ch-test: Canova and Hansen Test for Seasonal Stability
In uroot: Unit Root Tests for Seasonal Time Series
Description
Usage
Arguments
Details
Value
Note
References
See Also
Examples
Description
Canova and Hansen (CH) test statistic for the null hypothesis
of a stable seasonal pattern.
Usage
1
2
Arguments
x
a univariate seasonal time series.
type
a character string specifying the formulation of the test,
"dummy" for seasonal dummies or "trigonometric" for seasonal cycles.
lag1
logical, if TRUE a first order lag of the time series x is included
in the regression model. The default is FALSE.
NW.order
an integer, the lag truncation parameter to be used in
the Newey and West covariance matrix.
sid
an optional numeric vector, the target seasonal dummies or cycles to be tested.
By default all the individual and joint test statistics are returned.
xreg
an optional vector or matrix of external regressors with the same length or number of
rows as the length of the input time series x.
pvalue
a character specifying the method employed to compute p-values:
"RS", the default, interpolation based on response surface regressions;
"raw", interpolation in the tabulated values provided in the reference paper
for the Von Mises distribution.
rs.nobsreg
an integer indicating the number of points employed in the response surface
regression (only for pvalue = "RS").
Details
The seasons or seasonal cycles to be tested can be chosen through
an indicator variable defined in the argument sid.
By default, all the t-statistics
related to each individual dummy or cycle and the joint F-statistic
are returned.
If type = "dummy", the index of the target seasons can be specified in sid.
For example, in a quarterly series:
sid=c(2) returns the test statistic to the stability of the second quarter;
sid=c(1,3) returns the joint test statistic for the first and third quarters;
sid=c(1,2,3,4) returns the joint test statistic for the null of seasonal
stability at all seasons.
If type = "trigonometric", the indicator vector sid must be of length
floor(frequency(x)/2) and will consist of ones and zeros. Each element in
sid is related to each seasonal cycle according to the same order in which
the seasonal frequencies, w_j, are defined: w_j=2π j/S, j=1,...,Sh,
where S is the periodicity and Sh is floor(frequency(x)/2).
For example, in a monthly series:
sid=c(0,0,0,0,0,1) returns the test statistic to the stability of the cycle with
frequency w_6=π;
sid=c(1,0,0,0,0,1) returns the joint test statistic for cycles related
to frequencies w_1=π/6 and w_6=π;
sid=c(1,1,1,1,1,1) returns the joint test statistic for the stability of
all seasonal cycles.
The following keywords are also admitted:
sid="all", computes all the test statistic related to each individual season
or cycle as well as the joint test statistic for all seasons or cycles;
sid="joint" computes the joint test statistic for all seasons or cycles.
Value
A list of class "CHtest" with components:
statistics
the value of the test statistics.
pvalues
the p-values for each test statistics.
method
a character string describing the type of test.
data.name
a character string giving the name of the data.
type
the value of the input argument type.
fitted.model
the fitted regression model.
NW.order
the value of the input argument codeNW.order.
isNullxreg
logical, auxiliary element for print method. Were external
regressors defined in the argument xreg?
type.pvalue
character, the value of the input argument codepvalue.
pvlabels
a vector of characters containing a label related to each p-values.
Auxiliary element for print method.
The method print displays the test statistics and p-values;
summary shows the same output and includes the fitted regression model.
Note
When type = "dummy", the p-value for the joint test statistic
based on response surface regressions is not available. If pvalue = "RS",
the p-value reported for the joint test statistic in the trigonometric version is based
on the tables given in the reference paper, Canova and Hansen (1995).
When sid is a numeric (selected combination of dummies or cycles),
the reported p-values are based on interpolation in tables;
if pvalue = "RS", it is changed to "raw" and a warning is given.
References
Canova, F. and Hansen, Bruce E. (1995)
"Are seasonal patterns constant over time? A test for seasonal stability".
Journal of Business & Economic Statistics, 13(3), pp. 237-252.
DOI: http://dx.doi.org/10.1080/07350015.1995.10524598.
Díaz-Emparanza, I. and Moral, M. P. (2013).
Seasonal stability tests in gretl. An application to international tourism data.
Working paper: Biltoki D.T. 2013.03.
URL: https://addi.ehu.es/handle/10810/10577.
Gretl code: http://www.ehu.eus/ignacio.diaz-emparanza/packages/Canova_Hansen.gfn.
