Package 'wv'

Auto-Covariance and Correlation Functions

Description

The ACF function computes the estimated autocovariance or autocorrelation for both univariate and multivariate cases.

Usage

ACF(x, lagmax = 0, cor = TRUE, demean = TRUE)

Arguments

x	A matrix with dimensions $N \times S$ or N observations and S processes
lagmax	A integer indicating the max lag.
cor	A bool indicating whether the correlation (TRUE) or covariance (FALSE) should be computed.
demean	A bool indicating whether the data should be detrended (TRUE) or not (FALSE)

Details

lagmax default is $10*log10(N/m)$ where $N$ is the number of observations and $m$ is the number of series being compared. If lagmax supplied is greater than the number of observations, then one less than the total will be taken.

Value

An array of dimensions $N \times S \times S$.

Author(s)

Yunxiang Zhang

Examples

# Get Autocorrelation
m = ACF(datasets::AirPassengers)

# Get Autocovariance and do not remove trend from signal
m = ACF(datasets::AirPassengers, cor = FALSE, demean = FALSE)

---

Wavelet variance of IMU Data from an ADIS 16405 sensor

Description

This data set contains wavelet variance of gyroscope and accelerometer data from an ADIS 16405 sensor.

Usage

adis_wv

Format

A list of the following elements:

• "sensor": Name of the sensor.

• "freq": The frequency at which the error signal is measured.

• "n": Sample size of the data.

• "type": The types of sensors considered in the data.

• "axis": The axes of sensors considered in the data.

• "wvar": A list containing the computed wavelet variance based on the data.

Source

The IMU data comes from Department of Geomatics Engineering, University of Calgary.

---

AR(1) process to WV

Description

This function computes the Haar WV of an AR(1) process

Usage

ar1_to_wv(phi, sigma2, tau)

Arguments

phi	A double that is the phi term of the AR(1) process
sigma2	A double corresponding to variance of AR(1) process
tau	A vec containing the scales e.g. $2^{\tau}$

Details

This function is significantly faster than its generalized counter part arma_to_wv.

Value

A vec containing the wavelet variance of the AR(1) process.

Process Haar Wavelet Variance Formula

The Autoregressive Order $1$ (AR($1$)) process has a Haar Wavelet Variance given by:

$\frac{{2{\sigma ^2}\left( {4{\phi ^{\frac{{{\tau _j}}}{2} + 1}} - {\phi ^{{\tau _j} + 1}} - \frac{1}{2}{\phi ^2}{\tau _j} + \frac{{{\tau _j}}}{2} - 3\phi } \right)}}{{{{\left( {1 - \phi } \right)}^2}\left( {1 - {\phi ^2}} \right)\tau _j^2}}$

See Also

arma_to_wv, arma11_to_wv

---

ARMA process to WV

Description

This function computes the Haar Wavelet Variance of an ARMA process

Usage

arma_to_wv(ar, ma, sigma2, tau)

Arguments

ar	A vec containing the coefficients of the AR process
ma	A vec containing the coefficients of the MA process
sigma2	A double containing the residual variance
tau	A vec containing the scales e.g. $2^{\tau}$

Details

The function is a generic implementation that requires a stationary theoretical autocorrelation function (ACF) and the ability to transform an ARMA($p$,$q$) process into an MA($\infty$) (e.g. infinite MA process).

Value

A vec containing the wavelet variance of the ARMA process.

Process Haar Wavelet Variance Formula

The Autoregressive Order $p$ and Moving Average Order $q$ (ARMA($p$,$q$)) process has a Haar Wavelet Variance given by:

$\frac{{{\tau _j}\left[ {1 - \rho \left( {\frac{{{\tau _j}}}{2}} \right)} \right] + 2\sum\limits_{i = 1}^{\frac{{{\tau _j}}}{2} - 1} {i\left[ {2\rho \left( {\frac{{{\tau _j}}}{2} - i} \right) - \rho \left( i \right) - \rho \left( {{\tau _j} - i} \right)} \right]} }}{{\tau _j^2}}\sigma _X^2$

where $\sigma _X^2$ is given by the variance of the ARMA process. Furthermore, this assumes that stationarity has been achieved as it directly

See Also

ARMAtoMA_cpp, ARMAacf_cpp, and arma11_to_wv

---

ARMA(1,1) to WV

Description

This function computes the WV (haar) of an Autoregressive Order 1 - Moving Average Order 1 (ARMA(1,1)) process.

