cc.test: Testing zero cross-correlation

In testcorr: Testing Zero Correlation

Description

The function cc.test computes the test statistics for examining the null hypothesis of zero cross-correlation for bivariate time series given in Dalla, Giraitis and Phillips (2020).

Usage

cc.test(x, y, max.lag, alpha = 0.05, lambda = 2.576, plot = TRUE,
        table = TRUE, var.names = NULL, scale.font = 1)

Arguments

x	A numeric vector or a univariate numeric time series object or a data frame.
y	A numeric vector or a univariate numeric time series object or a data frame.
max.lag	Maximum lag at which to calculate the test statistics.
alpha	Significance level for hypothesis testing used in the plots. Default is 0.05.
lambda	Threshold in Q-tilde test statistics. Default is 2.576.
plot	Logical. If TRUE the sample cross-correlations with their confidence bands and the cumulative statistics with their critical values are plotted. Default is TRUE.
table	Logical. If TRUE the sample cross-correlations, the confidence bands, the test statistics and their p-values are printed out. Default is TRUE.
var.names	NULL or a character string specifying the variable names. If NULL and x,y have names, the names of x,y are used. If NULL and x,y have no names, the string c("x","y") is used. Default is NULL.
scale.font	A positive number indicating the scaling of the font size in the plots. Default is 1.

Details

The standard t and robust t-tilde statistics are for testing the null hypothesis H[0]:ρ[k]=0 at lags k=-max.lag,...,-1,0,1,max.lag, and the standard HB and robust Q-tilde statistics are for testing the null hypothesis H[0]:ρ[0]=...=ρ[m]=0 at lags m=-max.lag,...,-1,0,1,max.lag, where ρ[k] denotes the cross-correlation of x[t] and y[t-k] at lag k.

Value

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

lag	The lags used.
cc	The sample cross-correlations.
scb	The lower and upper limit of the confidence bands based on the standard test statistics.
rcb	The lower and upper limit of the confidence bands based on the robust test statistics.
t	The t test statistics.
pvt	The p-values for the t test statistics.
ttilde	The t-tilde test statistics.
pvtttilde	The p-values for the t-tilde test statistics.
hb	The HB test statistics.
pvhb	The p-values for the HB test statistics.
qtilde	The Q-tilde test statistics.
pvqtilde	The p-values for the Q-tilde test statistics.

Note

Missing values are not allowed.

Author(s)

Violetta Dalla, Liudas Giraitis and Peter C. B. Phillips

References

Dalla, V., Giraitis, L. and Phillips, P. C. B. (2020). "Robust Tests for White Noise and Cross-Correlation". Cowles Foundation, Discussion Paper No. 2194, https://cowles.yale.edu/sites/default/files/files/pub/d21/d2194-r.pdf.

Examples

x <- rnorm(100)
y <- rnorm(100)
cc.test(x, y, max.lag = 10)

Example output

Tests for zero cross-correlation of x and y

| Lag|     CC|  Stand. CB(95%)|  Robust CB(95%)| Lag|      t| p-value| t-tilde| p-value| Lag|    HB| p-value| Q-tilde| p-value|
|---:|------:|---------------:|---------------:|---:|------:|-------:|-------:|-------:|---:|-----:|-------:|-------:|-------:|
| -10|  0.085| (-0.196, 0.196)| (-0.189, 0.189)| -10|  0.851|   0.395|   0.884|   0.377| -10| 9.939|   0.536|  10.061|   0.525|
|  -9|  0.065| (-0.196, 0.196)| (-0.170, 0.170)|  -9|  0.654|   0.513|   0.752|   0.452|  -9| 9.135|   0.519|   9.279|   0.506|
|  -8| -0.097| (-0.196, 0.196)| (-0.168, 0.168)|  -8| -0.970|   0.332|  -1.132|   0.258|  -8| 8.666|   0.469|   9.202|   0.419|
|  -7| -0.118| (-0.196, 0.196)| (-0.165, 0.165)|  -7| -1.182|   0.237|  -1.407|   0.159|  -7| 7.644|   0.469|   7.921|   0.441|
|  -6|  0.025| (-0.196, 0.196)| (-0.194, 0.194)|  -6|  0.255|   0.799|   0.258|   0.797|  -6| 6.141|   0.523|   5.941|   0.547|
|  -5| -0.047| (-0.196, 0.196)| (-0.221, 0.221)|  -5| -0.469|   0.639|  -0.416|   0.678|  -5| 6.072|   0.415|   5.874|   0.437|
|  -4|  0.014| (-0.196, 0.196)| (-0.201, 0.201)|  -4|  0.138|   0.891|   0.134|   0.893|  -4| 5.840|   0.322|   5.702|   0.336|
|  -3|  0.164| (-0.196, 0.196)| (-0.246, 0.246)|  -3|  1.644|   0.100|   1.312|   0.190|  -3| 5.821|   0.213|   5.684|   0.224|
|  -2|  0.116| (-0.196, 0.196)| (-0.183, 0.183)|  -2|  1.158|   0.247|   1.238|   0.216|  -2| 3.033|   0.386|   3.963|   0.265|
|  -1| -0.022| (-0.196, 0.196)| (-0.187, 0.187)|  -1| -0.219|   0.827|  -0.229|   0.819|  -1| 1.666|   0.435|   3.169|   0.205|
|   0| -0.127| (-0.196, 0.196)| (-0.163, 0.163)|   0| -1.272|   0.203|  -1.525|   0.127|   0| 1.618|   0.203|   2.326|   0.127|
|   1|  0.028| (-0.196, 0.196)| (-0.159, 0.159)|   1|  0.285|   0.776|   0.351|   0.726|   1| 1.700|   0.427|   2.449|   0.294|
|   2|  0.206| (-0.196, 0.196)| (-0.205, 0.205)|   2|  2.058|   0.040|   1.971|   0.049|   2| 6.023|   0.110|   6.333|   0.096|
|   3|  0.056| (-0.196, 0.196)| (-0.178, 0.178)|   3|  0.564|   0.573|   0.621|   0.535|   3| 6.351|   0.174|   6.718|   0.152|
|   4| -0.104| (-0.196, 0.196)| (-0.194, 0.194)|   4| -1.040|   0.298|  -1.048|   0.295|   4| 7.478|   0.187|   7.817|   0.167|
|   5|  0.015| (-0.196, 0.196)| (-0.232, 0.232)|   5|  0.155|   0.877|   0.131|   0.896|   5| 7.503|   0.277|   7.834|   0.251|
|   6|  0.070| (-0.196, 0.196)| (-0.213, 0.213)|   6|  0.702|   0.483|   0.645|   0.519|   6| 8.027|   0.330|   8.250|   0.311|
|   7|  0.009| (-0.196, 0.196)| (-0.187, 0.187)|   7|  0.092|   0.927|   0.096|   0.924|   7| 8.036|   0.430|   8.259|   0.409|
|   8| -0.022| (-0.196, 0.196)| (-0.212, 0.212)|   8| -0.215|   0.830|  -0.199|   0.843|   8| 8.086|   0.525|   8.299|   0.504|
|   9| -0.054| (-0.196, 0.196)| (-0.182, 0.182)|   9| -0.544|   0.587|  -0.586|   0.558|   9| 8.411|   0.589|   8.642|   0.566|
|  10|  0.040| (-0.196, 0.196)| (-0.202, 0.202)|  10|  0.404|   0.686|   0.392|   0.695|  10| 8.593|   0.659|   8.796|   0.641|

testcorr documentation built on April 5, 2021, 5:06 p.m.