See Also
ch.rs.pvalue seasonal.cycles,
seasonal.dummies, uroot.raw.pvalue.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
library(uroot)
# example for the series "hours" with the same options
# employed in Canova and Hansen (1995)
data("ch-data")
hours <- diff(log(ch.data$hours))
res1 <- ch.test(x = hours, type = "dummy", lag1 = TRUE, NW.order = 4)
res1
# the auxiliary regression is stored in the element "fitted.model"
summary(res1$fit)
## Not run:
# this requires tables not included in the current version of the package
# see note in main documentation file, uroot-package
res2 <- ch.test(x = hours, type = "trigonometric", lag1 = TRUE, NW.order = 4)
res2
summary(res2$fit)
## End(Not run)
Example output
Canova and Hansen test for seasonal stability
data: hours
statistic pvalue
Quarter1 0.3173 0.1343
Quarter2 0.3974 0.0782 .
Quarter3 0.1578 0.4049
Quarter4 0.3396 0.1164
joint 1.128 0.0793 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Test type: seasonal dummies
NW covariance matrix lag order: 4
First order lag: yes
Other regressors: no
P-values: based on response surface regressions
Call:
lm(formula = x ~ 0 + xreg)
Residuals:
Min 1Q Median 3Q Max
-0.0091803 -0.0026042 0.0002348 0.0031443 0.0081779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
xreglag1 0.035674 0.110632 0.322 0.748
xregSD1 -0.011685 0.001172 -9.969 9.76e-16 ***
xregSD2 0.006545 0.001568 4.173 7.51e-05 ***
xregSD3 0.008175 0.001078 7.581 4.99e-11 ***
xregSD4 -0.007573 0.001243 -6.095 3.53e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003869 on 81 degrees of freedom
Multiple R-squared: 0.8428, Adjusted R-squared: 0.8331
F-statistic: 86.85 on 5 and 81 DF, p-value: < 2.2e-16
Canova and Hansen test for seasonal stability
data: hours
statistic pvalue
pi/2 0.265 0.5931
pi 0.7731 0.003 **
joint 1.0836 0.0092 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Test type: seasonal cycles
NW covariance matrix lag order: 4
First order lag: yes
Other regressors: no
P-values: based on response surface regressions
Call:
lm(formula = x ~ 0 + xreg)
Residuals:
Min 1Q Median 3Q Max
-0.0091803 -0.0026042 0.0002348 0.0031443 0.0081779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
xregc -0.0011346 0.0004365 -2.599 0.0111 *
xreglag1 0.0356740 0.1106325 0.322 0.7479
xregSD1 -0.0099302 0.0009574 -10.373 < 2e-16 ***
xregSD2 0.0070590 0.0012709 5.554 3.44e-07 ***
xregSD3 -0.0006206 0.0004229 -1.467 0.1462
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003869 on 81 degrees of freedom
Multiple R-squared: 0.8428, Adjusted R-squared: 0.8331
F-statistic: 86.85 on 5 and 81 DF, p-value: < 2.2e-16
uroot documentation built on Sept. 4, 2020, 5:06 p.m.
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Description Usage Arguments Details Value Note References See Also Examples
Description
Canova and Hansen (CH) test statistic for the null hypothesis of a stable seasonal pattern.
Usage
1 2 |
Arguments
x |
a univariate seasonal time series. |
type |
a character string specifying the formulation of the test,
|
lag1 |
logical, if |
NW.order |
an integer, the lag truncation parameter to be used in the Newey and West covariance matrix. |
sid |
an optional numeric vector, the target seasonal dummies or cycles to be tested. By default all the individual and joint test statistics are returned. |
xreg |
an optional vector or matrix of external regressors with the same length or number of
rows as the length of the input time series |
pvalue |
a character specifying the method employed to compute p-values:
|
rs.nobsreg |
an integer indicating the number of points employed in the response surface
regression (only for |
Details
The seasons or seasonal cycles to be tested can be chosen through
an indicator variable defined in the argument sid.
By default, all the t-statistics
related to each individual dummy or cycle and the joint F-statistic
are returned.
If type = "dummy", the index of the target seasons can be specified in sid.
For example, in a quarterly series:
sid=c(2) returns the test statistic to the stability of the second quarter;
sid=c(1,3) returns the joint test statistic for the first and third quarters;
sid=c(1,2,3,4) returns the joint test statistic for the null of seasonal
stability at all seasons.
If type = "trigonometric", the indicator vector sid must be of length
floor(frequency(x)/2) and will consist of ones and zeros. Each element in
sid is related to each seasonal cycle according to the same order in which
the seasonal frequencies, w_j, are defined: w_j=2π j/S, j=1,...,Sh,
where S is the periodicity and Sh is floor(frequency(x)/2).
For example, in a monthly series:
sid=c(0,0,0,0,0,1) returns the test statistic to the stability of the cycle with
frequency w_6=π;
sid=c(1,0,0,0,0,1) returns the joint test statistic for cycles related
to frequencies w_1=π/6 and w_6=π;
sid=c(1,1,1,1,1,1) returns the joint test statistic for the stability of
all seasonal cycles.