Usage

arma11_to_wv(phi, theta, sigma2, tau)

Arguments

phi	A double corresponding to the autoregressive term.
theta	A double corresponding to the moving average term.
sigma2	A double the variance of the process.
tau	A vec containing the scales e.g. $2^{\tau}$

Details

This function is significantly faster than its generalized counter part arma_to_wv

Value

A vec containing the wavelet variance of the ARMA(1,1) process.

Process Haar Wavelet Variance Formula

The Autoregressive Order $1$ and Moving Average Order $1$ (ARMA($1$,$1$)) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {\phi ,\theta ,{\sigma ^2}} \right) = - \frac{{2{\sigma ^2}\left( { - \frac{1}{2}{{(\theta + 1)}^2}\left( {{\phi ^2} - 1} \right){\tau _j} - (\theta + \phi )(\theta \phi + 1)\left( {{\phi ^{{\tau _j}}} - 4{\phi ^{\frac{{{\tau _j}}}{2}}} + 3} \right)} \right)}}{{{{(\phi - 1)}^3}(\phi + 1)\tau _j^2}}$

See Also

arma_to_wv

---

Calculate Theoretical Allan Variance for Stationary First-Order Autoregressive (AR1) Process

Description

This function allows us to calculate the theoretical allan variance for stationary first-order autoregressive (AR1) process.

Usage

av_ar1(n, phi, sigma2)

Arguments

n	An integer value for the size of the cluster.
phi	A double value for the autocorrection parameter $\phi$.
sigma2	A double value for the variance parameter $\sigma ^2$.

Value

A double indicating the theoretical allan variance for AR1 process.

Note

This function is based on the calculation of the theoretical allan variance for stationary AR1 process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang.) This calculation is fundamental and necessary for the study in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al. (IEEE Signal Processing Letters, 2017).

Author(s)

Yuming Zhang

Examples

av1 = av_ar1(n = 5, phi = 0.9, sigma2 = 1)
av2 = av_ar1(n = 8, phi = 0.5, sigma2 = 2)

---

Calculate Theoretical Allan Variance for Stationary White Noise Process

Description

This function allows us to calculate the theoretical allan variance for stationary white noise process.

Usage

av_wn(sigma2, n)

Arguments

sigma2	A double value for the variance parameter $\sigma ^2$.
n	An integer value for the size of the cluster.

Value

A double indicating the theoretical allan variance for the white noise process.

Note

This function is based on the calculation of the theoretical allan variance for stationary white noise process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang. This calculation is fundamental and necessary for the study in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al. (IEEE Signal Processing Letters, 2017).

Author(s)

Yuming Zhang

Examples

av1 = av_wn(sigma2 = 1, n = 5)
av2 = av_wn(sigma2 = 2, n = 8)

---

Comparison Between Multiple Wavelet Variances

Description

Displays plots of multiple wavelet variances of different time series accounting for CI values.

Usage

compare_wvar(
  ...,
  split = FALSE,
  add_legend = TRUE,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_wv = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ci_wv = NULL,
  point_cex = NULL,
  point_pch = NULL,
  names = NULL,
  cex_labels = 0.8,
  x_range = NULL,
  y_range = NULL
)

Arguments

...	One or more time series objects.
split	A boolean that, if TRUE, arranges the plots into a matrix-like format.
add_legend	A boolean that, if TRUE, adds a legend to the plot.
units	A string that specifies the units of time plotted on the x axes. Note: This argument will not be used if xlab is specified.
xlab	A string that gives a title for the x axes.
ylab	A string that gives a title for the y axes.
main	A string that gives an overall title for the plot.
col_wv	A string that specifies the color of the wavelet variance lines.
col_ci	A string that specifies the color of the confidence interval shade.
nb_ticks_x	An integer that specifies the maximum number of ticks for the x-axis.
nb_ticks_y	An integer that specifies the maximum number of ticks for the y-axis.
legend_position	A string that specifies the position of the legend (use legend_position = NA to remove legend).
ci_wv	A boolean that determines whether confidence interval polygons will be drawn.
point_cex	A double that specifies the size of each symbol to be plotted.
point_pch	A double that specifies the symbol type to be plotted.
names	A string that specifies the name of the WVAR objects.
cex_labels	A double that specifies the magnification of the labels (x and y).
x_range	A vector that specifies the range of values on the x axis (default NULL).
y_range	A vector that specifies the range of values on the y axis (default NULL).

