Class "blocks"

Description

A class for overlapped blocks of the time series associated with the given spatial points specified through the function couples. Thus, it is necessary to execute couples first and then blocks

Usage

blocks(lb, ls, matdata, pardata1, pardata2, stpairs)

## S4 method for signature 'blocks'
boxplot(x, i, j, ...)

## S4 method for signature 'blocks'
show(object)

## S4 method for signature 'blocks'
x[i, j, drop = FALSE]

## S4 method for signature 'blocks'
summary(object, i, j)

Arguments

Details

A message informs the user of the number of blocks extracted

Slots

mat.block

matrix of dimension (lb x overall number of blocks); the columns of this matrix are associated with the different blocks, of length equal to lb, that can be extracted from the time series related to the selected spatial points defined in the slot stpairs of couples, identified as stpairs@sel.staz

array.block

array of dimension (lb x number of blocks for each selected spatial points x number of spatial points). In each table of this array, the overlapped blocks for each spatial location are available

sel.staz

numeric or character; contains the ID codes of the selected spatial points

Note

• "Error in matdata[, clvr]: subscript out of bounds" appears if pardata2 does not exist in the argument matdata

• If "Error in matdata[, clvr]" appears, no data for some of the spatial points, specified in stpairs, are available. The user has to go back to couples and revise the vector of the selected spatial points (sel.staz and sp.couples.in arguments)

• A stop occurs if more than 75% of consecutive data are missing in the time series, since a large number of missing values do not guarantee the reliability of the tests

• A stop occurs if the length of the time series for each spatial points is less than 29

• A message appears if the length of the time series for each spatial point is greater than 29 and less than 89, since the length of the time series is low and may not guarantee the reliability of the tests

• A stop occurs if more than 80% of consecutive data are missing in one of the blocks, since the estimation of the covariance matrix is not reliable, when a large number of missing values occur

• If, in the last block of each selected spatial point, more than 15% of data are missing a warning message appears, since the estimation of the covariance matrix, when a large number of missing values occurs, is not reliable

• A warning message appears if the number of blocks, computed by fixing lb and ls, is less than 5. It is convenient that the number of blocks is close to the number of spatio-temporal comparisons defined in couples. This avoids singolarity in computing test statistics

References

Cappello, C., De Iaco, S., Posa, D., 2018, Testing the type of non-separability and some classes of space-time covariance function models. Stochastic Environmental Research and Risk Assessment, 32 17–35

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Palma, M., Posa, D., 2016. A general procedure for selecting a class of fully symmetric space-time covariance functions. Environmentrics, 27(4) 212–224.

Li, B., Genton, M.G., Sherman, M., 2007, A nonparametric assessment of properties of spacetime covariance functions. Journal of the American Statistical Association, 102 736–744.

See Also

couples

read.STdata

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #


sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

block.sym <- blocks(lb = 40, ls = 10, matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.sym)

### methods for blocks
#1. show
block.sym

#2. [  extract
block.sym[1,] #select the 1st block of each spatial location
block.sym[,1] #select all blocks of the 1st spatial location
block.sym[1:2, 1:3] #select the first two blocks of the first 3 spatial locations

#3. summary
summary(block.sym, 1:2, 1:3) #to obtain the summary associated to the first
#two blocks of the first 3 spatial locations

summary(block.sym, 0, 1) #to obtain the summary associated to all blocks of
#the 1st spatial location

#4. boxplot
boxplot(block.sym, 1:5, 1:2) #boxplots of the first 5 blocks of associated to
#the first 2 spatial locations

boxplot(block.sym, 0 ,1) #boxplots of all blocks of associated to the 1st
#spatial location

Class "couples"

Description

A class for spatial points and the corresponding temporal lags to be analyzed in order to test some covariance properties and some well known classes of space-time covariance functions models

Usage

couples(
  sel.staz,
  sp.couples.in,
  t.couples.in,
  typetest = "sym",
  typecode = numeric()
)

## S4 method for signature 'couples'
show(object)

## S4 method for signature 'couples'
x[i, by.row = FALSE, drop = FALSE]

## S4 method for signature 'couples'
summary(object)

Arguments

Details

It is important to point out that:

