Description Usage Arguments Details Value Note References See Also Examples
Canova and Hansen (CH) test statistic for the null hypothesis of a stable seasonal pattern.
1 2 
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 pvalues:

rs.nobsreg 
an integer indicating the number of points employed in the response surface
regression (only for 
The seasons or seasonal cycles to be tested can be chosen through
an indicator variable defined in the argument sid
.
By default, all the tstatistics
related to each individual dummy or cycle and the joint Fstatistic
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.
A list of class "CHtest"
with components:
statistics 
the value of the test statistics. 
pvalues 
the pvalues 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 pvalues.
Auxiliary element for 
The method print
displays the test statistics and pvalues;
summary
shows the same output and includes the fitted regression model.
When type = "dummy"
, the pvalue for the joint test statistic
based on response surface regressions is not available. If pvalue = "RS"
,
the pvalue 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 pvalues are based on interpolation in tables;
if pvalue = "RS"
, it is changed to "raw"
and a warning is given.
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. 237252. DOI: http://dx.doi.org/10.1080/07350015.1995.10524598.
DíazEmparanza, 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.diazemparanza/packages/Canova_Hansen.gfn.
ch.rs.pvalue
seasonal.cycles
,
seasonal.dummies
, uroot.raw.pvalue
.
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("chdata")
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, urootpackage
res2 < ch.test(x = hours, type = "trigonometric", lag1 = TRUE, NW.order = 4)
res2
summary(res2$fit)
## End(Not run)

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
Pvalues: 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 9.76e16 ***
xregSD2 0.006545 0.001568 4.173 7.51e05 ***
xregSD3 0.008175 0.001078 7.581 4.99e11 ***
xregSD4 0.007573 0.001243 6.095 3.53e08 ***

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003869 on 81 degrees of freedom
Multiple Rsquared: 0.8428, Adjusted Rsquared: 0.8331
Fstatistic: 86.85 on 5 and 81 DF, pvalue: < 2.2e16
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
Pvalues: 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 < 2e16 ***
xregSD2 0.0070590 0.0012709 5.554 3.44e07 ***
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 Rsquared: 0.8428, Adjusted Rsquared: 0.8331
Fstatistic: 86.85 on 5 and 81 DF, pvalue: < 2.2e16
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