950, 1), end = c(1979, 12))

data <- list(x = x, dp = matrix(dp, ncol = ncol(dp)))

dwt <- stepwise.VT(data, mode = mode, wf = wf, flag = "biased")

### plot transformed predictor before and after
cpy <- dwt$cpy
op <- par(mfrow = c(length(cpy), 1), mar = c(2, 3, 2, 1))
for (i in seq_along(cpy)) {
  ts.plot(cbind(dwt$dp[, i], dwt$dp.n[, i]), xlab = "NA", col = 1:2)
}
par(op)