• both positive and negative temporal lags are automatically considered in the slot @couples.st and @tl.couples for symmetry test (typetest = "sym"), separability test (typetest = "sep") and type of non separability tests (typetest = "tnSep"). If the symmetry hyphotesis has not been rejected, only positive temporal lags might be considered for the test on separability and type of non separability (typetest = "sep" and typetest = "tnSep"), hence the specific setzero method must be used to set the negative temporal lags equal to zero

• for typetest = "tnSep" the temporal lags should be chosen according to the results of the sample non separability ratios, plotted through a boxplot classified for temporal lags (see sepindex for more details)

• for model tests (typetest equal to "productSum", "intProduct" and "gneiting"), the number of analyzed spatial points must be used to create at least 3 spatial couples or multiple of 3, such that each triplet satisfies the condition \[||\mathbf{h}_{1}||^{2\gamma} - ||\mathbf{h}_{2}||^{2\gamma} = ||\mathbf{h}_{2}||^{2\gamma}-||\mathbf{h}_{3}||^{2\gamma}\] where \(\gamma \in ]0,1]\) only for typetest = "intProduct" and "gneiting". The number of positive temporal lags must be at least 3, or multiple of 3, too. The condition \[u_{1}^{2\alpha}-u_{2}^{2\alpha}=u_{2}^{2\alpha}-u_{3}^{2\alpha}\] where \(\alpha \in ]0,1]\) must be satisfied for each triplet (only for typetest = "intProduct" and "gneiting"), as clarified in Cappello et al., 2018. The values of \(\gamma\) and \(\alpha\) are usually fixed equal to 0.5 or 1 according that the behavior near the origin of the spatial and temporal marginal covariograms is linear or quadratic, respectively. Note that for each spatial triplet and each temporal triplet, 6 contrasts can be defined. However, for typetest = "intProduct" (test on the integrated model) the user has to set arbitrarily one temporal lag equal to zero for each spatial triplet in order to delete redundant contrasts, through the specific setzero method

Slots

couples.st

matrix, in which the first two columns contain the couples of spatial points (denoted with order numbers) to be analyzed and the other columns the temporal lags associated with each spatial couples

sel.staz

numeric or character, contains the ID codes of the selected spatial points

sp.couples

data.frame, contains the couples of order numbers associated with the spatial points to be analyzed and the couples of the ID codes

tl.couples

numeric, contains the temporal lags associated to the couples of the selected spatial points

typetest

character; contains the code of the test to be performed

Note

Errors occur if

• some spatial points, given in the sequence at the beginning of the function, have not been used to generate the couples of spatial points

• there is at least one spatial couple with no specification of temporal lags

• no temporal lags have been specified

• the number of spatial points fixed in sel.staz is less than 2

• the construction of the sp.couples.in is not consistent with the test to be performed

References

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

See Also

setzero

Examples

sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

### methods for couples
#1. show
couples.sym

#2. [ extract
couples.sym[3, by.row = FALSE]
couples.sym[3, by.row = TRUE]

#3. summary
summary(couples.sym)

Class "covablocks"

Description

A class for the sample spatio-temporal covariances to be computed for each block of data and for the selected spatial and temporal lags fixed in stpairs (output from couples). Depending on the type of test the empirical variance, the sample spatial and temporal marginal covariances for each block of data are also computed. Moreover, the sample covariances between the spatio-temporal covariances at the specified spatial and temporal lags are determined.

Usage

covablocks(stblocks, stpairs, typetest = "sym")

## S4 method for signature 'covablocks'
show(object)

Arguments

Details

• If typetest is equal to "sym" (symmetry test) or "intProduct" (test on the integrated product class of models) mat.cova.h and mat.cova.u are not available

• If typetest is equal to "gneiting" (test on the Gneiting class of models) mat.cova.h is not available

• If temporal lags in stpairs are not consistent with block length (lb) in stblocks an error message will be returned

• If the proportion between the maximum temporal lag in stpairs and the block length (lb) in stblocks is greater than 0.25 a warning message will be returned since the covariance estimation might not be reliable

Slots

mat.cova

matrix of sample spatio-temporal covariances for each block, computed for the spatial and temporal lags given in stpairs (object of class couples)

mat.cova.h

matrix of sample spatial marginal covariances for the specified lags

mat.cova.u

matrix of sample temporal marginal covariances for the specified lags

mat.cova.cova

matrix of sample covariances between space-time covariances for each block, computed for the spatial and temporal lags given in stpairs (object of class couples)

typetest

character, contains the code of the test to be performed

References

Cappello, C., De Iaco, S., Posa, D., 2018, Testing the type of non-separability and some classes of space-time covariance function models. Stochastic Environmental Research and Risk Assessment, 32 17–35

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Palma, M., Posa, D., 2016. A general procedure for selecting a class of fully symmetric space-time covariance functions. Environmentrics, 27(4) 212–224.

