Srho.test {tseriesEntropy}

Entropy Test For Serial And Cross Dependence For Categorical Sequences

Description

Bootstrap/permutation tests of serial and cross dependence for integer or categorical sequences.

Usage

Srho.test(x, y, lag.max=10, B = 1000, stationary = TRUE, plot = TRUE,
quant = c(0.95, 0.99), nor = FALSE)

Arguments

x, y

integer or factor time series objects or vectors. (y is missing in the univariate case).

lag.max

maximum lag at which to calculate Srho; the default is 10.

B

number of bootstrap/permutation replications.

stationary

logical. If TRUE assumes stationarity and computes marginal probabilities by using all the N observations. If FALSE uses N-k observations where k is the lag.

plot

logical. If TRUE(the default) produces a plot of Srho together with permutation confidence bands under the null hypothesis of independence.

quant

quantiles to be specified for the computation of the significant lags and the plot of confidence bands. Up to 2 quantiles can be specified. Defaults are 95% and 99%.

nor

logical. If TRUE normalizes Srho with respect to its attainable maximum. Defaults to FALSE.

Details

Univariate version: test for serial dependence

Srho.test(x, lag.max, B = 1000,
stationary = TRUE, plot = TRUE, quant = c(0.95, 0.99), nor = FALSE)

Bivariate version: test for cross dependence

Srho.test(x, y, lag.max, B = 1000,
stationary = TRUE, plot = TRUE, quant = c(0.95, 0.99), nor = FALSE)

Value

An object of class "Srho.test", which is a list with the following elements:

.Data

vector of lag.max elements containing Srho computed at each lag.

quantiles

Object of class "matrix": contains the quantiles of the bootstrap/permutation distribution under the null hypothesis.

test.type

Object of class "character": contains a description of the type of test performed.

significant.lags

Object of class "list": contains the lags at which Srho exceeds the confidence bands at quant% under the null hypothesis.

p.value

Object of class "numeric": contains the bootstrap p-value for each lag.

lags

integer vector that 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.

Warning

Unlike ccf the lag k value returned by Srho.test(x,y) estimates Srho between x[t] and y[t+k]. The result is returned invisibly if plot is TRUE.

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.

See Also

See also Srho, Srho.ts. The function Srho.test.ts implements the same test for numeric data.

Examples

set.seed(12)
x <- as.integer(rbinom(n=30,size=4,prob=0.5))
y <- as.integer(rbinom(n=30,size=4,prob=0.5))
z <- as.integer(c(4,abs(x[-30]*2-2))-rbinom(n=30,size=1,prob=1/2))

# no dependence
Srho.test(x,lag.max=4)   # univariate
Srho.test(x,y,lag.max=4) # bivariate

# lag 1 dependence
Srho.test(x,z,lag.max=4) # bivariate