Author(s)

Stephane Guerrier and Justin Lee

Examples

set.seed(999)
n = 10^4
Xt = arima.sim(n = n, list(ar = 0.10))
Yt = arima.sim(n = n, list(ar = 0.35))
Zt = arima.sim(n = n, list(ar = 0.70))
Wt = arima.sim(n = n, list(ar = 0.95))

wv_Xt = wvar(Xt)
wv_Yt = wvar(Yt)
wv_Zt = wvar(Zt)
wv_Wt = wvar(Wt)

compare_wvar(wv_Xt, wv_Yt, wv_Zt, wv_Wt)

---

Combined Plot Comparison Between Multiple Wavelet Variances

Description

This is a helper function for the compare_var() function. This method accepts the same set of arguments as compare_wvar and returns a single plot that compares multiple wavelet variances of different time series accounting for CI values.

Usage

compare_wvar_no_split(graph_details)

Arguments

graph_details

List of inputs

Author(s)

Stephane Guerrier, Justin Lee, and Nathanael Claussen

---

Multi-Plot Comparison Between Multiple Wavelet Variances

Description

This is a helper function for the compare_var() function. This method accepts the same set of arguments as compare_wvar and returns a comparision of multiple wavelet variances of different time series accounting for CI values as a set of different plots.

Usage

compare_wvar_split(graph_details)

Arguments

graph_details

List of inputs

Author(s)

Stephane Guerrier, Justin Lee, and Nathanael Claussen

---

Drift to WV

Description

This function compute the WV (haar) of a Drift process

Usage

dr_to_wv(omega, tau)

Arguments

omega	A double corresponding to the slope of the drift
tau	A vec containing the scales e.g. $2^{\tau}$

Value

A vec containing the wavelet variance of the drift.

Process Haar Wavelet Variance Formula

The Drift (DR) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {{\omega }} \right) = \frac{{\tau _j^2{\omega ^2}}}{{16}}$

---

Discrete Wavelet Transform

Description

Calculation of the coefficients for the discrete wavelet transformation

Usage

dwt(x, nlevels = floor(log2(length(x))), filter = "haar")

Arguments

x	A vector with dimensions N x 1.
nlevels	A integer indicating the $J$ levels of decomposition.
filter	A string indicating the filter name

Details

Performs a level $J$ decomposition of the time series using the pyramid algorithm. The default $J$ is determined by $floor\left(log_2 \left(length\left(x\right)\right)\right)$

Value

A field<vec> that contains the wavelet coefficients for each decomposition level

Author(s)

James Balamuta, Justin Lee and Stephane Guerrier

Examples

set.seed(999)
x = rnorm(2^8)
ret = dwt(x)

summary(ret)

plot(ret)

---

Wavelet variance of IMU Data from IMAR Gyroscopes

Description

This data set contains wavelet variance of IMAR gyroscopes data.

Usage

imar_wv

Format

A list of the following elements:

• "sensor": Name of the sensor.

• "freq": The frequency at which the error signal is measured.

• "n": Sample size of the data.

• "type": The types of sensors considered in the data.

• "axis": The axes of sensors considered in the data.

• "wvar": A list containing the computed wavelet variance based on the data.

Source

The IMU data comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

---

Wavelet variance of IMU Data from a KVH1750 IMU sensor

Description

This data set contains wavelet variance of gyroscope and accelerometer data from an KVH1750 sensor.

Usage

kvh1750_wv

Format

A list of the following elements:

• "sensor": Name of the sensor.

• "freq": The frequency at which the error signal is measured.

• "n": Sample size of the data.

• "type": The types of sensors considered in the data.

• "axis": The axes of sensors considered in the data.

• "wvar": A list containing the computed wavelet variance based on the data.

Source

The IMU data comes from Department of Geomatics Engineering, University of Calgary.

---

Wavelet variance of IMU Data from a LN200 sensor

Description

This data set contains wavelet variance of LN200 gyroscope and accelerometer data.

Usage

ln200_wv

Format

A list of the following elements:

• "sensor": Name of the sensor.

• "freq": The frequency at which the error signal is measured.

• "n": Sample size of the data.

• "type": The types of sensors considered in the data.

• "axis": The axes of sensors considered in the data.

• "wvar": A list containing the computed wavelet variance based on the data.

Source

The IMU data comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

---

Moving Average Order 1 (MA(1)) to WV

Description

This function computes the WV (haar) of a Moving Average order 1 (MA1) process.

Usage

ma1_to_wv(theta, sigma2, tau)

Arguments

theta	A double corresponding to the moving average term.
sigma2	A double the variance of the process.
tau	A vec containing the scales e.g. $2^{\tau}$

Details

This function is significantly faster than its generalized counter part arma_to_wv.

