Using mlrv to anaylze data

Data analysis in the paper of Bai and Wu (2023b).

Loading data

Hong Kong circulatory and respiratory data.

library(mlrv)
library(foreach)
library(magrittr)

data(hk_data)
colnames(hk_data) = c("SO2","NO2","Dust","Ozone","Temperature",
                      "Humidity","num_circu","num_respir","Hospital Admission",
                      "w1","w2","w3","w4","w5","w6")
n = nrow(hk_data)
t = (1:n)/n
hk = list()

hk$x = as.matrix(cbind(rep(1,n), scale(hk_data[,1:3])))
hk$y = hk_data$`Hospital Admission`

Test for long memory

pvmatrix = matrix(nrow=2, ncol=4)
###inistialization
setting = list(B = 5000, gcv = 1, neighbour = 1)
setting$lb = floor(10/7*n^(4/15)) - setting$neighbour 
setting$ub = max(floor(25/7*n^(4/15))+ setting$neighbour,             
                  setting$lb+2*setting$neighbour+1)

Using the plug-in estimator for long-run covariance matrix function.

setting$lrvmethod =0. 

i=1
# print(rule_of_thumb(y= hk$y, x = hk$x))
for(type in c("KPSS","RS","VS","KS")){
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x), setting, mvselect = -2)
  print(paste("p-value",result_reg))
  pvmatrix[1,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "p-value 0.312"
## [1] "RS"
## [1] "p-value 0.2952"
## [1] "VS"
## [1] "p-value 0.136"
## [1] "KS"
## [1] "p-value 0.405"

Debias difference-based estimator for long-run covariance matrix function.

setting$lrvmethod =1

i=1
for(type in c("KPSS","RS","VS","KS"))
{
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x), setting, mvselect = -2)
  print(paste("p-value",result_reg))
  pvmatrix[2,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "p-value 0.5032"
## [1] "RS"
## [1] "p-value 0.91"
## [1] "VS"
## [1] "p-value 0.7324"
## [1] "KS"
## [1] "p-value 0.6394"

Output

rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")

	KPSS	RS	VS	KS
plug	0.3120	0.2952	0.1360	0.4050
diff	0.5032	0.9100	0.7324	0.6394

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Thu Feb 27 07:36:46 2025
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.312 & 0.295 & 0.136 & 0.405 \\ 
##   diff & 0.503 & 0.910 & 0.732 & 0.639 \\ 
##    \hline
## \end{tabular}
## \end{table}

Sensitivity Check

Using parameter `shift’ to multiply the GCV selected bandwidth by a factor. - Shift = 1.2 with plug-in estimator.

pvmatrix = matrix(nrow=2, ncol=4)
setting$lrvmethod = 0
i=1
for(type in c("KPSS","RS","VS","KS")){
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x),
                                             setting,
                                        mvselect = -2, shift = 1.2)
  print(paste("p-value",result_reg))
  pvmatrix[1,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "p-value 0.4488"
## [1] "RS"
## [1] "p-value 0.3598"
## [1] "VS"
## [1] "p-value 0.1234"
## [1] "KS"
## [1] "p-value 0.5694"

Shift = 1.2 with debias difference-based estimator. Choosing verbose_dist = TRUE can print more intermediate results, the exact values of smoothing parameters, the test statistic, the summary of bootstrap distribution and the p-value.

