Package 'IndGenErrors'

Cross-correlations for testing independence between the innovations of 2 series of same length

Description

This function computes the cross-correlations between x(t) and y(t-l), for l=-lag,.., lag, and also the combination (Wald's type) of these statistics.

Usage

crosscor_2series(x, y, lag, graph = TRUE)

Arguments

x	Pseudo-observations (or residuals) of first series
y	Pseudo-observations (or residuals) of second series
lag	Maximum number of lags around 0
graph	Set to TRUE for a correlogram for all possible lags.

Value

stat	Cross-correlations for all lags
LB	Sum of squares of cross-correlations
pvalue	P-value of LB
subsets	c(-lag:lag)
n	length of the time series

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

Examples

data(gas)
outr <-crosscor_2series(gas$xres,gas$yres,3)

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Cross-correlations statistics for testing independence between the innovations of 3 series of same length

Description

This function computes the cross-correlations for all lags = -lag2, .. lag2, for all pairs, and for pair of lags = (-lag3,-lag3),...(lag3,lag3) for the three series3.

Usage

crosscor_3series(x, y, z, lag2, lag3)

Arguments

x	Pseudo-observations (or residuals) of first series.
y	Pseudo-observations (or residuals) of second series.
z	Pseudo-observations (or residuals) of third series.
lag2	Maximum number of lags around 0 for pairs of series.
lag3	Maximum number of lags around 0 for the three series.

Value

LB	Cross-correlations for all lags and for all subsets
H	Sum of squares of cross-correlations for all subsets
pvalue	P-value of LB for all subsets and H
n	length of the time series

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

Examples

# Romano-Siegel's example #
data(romano_ex)
outr = crosscor_3series(romano_ex$x,romano_ex$y,romano_ex$z,5,2)

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Cross-correlogram

Description

This function, used in crosscor_2series and crosscor_3series plots the graphs of the cross-correlation statistics.

Usage

CrossCorrelogram(object, comb, rot = 0)

Arguments

object	List of the output (statistics, pvalues) from crosscor_2series and crosscor_3series
comb	Name (string) of series, e.g., comb="(x,y)"
rot	Rotation of labels (default=0)

Value

Output

No values are returned; only the graph is printed

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

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Cramer-von Mises Moebius statistics for testing independence between the innovations of 2 series of same length

Description

This function computes the Cramer-von Mises statistics between x(t) and y(t-l), for l=-lag,.., lag, and also the combinations of the p-values of these statistics.

Usage

cvm_2series(x, y, lag, graph = TRUE)

Arguments

x	Pseudo-observations (or residuals) of first series
y	Pseudo-observations (or residuals) of second series
lag	Maximum number of lags around 0
graph	Set to TRUE for a dependogram for all possible lags.

Value

cvm	Cramer-von Mises statistics for all lags
Wstat	Sum of (unbiased) Cramer-von Mises statistics
Fstat	Combination of p-values of the Cramer-von Mises statistics
pvalue	List of p-values for the cvm, Wstat, and Fstat

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

Examples

data(gas)
out <-cvm_2series(gas$xres,gas$yres,3)

---

Cramer-von Mises Moebius statistics for testing independence between the innovations of 3 series of same length

Description

This function computes the Cramer-von Mises statistics between x(t), y(t-l2), z(t-l3), for l2=-lag2,.., lag2, l3=-lag3,.., lag3,and also the combinations of these statistics.

Usage

cvm_3series(x, y, z, lag2, lag3)

Arguments

x	Pseudo-observations (or residuals) of first series.
y	Pseudo-observations (or residuals) of second series.
z	Pseudo-observations (or residuals) of third series.
lag2	Maximum number of lags around 0 for pairs of series.
lag3	Maximum number of lags around 0 for the three series.

Value

cvm	Cramer-von Mises statistics for all lags and for all subsets
Wstat	Sum of (unbiased) Cramer-von Mises statistics for all subsets
Fstat	Combination of p-values of the Cramer-von Mises statistics
pvalue	List of p-values for the cvm, Wstat, and Fstat

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

Examples

set.seed(1)
x0 = rnorm(100); y = rnorm(100); z = rnorm(100);

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Dependogram for Cramer-von Mises statistics

Description

This function, used in cvm_2series and cvm_3series draws the P-values of the Moebius Cramer-von Mises statistics.

Usage

Dependogram(object, stat, rot = 0)

Arguments

object	List of the output (statistics, pvalues) from cvm_2series and cvmr_3series
stat	Name (string) of statistics to be used
rot	Rotation of labels (default=0)

Value

Output

No values are returned; only the graph is printed

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

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Standardized residuals of weekly log-returns of gas and oil prices in Canada from 2008 to end of February 2011

Description

Data frame containg xres (standardized residuals of gas prices from a ARMA(2,2) model) and yres (standardized residuals of oil prices from a ARMA(1,1)-GARCH(1,1) model).

Usage

data(gas)

Format

Residuals

Examples

data(gas)
plot(gas$xres)

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Simulated values of a Romano & Siegel example

Description

Data frame containing 100 values of x,y,z generated as follows: x0 = rnorm(100); y = rnorm(100); z = rnorm(100); x = abs(x0)*sign(y*z). All pairs are independent but the three series are not.

Usage

data(romano_ex)

Format

dataframe

Examples

data(romano_ex)
plot(romano_ex$x)

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