Li, B., Genton, M.G., Sherman, M., 2007, A nonparametric assessment of properties of spacetime covariance functions. Journal of the American Statistical Association, 102 736–744.

See Also

blocks

couples

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

block.sym <- blocks(lb = 40, ls = 10, matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.sym)

covabl.sym <- covablocks(stblocks = block.sym, stpairs = couples.sym, typetest = "sym")

### method for covablock
#1. show
covabl.sym

Class "covaprop"

Description

A function for testing some properties (symmetry, separability, type of non-separability) of spatio-temporal covariance functions and some classes of space-time covariance models

Usage

covaprop(cblock, cstat, nonseptype = NULL, sign.level = 0.05)

## S4 method for signature 'covaprop'
show(object)

Arguments

Details

• A message helps to decide for either reject the null hypothesis in favor of the alternative or not reject it, at a specific level of significance

• The test on full symmetry (when the slot @typetest is equal to "sym") represents the first step for the selection of a suitable class of spatio-temporal covariance functions. According to the definition of full symmetry, the null hypothesis to be tested is \[H_0: C(\mathbf{h},u) - C(\mathbf{h},-u)=0\]

• The test of separability (when the slot @typetest is equal to "sep") represents the second step of the testing procedure. According to the definition of separability, the null hypothesis to be tested is \[H_0: C(\mathbf{h}, u)/C(\mathbf{h}, 0) - C(\mathbf{0}, u)/C(\mathbf{0},0)=0\]

• The test on the type of non separability (when the slot @typetest is equal to "tnSep") represents the third step for the selection of a suitable class of space-time covariance functions. According to the definition of type of non separability, the null hypothesis to be tested is that the non separability is non negative \[H_0: C(\mathbf{h},u)/C(\mathbf{h},0) - C(\mathbf{0},u)/C(\mathbf{0},0) > 0\] or \[H_0: C(\mathbf{h},u)/C(\mathbf{h},0) - C(\mathbf{0},u)/C(\mathbf{0},0) < 0\] if the null hypothesis to test is that the non separability is non positive

• If the slot @typetest is equal to "productSum" "intProduct" or "gneiting", the goodness of a specific class of space-time covariance function will be tested. For this testing procedure the generic null hypothesis is: \[H_0: \mathbf{Af(G)}=0\]

For the analytic expression of each test statistic and its probability distribution see Cappello et al. (2018). In the same contribution the different f(G) are given for each test to be computed.

Slots

test.statistics

numeric, the value of the test statistic

p.value

numeric, the lower tail p value of the test statistic

df

numeric, the degrees of freedom, if available

typetest

character, contains the code of the test to be performed

Note

• A stop occurs if the type of test set in cblock is not consistent with the type of test set in cstat.

• If the message Error in solve.default(): system is computationally singular:... appears, the inverse of the matrix involved in the test statistic in (9) of Cappello et al. (2020) is computationally singular. In order to overcome this numerical problem often related to the tests on the models, the object stpairs (of class couples) has to be modified. In particular, by considering that for each spatial triplet and each temporal triplet 6 contrasts can be defined, it is advisable to adopt one of the following options: 1) set equal to zero one of the highest temporal lags, for each spatial and each temporal triplet, through the specific setzero method, 2) substitute triplets associated with long spatial or temporal distances with others characterized by lower distances. Then, the user has to run again blocks, covablocks, covastatM and covaprop. The above error message also occurs if there are at least two spatial triplets, where:

  • two couples are replicated;

  • one couple is replicated.

  In such cases it is enough to set equal to zero one temporal lag for each temporal triplet associated to the couples involved in the replications.

References

Cappello, C., De Iaco, S., Posa, D., 2018, Testing the type of non-separability and some classes of space-time covariance function models. Stochastic Environmental Research and Risk Assessment, 32 17–35

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Palma, M., Posa, D., 2016. A general procedure for selecting a class of fully symmetric space-time covariance functions. Environmentrics, 27(4) 212–224.