Value

A vec containing the wavelet variance of the MA(1) process.

Process Haar Wavelet Variance Formula

The Moving Average Order $1$ (MA($1$)) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {\theta ,{\sigma ^2}} \right) = \frac{{\left( {{{\left( {\theta + 1} \right)}^2}{\tau _j} - 6\theta } \right){\sigma ^2}}}{{\tau _j^2}}$

See Also

arma_to_wv, arma11_to_wv

---

Maximum Overlap Discrete Wavelet Transform

Description

Calculates the coefficients for the discrete wavelet transformation

Usage

modwt(x, nlevels = floor(log2(length(x) - 1)), filter = "haar")

Arguments

x	A vector with dimensions N x 1.
nlevels	A integer indicating the $J$ levels of decomposition.
filter	A string indicating the filter name

Details

Performs a level $J$ decomposition of the time series using the pyramid algorithm. The default $J$ is determined by $floor\left(log_2 \left(length\left(x\right)\right)\right)$

Value

A field<vec> that contains the wavelet coefficients for each decomposition level

Author(s)

James Balamuta, Justin Lee and Stephane Guerrier

Examples

set.seed(999)
x = rnorm(100)
ret = modwt(x)

summary(ret)

plot(ret)

---

Wavelet variance of IMU Data from a navchip sensor

Description

This data set contains wavelet variance of gyroscope and accelerometer data from a navchip sensor.

Usage

navchip_wv

Format

A list of the following elements:

• "sensor": Name of the sensor.

• "freq": The frequency at which the error signal is measured.

• "n": Sample size of the data.

• "type": The types of sensors considered in the data.

• "axis": The axes of sensors considered in the data.

• "wvar": A list containing the computed wavelet variance based on the data.

Source

The IMU data of the navchip sensor comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

---

Quantisation Noise (QN) to WV

Description

This function compute the Haar WV of a Quantisation Noise (QN) process

Usage

qn_to_wv(q2, tau)

Arguments

q2	A double corresponding to variance of drift
tau	A vec containing the scales e.g. $2^{\tau}$

Value

A vec containing the wavelet variance of the QN.

Process Haar Wavelet Variance Formula

The Quantization Noise (QN) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {{Q^2}} \right) = \frac{{6{Q^2}}}{{\tau _j^2}}$

---

Comparison between classical and robust Wavelet Variances

Description

Displays a plot of the wavelet variances (classical and robust) for a given time series accounting for CI values.

Usage

robust_eda(
  x,
  eff = 0.6,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_wv = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ...
)

Arguments

x	A time series objects.
eff	An integer that specifies the efficiency of the robust estimator.
units	A string that specifies the units of time plotted on the x axis.
xlab	A string that gives a title for the x axis.
ylab	A string that gives a title for the y axis.
main	A string that gives an overall title for the plot.
col_wv	A string that specifies the color of the wavelet variance line.
col_ci	A string that specifies the color of the confidence interval shade.
nb_ticks_x	An integer that specifies the maximum number of ticks for the x-axis.
nb_ticks_y	An integer that specifies the maximum number of ticks for the y-axis.
legend_position	A string that specifies the position of the legend (use legend_position = NA to remove legend).
...	Additional arguments affecting the plot.

Value

Plot of wavelet variance and confidence interval for each scale.

Author(s)

Stephane Guerrier, Nathanael Claussen, and Justin Lee

Examples

set.seed(999)
n = 10^4
Xt = rnorm(n)
wv = wvar(Xt)

plot(wv)
plot(wv, main = "Simulated white noise", xlab = "Scales")
plot(wv, units = "sec", legend_position = "topright")
plot(wv, col_wv = "darkred", col_ci = "pink")

---

Random Walk to WV

Description

This function compute the WV (haar) of a Random Walk process

Usage

rw_to_wv(gamma2, tau)

Arguments

gamma2	A double corresponding to variance of RW
tau	A vec containing the scales e.g. $2^{\tau}$

Value

A vec containing the wavelet variance of the random walk.

Process Haar Wavelet Variance Formula

The Random Walk (RW) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {{\gamma ^2}} \right) = \frac{{\left( {\tau _j^2 + 2} \right){\gamma ^2}}}{{12{\tau _j}}}$

---

Create the ts.model obj.desc given split values

Description

Computes the total phi and total theta vector length.

