Srho.ts {tseriesEntropy}

Entropy Measure Of Serial And Cross Dependence

Description

Entropy based measure of serial and cross dependence for continuous data. For integer/categorical data see Srho. Implements a normalized version of the Hellinger/Matusita distance. As shown in the references the metric measure is a proper distance.

Usage

Srho.ts(x, y, lag.max = 10, bw = c("reference", "mlcv", "lscv", "scv", "pi"),
bdiag=TRUE, method = c("integral", "summation"), plot = TRUE, tol = 0.001, ...)

Arguments

x, y

univariate numeric time series object or numeric vectors (y is missing in the univariate case).

lag.max

maximum lag at which to calculate Srho; default is 10

bw

Object of class "character": bandwidth selection method, can be "reference", "mlcv", "lscv", "scv", "pi".

bdiag

Object of class "logical": if TRUE uses the diagonal version of the bandwidth selectors lscv, scv, pi.

method

Object of class "character": computation method, can be "integral" or "summation".

plot

logical. If TRUE (the default) Srho is plotted.

tol

max. tolerance, passed to hcubature.

...

further arguments, typically passed to hcubature.

Details

Univariate version: serial entropy

Srho.ts(x, lag.max = 10,
 bw = c("reference", "mlcv", "lscv", "scv", "pi"), bdiag=TRUE,
 method = c("integral", "summation"), plot = TRUE, tol = 0.001)

Bivariate version: cross entropy

Srho.ts(x, y, lag.max = 10,
 bw = c("reference", "mlcv", "lscv", "scv", "pi"), bdiag=TRUE,
 method = c("integral", "summation"), plot = TRUE, tol = 0.001)

The bandwidth selection methods are the following:

reference:

reference criterion.

mlcv:

maximum likelihood cross-validation.

lscv:

least-squares cross-validation, see Hlscv.

scv:

smoothed cross-validation, see Hscv

pi:

plugin, see Hpi

If bdiag = TRUE (the default), the diagonal bandwidth selectors Hlscv.diag, Hscv.diag, Hpi.diag are used.

Value

An object of class "Srho.ts", with the following slots:

.Data

Object of class "numeric": contains Srho computed on the data set.

method

Object of class "character": computation method

bandwidth

Object of class "character": bandwidth selection method.

lags

Object of class "integer": contains the lags at which Srho is computed.

stationary

Object of class "logical": TRUE if the stationary version is computed.

data.type

Object of class "character": contains the data type.

notes

Object of class "character": additional notes.

Author(s)

Simone Giannerini<[e-mail]>

References

Granger C. W. J., Maasoumi E., Racine J., (2004) A dependence metric for possibly nonlinear processes. Journal of Time Series Analysis, 25(5), 649–669.

Maasoumi E., (1993) A compendium to information theory in economics and econometrics. Econometric Reviews, 12(2), 137–181.

Giannerini S., Maasoumi E., Bee Dagum E., (2015), Entropy testing for nonlinear serial dependence in time series, Biometrika, 102(3), 661–675 doi:10.1093/biomet/asv007.

See Also

Srho.test.ts, hcubature, ks. The function Srho implements the same measure for integer/categorical data.

Examples

set.seed(11)
x <- arima.sim(list(order = c(1,0,0), ar = 0.8), n = 50)
S <- Srho.ts(x,lag.max=5,method="integral",bw="mlcv")

# creates a nonlinear dependence at lag 1
y <- c(runif(1),x[-50]^2*0.8-0.3)
S <- Srho.ts(x,y,lag.max=3,method="integral",bw="mlcv")