Li, B., Genton, M.G., Sherman, M., 2007, A nonparametric assessment of properties of spacetime covariance functions. Journal of the American Statistical Association, 102 736–744.

See Also

couples

blocks

covablocks

covastat

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

#--Example 1: test on symmetry--#

sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

block.sym <- blocks(lb = 40, ls = 10, matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.sym)

covabl.sym <- covablocks(stblocks = block.sym, stpairs = couples.sym, typetest = "sym")

covast.sym <- covastat(matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.sym, typetest = "sym")

test.sym <- covaprop(cblock = covabl.sym, cstat = covast.sym, nonseptype = NULL,
sign.level = 0.05)

#--Example 2: test on the Gneiting model--#
sel.staz.mod <- c("DETH061", "DEBY047", "DEHE051", "DEUB029", "DENI019",
"DENI051", "DETH026", "DESN049")

sp.couples.in.mod <- matrix(data = c("DETH061", "DEBY047",
                                    "DEHE051", "DEUB029",
                                    "DENI019", "DENI051",
                                    "DEHE051", "DETH026",
                                    "DEBY047", "DESN049",
                                    "DETH026", "DETH061"),
                           ncol = 2, byrow = TRUE)
                           t.couples.in.mod <- c(1, 2, 3)

couples.mod <- couples(sel.staz = sel.staz.mod,
sp.couples.in = sp.couples.in.mod, t.couples.in = t.couples.in.mod,
typetest = "gneiting", typecode = character())

zero.index <- matrix(data = c(3, 7, 6, 7), ncol = 2, byrow = TRUE)

couples.mod <- setzero(x = couples.mod, zero = FALSE, index = zero.index, value = 0)

block.mod <- blocks(lb = 60, ls = 10, matdata = rr_13, pardata1 = 1,
pardata2 = 1, stpairs = couples.mod)

covabl.gn <- covablocks(stblocks = block.mod, stpairs = couples.mod,
typetest = "gneiting")

covast.gn <- covastatM(matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.mod, typetest = "gneiting", beta.data = seq(0.5, 1, by=0.1))

test.gn <- covaprop(cblock = covabl.gn, cstat = covast.gn, nonseptype = NULL,
sign.level = 0.05)

### method for covaprop
#1. show
test.sym

Class "covastat"

Description

A class for the sample spatio-temporal covariances for the specified spatial and temporal lags, given in stpairs (object of class couples), for symmetry, separability and type of non separability tests. Depending on the type of test, the empirical variance, the sample spatial and temporal marginal covariances are also computed

Usage

covastat(matdata, pardata1, pardata2, stpairs, typetest = "sym")

## S4 method for signature 'covastat'
show(object)

Arguments

Details

• A message appears on the user's console if the G vector contains spatio-temporal negative covariances. The message returns the negative value/values and it will help to identify the spatial and the temporal lags involved

• If typetest = "sym" (symmetry test) cova.h, cova.u, f.G and B are not available

Slots

G

matrix, containing the spatio-temporal covariances for the specified lags. For all tests, except for the symmetry test (typetest = "sym"), the sample variance and the sample spatial and temporal marginal covariances are also computed and stored in G

cova.h

matrix, containing the sample spatial marginal covariances for the specified lags

cova.u

matrix, containing the sample temporal marginal covariances for the specified lags

f.G

array, containing the computation of specific functions of the elements of G, see references

B

matrix, containing the computation of the derivatives of each element of f.G with respect to each element of G

A

contrast matrix

typetest

character, contains the code of the test to be performed

Note

• A stop occurs if the number of spatial points fixed in stpairs (object of class couples) is less than 2

• A stop occurs if more than 75\ series, since a large number of missing values do not guarantee the reliability of the tests

References

Cappello, C., De Iaco, S., Posa, D., 2018, Testing the type of non-separability and some classes of space-time covariance function models. Stochastic Environmental Research and Risk Assessment, 32 17–35

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Palma, M., Posa, D., 2016. A general procedure for selecting a class of fully symmetric space-time covariance functions. Environmentrics, 27(4) 212–224.

Li, B., Genton, M.G., Sherman, M., 2007, A nonparametric assessment of properties of spacetime covariance functions. Journal of the American Statistical Association, 102 736–744.