The following keywords are also admitted:
sid="all", computes all the test statistic related to each individual season
or cycle as well as the joint test statistic for all seasons or cycles;
sid="joint" computes the joint test statistic for all seasons or cycles.
Value
A list of class "CHtest" with components:
statistics |
the value of the test statistics. |
pvalues |
the p-values for each test statistics. |
method |
a character string describing the type of test. |
data.name |
a character string giving the name of the data. |
type |
the value of the input argument |
fitted.model |
the fitted regression model. |
NW.order |
the value of the input argument codeNW.order. |
isNullxreg |
logical, auxiliary element for |
type.pvalue |
character, the value of the input argument codepvalue. |
pvlabels |
a vector of characters containing a label related to each p-values.
Auxiliary element for |
The method print displays the test statistics and p-values;
summary shows the same output and includes the fitted regression model.
Note
When type = "dummy", the p-value for the joint test statistic
based on response surface regressions is not available. If pvalue = "RS",
the p-value reported for the joint test statistic in the trigonometric version is based
on the tables given in the reference paper, Canova and Hansen (1995).
When sid is a numeric (selected combination of dummies or cycles),
the reported p-values are based on interpolation in tables;
if pvalue = "RS", it is changed to "raw" and a warning is given.
References
Canova, F. and Hansen, Bruce E. (1995) "Are seasonal patterns constant over time? A test for seasonal stability". Journal of Business & Economic Statistics, 13(3), pp. 237-252. DOI: http://dx.doi.org/10.1080/07350015.1995.10524598.
Díaz-Emparanza, I. and Moral, M. P. (2013). Seasonal stability tests in gretl. An application to international tourism data. Working paper: Biltoki D.T. 2013.03. URL: https://addi.ehu.es/handle/10810/10577. Gretl code: http://www.ehu.eus/ignacio.diaz-emparanza/packages/Canova_Hansen.gfn.
See Also
ch.rs.pvalue seasonal.cycles,
seasonal.dummies, uroot.raw.pvalue.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | library(uroot)
# example for the series "hours" with the same options
# employed in Canova and Hansen (1995)
data("ch-data")
hours <- diff(log(ch.data$hours))
res1 <- ch.test(x = hours, type = "dummy", lag1 = TRUE, NW.order = 4)
res1
# the auxiliary regression is stored in the element "fitted.model"
summary(res1$fit)
## Not run:
# this requires tables not included in the current version of the package
# see note in main documentation file, uroot-package
res2 <- ch.test(x = hours, type = "trigonometric", lag1 = TRUE, NW.order = 4)
res2
summary(res2$fit)
## End(Not run)
|
Example output
Canova and Hansen test for seasonal stability
data: hours
statistic pvalue
Quarter1 0.3173 0.1343
Quarter2 0.3974 0.0782 .
Quarter3 0.1578 0.4049
Quarter4 0.3396 0.1164
joint 1.128 0.0793 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Test type: seasonal dummies
NW covariance matrix lag order: 4
First order lag: yes
Other regressors: no
P-values: based on response surface regressions
Call:
lm(formula = x ~ 0 + xreg)
Residuals:
Min 1Q Median 3Q Max
-0.0091803 -0.0026042 0.0002348 0.0031443 0.0081779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
xreglag1 0.035674 0.110632 0.322 0.748
xregSD1 -0.011685 0.001172 -9.969 9.76e-16 ***
xregSD2 0.006545 0.001568 4.173 7.51e-05 ***
xregSD3 0.008175 0.001078 7.581 4.99e-11 ***
xregSD4 -0.007573 0.001243 -6.095 3.53e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003869 on 81 degrees of freedom
Multiple R-squared: 0.8428, Adjusted R-squared: 0.8331
F-statistic: 86.85 on 5 and 81 DF, p-value: < 2.2e-16
Canova and Hansen test for seasonal stability
data: hours
statistic pvalue
pi/2 0.265 0.5931
pi 0.7731 0.003 **
joint 1.0836 0.0092 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Test type: seasonal cycles
NW covariance matrix lag order: 4
First order lag: yes
Other regressors: no
P-values: based on response surface regressions
Call:
lm(formula = x ~ 0 + xreg)
Residuals:
Min 1Q Median 3Q Max
-0.0091803 -0.0026042 0.0002348 0.0031443 0.0081779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
xregc -0.0011346 0.0004365 -2.599 0.0111 *
xreglag1 0.0356740 0.1106325 0.322 0.7479
xregSD1 -0.0099302 0.0009574 -10.373 < 2e-16 ***
xregSD2 0.0070590 0.0012709 5.554 3.44e-07 ***
xregSD3 -0.0006206 0.0004229 -1.467 0.1462
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003869 on 81 degrees of freedom
Multiple R-squared: 0.8428, Adjusted R-squared: 0.8331
F-statistic: 86.85 on 5 and 81 DF, p-value: < 2.2e-16
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