Usage

sarma_objdesc(ar, ma, sar, sma, s, i, si)

Arguments

ar	A vec containing the non-seasonal phi parameters.
ma	A vec containing the non-seasonal theta parameters.
sar	A vec containing the seasonal phi parameters.
sma	A vec containing the seasonal theta parameters.
s	An unsigned integer containing the frequency of seasonality.
i	An unsigned integer containing the number of non-seasonal differences.
si	An unsigned integer containing the number of seasonal differences.

Value

A vec with rows:

np

Number of Non-Seasonal AR Terms

nq

Number of Non-Seasonal MA Terms

nsp

Number of Seasonal AR Terms

nsq

Number of Seasonal MA Terms

nsigma

Number of Variances (always 1)

s

Season Value

i

Number of non-seasonal differences

si

Number of Seasonal Differences

---

Haar filter for a spatial case

Description

Haar filter for a spatial case

Usage

sp_hfilter(jscale)

Arguments

jscale

An int of the Number of Scales

---

Compute the Spatial Wavelet Coefficients

Description

Compute the Spatial Wavelet Coefficients

Usage

sp_modwt_cpp(X, J1, J2)

Arguments

X	is a matrix with row, col orientation
J1, J2	is the levels of decomposition along the rows, columns

Details

By default this function will return the wavelet coefficient in addition to the wavelet

Value

A list of vectors containing the wavelet coefficients.

---

Cross Covariance of Matrix

Description

Calculates the Cross-covariance between multiple wavelet transfomations (dwt or modwt)

Usage

wccv(x, decomp = "modwt", filter = "haar", nlevels = NULL)

Arguments

x	A vector with dimensions N x M.
decomp	A string that indicates whether to use the "dwt" or "modwt" decomposition.
filter	A string that specifies what 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))).

Details

If nlevels is not specified, it is set to $\left\lfloor {{{\log }_2}\left( {length\left( x \right)} \right)} \right\rfloor$

Value

Returns a matrix of lists of all the possible pair cross-covariance, variance of each wavelet cross-covariance and its 95

Author(s)

Justin Lee

---

Mapping to log10 scale

Description

Map x to the value in log10 scale

Usage

wccv_get_y(x, tick_y_min, tick_y_step)

Arguments

x	A vector with dimensions J x 1.
tick_y_min	A negtive integer the minimum power of 10, which corresponds to the smallest scale on y-axis.
tick_y_step	An integer indicating the increment of the sequence.

Details

tick_y_min is usually chosen as $floor(min(log10(abs(x))))$

Value

A field<vec> that contains values in log10 scale.

Author(s)

James Balamuta and Justin Lee

Examples

x = 2^(-1:-9)
y.min = floor(min(log10(abs(x))))
y.step = 2
wccv_get_y(x, y.min, y.step)

---

Cross Covariance of a TS Pair

Description

Calculates the Cross-covariance between two wavelet transfomations (dwt or modwt)

Usage

wccv_pair(x, y, decomp = "modwt", filter = "haar", nlevels = NULL)

Arguments

x	A vector with dimensions N x 1.
y	A vector with dimensions N x 1.
decomp	A string that indicates whether to use the "dwt" or "modwt" decomposition.
filter	A string that specifies what 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))).

Details

If nlevels is not specified, it is set to $\left\lfloor {{{\log }_2}\left( {length\left( x \right)} \right)} \right\rfloor$

Value

Returns a list of a matrix containing cross-covariance, variance of each wavelet cross-covariance and its 95

Author(s)

Justin Lee

---

Gaussian White Noise to WV

Description

This function compute the Haar WV of a Gaussian White Noise process

Usage

wn_to_wv(sigma2, tau)

Arguments

sigma2	A double corresponding to variance of WN
tau	A vec containing the scales e.g. $2^{\tau}$

Value

A vec containing the wavelet variance of the white noise.

Process Haar Wavelet Variance Formula

The Gaussian White Noise (WN) process has a Haar Wavelet Variance given by:

$\nu _j^2\left( {{\sigma ^2}} \right) = \frac{{{\sigma ^2}}}{{\tau _j^2}}$

---

Wavelet Variance

Description

Calculates the (MO)DWT wavelet variance

Usage

wvar(x, ...)

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

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

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

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

## Default S3 method:
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.

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.

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

Author(s)

James Balamuta, Justin Lee and Stephane Guerrier

Examples

set.seed(999)
x = rnorm(100)

# Default
wvar(x)

# Robust
wvar(x, robust = TRUE, eff=0.3)

# Classical
wvar(x, robust = FALSE, eff=0.3)

# 90% Confidence Interval 
wvar(x, alpha = 0.10)

---