See Also

couples

read.STdata

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

covast.sym <- covastat(matdata = rr_13, pardata1 = 1, pardata2 = 1,
stpairs = couples.sym, typetest = "sym")

### method for covastat
#1. show
covast.sym

Class "covastatM"

Description

A class for the sample spatio-temporal covariances for the specified spatial and temporal lags, given in stpairs (object of class couple), for the test on the type of class of models. Depending on the type of test, the empirical variance, the sample spatial and temporal marginal covariances are also computed

Usage

covastatM(
  matdata,
  pardata1,
  pardata2,
  stpairs,
  typetest = "productSum",
  beta.data = NULL
)

## S4 method for signature 'covastatM'
show(object)

Arguments

Details

• If typetest = "intProduct" (test on the integrated product class of models) cova.h and cova.u are not available

• If typetest = "gneiting" (test on the Gneiting class of models), cova.h is not available

• A message appears on the user's console if the G vector contains spatio-temporal negative covariances. The message returns the negative value/values and it will help to identify the spatial and the temporal lags involved

Slots

G

matrix, containing the spatio-temporal covariances for the specified lags. For all tests, the sample variance and the sample spatial and temporal marginal covariances are also computed and stored in G

cova.h

matrix, containing the sample spatial marginal covariances for the specified lags

cova.u

matrix, containing the sample temporal marginal covariances for the specified lags

f.G

array, containing the computation of specific functions of the elements of G, see references

B

matrix, containing the computation of the derivatives of each element of f.G with respect to each element of G

A

contrast matrix

beta.data

vector, containing the different values of the parameter beta, available only for the test on the Gneiting class of model (typetest = "gneiting")

typetest

character, contains the code of the test to be performed

Note

• A stop occurs if the number of spatial points fixed in stpairs (object of class couples) is less than 2

• A stop occurs if more than 75\ series, since a large number of missing values do not guarantee the reliability of the tests

References

Cappello, C., De Iaco, S., Posa, D., 2018, Testing the type of non-separability and some classes of space-time covariance function models. Stochastic Environmental Research and Risk Assessment, 32 17–35

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Palma, M., Posa, D., 2016. A general procedure for selecting a class of fully symmetric space-time covariance functions. Environmentrics, 27(4) 212–224.

Li, B., Genton, M.G., Sherman, M., 2007, A nonparametric assessment of properties of spacetime covariance functions. Journal of the American Statistical Association, 102 736–744.

See Also

couples

read.STdata

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

sel.staz.mod <- c("DERP016", "DENW065", "DENW063", "DEHE046", "DEUB029",
"DETH061", "DENW068", "DETH026", "DENI051")

sp.couples.in.mod <- matrix(data = c("DERP016", "DENW065", "DENW063", "DEHE046",
                                    "DEUB029", "DETH061", "DEHE046", "DENW063",
                                    "DERP016", "DENW068", "DETH026", "DENI051",
                                    "DEUB029", "DETH061", "DENI051", "DETH061",
                                    "DERP016", "DEUB029"),
                           ncol = 2, byrow = TRUE)

t.couples.in.mod <- c(1, 2, 3)

couples.mod <- couples(sel.staz = sel.staz.mod, sp.couples.in =
                        sp.couples.in.mod, t.couples.in = t.couples.in.mod,
                      typetest = "productSum", typecode = character())

zero.index <- matrix(data=c(3, 7, 6, 7, 9, 7), ncol=2, byrow = TRUE)

couples.mod <- setzero(x = couples.mod, zero = FALSE, index = zero.index, value = 0)

covast.ps <- covastatM(matdata = rr_13, pardata1 = 1, pardata2 = 1,
                       stpairs = couples.mod, typetest = "productSum", beta.data = NULL)

### method for covastat
#1. show
covast.ps

Imports a text file in R

Description

A function for importing a text file containing spatio-temporal data. In particular, it (a) generates the spatial and temporal IDs, (b) converts the time series of each spatial point (with non-existing values for some dates) into a regularly spaced object within the observed time period, by filling the missing dates with ‘NA’ (c) converts the data into a STFDF, according to the standard of the spacetime package, or into a data frame

