Calculates the (MO)DWT wavelet variance

wvar(x, ...)

# S3 method for lts
wvar(
  x,
  decomp = "modwt",
  filter = "haar",
  nlevels = NULL,
  alpha = 0.05,
  robust = FALSE,
  eff = 0.6,
  to.unit = NULL,
  ...
)

# S3 method for gts
wvar(
  x,
  decomp = "modwt",
  filter = "haar",
  nlevels = NULL,
  alpha = 0.05,
  robust = FALSE,
  eff = 0.6,
  to.unit = NULL,
  ...
)

# S3 method for ts
wvar(
  x,
  decomp = "modwt",
  filter = "haar",
  nlevels = NULL,
  alpha = 0.05,
  robust = FALSE,
  eff = 0.6,
  to.unit = NULL,
  ...
)

# S3 method for imu
wvar(
  x,
  decomp = "modwt",
  filter = "haar",
  nlevels = NULL,
  alpha = 0.05,
  robust = FALSE,
  eff = 0.6,
  to.unit = NULL,
  ...
)

# S3 method for default
wvar(
  x,
  decomp = "modwt",
  filter = "haar",
  nlevels = NULL,
  alpha = 0.05,
  robust = FALSE,
  eff = 0.6,
  freq = 1,
  from.unit = NULL,
  to.unit = NULL,
  ...
)

Arguments

x

A vector with dimensions N x 1.

...

Further arguments passed to or from other methods.

decomp

A string that indicates whether to use a "dwt" or "modwt" decomposition.

filter

A string that specifies which wavelet filter to use.

nlevels

An integer that indicates the level of decomposition. It must be less than or equal to floor(log2(length(x))).

alpha

A double that specifies the significance level which in turn specifies the \(1-\alpha\) confidence level.

robust

A boolean that triggers the use of the robust estimate.

eff

A double that indicates the efficiency as it relates to an MLE.

to.unit

A string indicating the unit to which the data is converted.

freq

A numeric that provides the rate of samples.

from.unit

A string indicating the unit from which the data is converted.

Value

A list with the structure:

  • "variance": Wavelet Variance

  • "ci_low": Lower CI

  • "ci_high": Upper CI

  • "robust": Robust active

  • "eff": Efficiency level for Robust calculation

  • "alpha": p value used for CI

  • "unit": String representation of the unit

Details

The default value of nlevels will be set to \(\left\lfloor {{{\log }_2}\left( {length\left( x \right)} \right)} \right\rfloor\), unless otherwise specified.

Examples

set.seed(999) x = rnorm(100) # Default wvar(x)
#> Variance Low CI High CI #> 2 0.45217782 0.316045047 0.7004281 #> 4 0.23033971 0.140751059 0.4440086 #> 8 0.13710252 0.069880858 0.3811887 #> 16 0.05160384 0.020543745 0.2878292 #> 32 0.01172383 0.003282007 0.3685303
# Robust wvar(x, robust = TRUE, eff=0.3)
#> Variance Low CI High CI #> 2 0.549798561 0.247597207 1.1008897 #> 4 0.239947099 0.069559083 0.6463224 #> 8 0.131799969 0.013817225 0.5602029 #> 16 0.061956778 0.013817225 0.5797696 #> 32 0.007484438 0.003742219 0.4233586
# Classical wvar(x, robust = FALSE, eff=0.3)
#> Variance Low CI High CI #> 2 0.45217782 0.316045047 0.7004281 #> 4 0.23033971 0.140751059 0.4440086 #> 8 0.13710252 0.069880858 0.3811887 #> 16 0.05160384 0.020543745 0.2878292 #> 32 0.01172383 0.003282007 0.3685303
# 90% Confidence Interval wvar(x, alpha = 0.10)
#> Variance Low CI High CI #> 2 0.45217782 0.334461347 0.6516656 #> 4 0.23033971 0.152096918 0.3978812 #> 8 0.13710252 0.077666345 0.3200430 #> 16 0.05160384 0.023732362 0.2119612 #> 32 0.01172383 0.004018555 0.1908247