Usage

read.STdata(
  file,
  header = FALSE,
  dec = ".",
  sep = "",
  iclx,
  icly,
  iclt,
  icldate = c(icl.date = 0, iclty = 0, icltm = 0, icltd = 0),
  icltime = c(icl.time = 0, icltH = 0, icltM = 0, icltS = 0),
  iclvr,
  iclsp = 0,
  missing.v = NA,
  save.as = "data.frame",
  date.format = c("code", format = NA),
  bytime = NA,
  tlag,
  time.zone = ""
)

Arguments

Details

• Uncomplete time series, for each spatial point, are filled with NA

• Some checks on the admissibility of the supported classes of dates are implemented

• Time indexes for temporal points are coded for data.frame output by using consecutive numbers starting from 1 (column 'timeIndex')

• The spatial points are coded by using the string 'id' and the consecutive numbers starting from 1 (column 'spatialIndex')

Value

object of the STFDF-class or data.frame, which contains coordinates of the spatial points, the spatial IDs, the temporal IDs, the dates (if available in the input file) and the observed values of the variable of interest

References

Bivand, R. S., Pebesma, E., Gomez-Rubio, V., 2013, Applied spatial data analysis with R, Second edition. New York: Springer. https://asdar-book.org/

Grolemund, G, Wickham, H., 2011, Dates and Times Made Easy with lubridate. Journal of Statistical Software, 40(3) 1–25.

Pebesma, E.J., 2012, spacetime: Spatio-Temporal Data in R. Journal of Statistical Software, 51(7) 1–30.

Zeileis, A., Grothendieck. G., 2005, zoo: S3 Infrastructure for Regular and Irregular Time Series. Journal of Statistical Software, 14(6) 1–27.

See Also

STFDF-class

read.table

yearmon

yearqtr

Dates for dates without times

DateTimeClasses

timezones for OlsonNames

Examples

#example 1: import a text file, with dates stored in a single column (the 4th)
# and fill missing time points in monthly time series, with time lag equal to one


## Not run
## To run example 1 paste and copy the following lines (without the symbol '#')
## in the console:
#file_date <- system.file("extdata", "file_date.txt", package = "covatest")
#db.date <- read.STdata(file = file_date, header = TRUE, iclx = 2, icly = 3, iclt = 0,
#icldate = c(icl.date = 4, iclty = 0, icltm = 0, icltd = 0),
#icltime = c(icl.time = 0, icltH =0, icltM = 0, icltS = 0),
#iclvr = 5, iclsp = 1, missing.v = -99999, save.as = "data.frame",
#date.format = c("Date", "%d-%m-%Y"), bytime = "%m", tlag = 1)


#example 2: import a text file, with dates and times stored in different columns
# (from the 4th to the 9th) and fill missing time points in hourly time series,
# with time lag equal to three

## Not run
## To run example 2 paste and copy the following lines (without the symbol '#')
## in the console:
#file_datetime <- system.file("extdata", "file_datetime.txt", package = "covatest")
#db.datetime <- read.STdata(file = file_datetime, header = TRUE, iclx = 2, icly = 3, iclt = 0,
#icldate = c(icl.date = 0, iclty = 6, icltm = 5, icltd = 4),
#icltime = c(icl.time = 0, icltH = 7, icltM = 8, icltS = 9),
#iclvr = 10, iclsp = 1, missing.v = -99999, save.as = "data.frame",
#date.format = c("POSIX", "%Y %m %d %H %M %S"), bytime = "%H", tlag = 3)


#example 3: import a text file, with dates and times stored in different columns
# (from the 4th to the 9th) and fill missing time points in quarterly time series,
# with time lag equal to one

## Not run
## To run example 3 paste and copy the following lines (without the symbol '#')
## in the console:
#file_yq <- system.file("extdata", "file_yq.txt", package = "covatest")
#db.yq <- read.STdata(file = file_yq, header = TRUE, iclx = 2, icly = 3, iclt = 0,
#icldate = c(icl.date = 4, iclty = 0, icltm = 0, icltd = 0),
#icltime = c(icl.time = 0, icltH =0, icltM = 0, icltS = 0),
#iclvr = 5, iclsp = 1, missing.v = -99999, save.as = "data.frame",
#date.format = c("yearqtr", "%Y-Q%q"), bytime = "%q", tlag = 1)

Class "sepindex"

Description

A class for the non separability index (r) for different spatial and temporal lags: \[r(\mathbf{h}, u, \Theta)= \rho(\mathbf{h}, u;\Theta)/ [\rho(\mathbf{h},0;\Theta)\rho(\mathbf{0},u;\Theta)]\] with \(\rho(\mathbf{h}, u;\Theta)>0\); \(\rho(\mathbf{h},0;\Theta)>0\) and \(\rho(\mathbf{0},u;\Theta)>0\). On the basis of this index, the type of non separability of the covariance function can be analyzed.

Usage

sepindex(vario_st, nt, ns, globalSill)

## S4 method for signature 'sepindex'
boxplot(x, ...)

## S4 method for signature 'sepindex'
show(object)

## S4 method for signature 'sepindex'
x[i, j, drop = FALSE]

## S4 method for signature 'sepindex'
summary(object)

Arguments

Slots

sep.index.ratio

the empirical non separability index ratio and the corresponding spatio-temporal lags

cov.st

the spatio-temporal sample covariance function and the corresponding spatio-temporal lags

cov.tm

the purely temporal sample covariance function and the corresponding temporal lags

cov.sp

the purely spatial sample covariance function and the corresponding spatial lags

References

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Posa, D., 2013, Positive and negative non-separability for space-time covariance models. Journal of Statistical Planning and Inference, 143 378–391.

Gräler, B., Pebesma, E.J., Heuvelink G., 2016, Spatio-Temporal Interpolation Using gstat. The R Journal, 8(1) 204–218.

Pebesma, E.J., 2004, Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30 683–691.

Rodriguez, A., Diggle, P.J., 2010, A class of convolution-based models for spatio-temporal processes with non-separable covariance structure. Scandinavian Journal of Statistics, 37(4) 553–567.

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

#compute the Global Sill
C00_13 <- var(rr_13[,,"PM10"]@data[[1]], na.rm = TRUE)

#estimate the spatio-temporal variogram by using the function variogramST
#of the package gstat.
#For this aim see vv_13.Rd
data(vv_13)
nonsep.index <- sepindex(vario_st = vv_13, nt = 16, ns = 4, globalSill = C00_13)

##methods for sepindex

#1. show
nonsep.index

#2. summary
summary(nonsep.index)

#3. boxplot
boxplot(nonsep.index, ylab="Non-separability ratio")

#4. [ extract
nonsep.index[1:8, ] #selection of the first 8 rows
nonsep.index[1:8, 1:2] #selection of the first 2 columns

setzero

Description

Through the function couples, m spatial couples and n temporal lags are provided, hence a set of m x n spatio-temporal lags are defined. If some of these lags are not required for the specific test, they can be set equal to zero by using the setzero method for object of class couples

Usage

setzero(x, zero = TRUE, index = NULL, value)

## S4 method for signature 'couples'
setzero(x, zero = TRUE, index = NULL, value)

Arguments

See Also

couples

Examples

sel.staz.sym <- c("DERP016", "DENW065", "DEHE051", "DETH026", "DENW063", "DENI019",
"DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049")

sp.couples.in.sym <- matrix(data = c("DERP016", "DENW065", "DEHE051", "DETH026",
"DENW063", "DENI019", "DENW068", "DEHE046", "DEUB029", "DEBY047", "DETH061", "DESN049"),
ncol = 2, byrow = TRUE)

t.couples.in.sym <- c(1, 2)

couples.sym <- couples(sel.staz = sel.staz.sym, sp.couples.in = sp.couples.in.sym,
t.couples.in = t.couples.in.sym, typetest = "sym", typecode = character())

zero.index <- matrix(data=c(1,3,1,4,2,5,2,6), ncol=2, byrow = TRUE)

setzero(couples.sym, zero = FALSE, index = zero.index, value = 0)

Precomputed variogram for PM10 in data set air

Description

Precomputed variogram for PM10 in a subset of the air quality data set air

Usage

data(vv_13)

Format

Object of class StVariogram

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)


data(air)

ls()

if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))

rr <- rural[,"2005::2010"]

unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))

r5to10 = rr[-unsel,]

rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

## Not run
## To estimate the spatio-temporal variogram, paste and copy the following lines
## (without the symbol '#') in the console:
#
## vv_13 is obtained by running the function variogramST of the package gstat,
## as follows
#
# vv_13 <- gstat::variogramST(PM10~1, rr_13, width=60, cutoff = 220, tlags=0:15)
## End (Not run)