setting$lrvmethod =1
i=1
for(type in c("KPSS","RS","VS","KS"))
{
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x),
                                             setting,
                                        mvselect = -2, verbose_dist = TRUE, shift = 1.2)
  print(paste("p-value",result_reg))
  pvmatrix[2,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "gcv 0.193398841583897"
## [1] "m 8 tau_n 0.382134206312301"
## [1] "test statistic: 141.654657280932"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   10.10   69.61  139.66  225.35  294.26 2128.11 
## [1] "p-value 0.4946"
## [1] "RS"
## [1] "gcv 0.193398841583897"
## [1] "m 15 tau_n 0.382134206312301"
## [1] "test statistic: 1067.76713443354"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   535.3  1016.1  1227.2  1291.8  1497.2  3033.7 
## [1] "p-value 0.688"
## [1] "VS"
## [1] "gcv 0.193398841583897"
## [1] "m 18 tau_n 0.382134206312301"
## [1] "test statistic: 103.342038019402"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.72   76.03  117.69  156.78  194.33 1570.88 
## [1] "p-value 0.5774"
## [1] "KS"
## [1] "gcv 0.193398841583897"
## [1] "m 14 tau_n 0.332134206312301"
## [1] "test statistic: 671.676091515896"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   297.4   687.9   910.5   979.0  1196.2  2896.3 
## [1] "p-value 0.7708"

Results of shift = 1.2

rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")

	KPSS	RS	VS	KS
plug	0.4488	0.3598	0.1234	0.5694
diff	0.4946	0.6880	0.5774	0.7708

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Thu Feb 27 07:37:21 2025
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.449 & 0.360 & 0.123 & 0.569 \\ 
##   diff & 0.495 & 0.688 & 0.577 & 0.771 \\ 
##    \hline
## \end{tabular}
## \end{table}

Shift = 0.8 with plug-in estimator.

pvmatrix = matrix(nrow=2, ncol=4)
setting$lrvmethod =0

i=1
for(type in c("KPSS","RS","VS","KS")){
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x),
                                             setting,
                                        mvselect = -2,  shift = 0.8)
  print(paste("p-value",result_reg))
  pvmatrix[1,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "p-value 0.173"
## [1] "RS"
## [1] "p-value 0.1992"
## [1] "VS"
## [1] "p-value 0.0908"
## [1] "KS"
## [1] "p-value 0.2608"

Shift = 0.8 with the debias difference-based estimator.

setting$lrvmethod =1

i=1
for(type in c("KPSS","RS","VS","KS"))
{
  setting$type = type
  print(type)
  result_reg = heter_covariate(list(y= hk$y, x = hk$x),
                                             setting,
                                        mvselect = -2, verbose_dist = TRUE, shift = 0.8)
  print(paste("p-value",result_reg))
  pvmatrix[2,i] = result_reg
  i = i + 1
}

## [1] "KPSS"
## [1] "gcv 0.128932561055931"
## [1] "m 8 tau_n 0.382134206312301"
## [1] "test statistic: 166.543448031108"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.31  100.54  192.85  323.39  399.68 4463.93 
## [1] "p-value 0.5526"
## [1] "RS"
## [1] "gcv 0.128932561055931"
## [1] "m 9 tau_n 0.332134206312301"
## [1] "test statistic: 998.08124125936"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   430.5  1007.0  1212.3  1278.1  1485.7  3244.3 
## [1] "p-value 0.759"
## [1] "VS"
## [1] "gcv 0.128932561055931"
## [1] "m 9 tau_n 0.332134206312301"
## [1] "test statistic: 78.0587445148257"
## [1] "Bootstrap distribution"
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##    9.864   64.254  110.357  157.890  200.452 1718.512 
## [1] "p-value 0.6654"
## [1] "KS"
## [1] "gcv 0.128932561055931"
## [1] "m 10 tau_n 0.382134206312301"
## [1] "test statistic: 709.345279801765"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   294.1   713.0   928.0   998.9  1215.5  2829.4 
## [1] "p-value 0.7558"

Results of shift = 0.8

rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")

	KPSS	RS	VS	KS
plug	0.1730	0.1992	0.0908	0.2608
diff	0.5526	0.7590	0.6654	0.7558

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Thu Feb 27 07:37:53 2025
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.173 & 0.199 & 0.091 & 0.261 \\ 
##   diff & 0.553 & 0.759 & 0.665 & 0.756 \\ 
##    \hline
## \end{tabular}
## \end{table}

Test for structure stability

Test if the coefficient function of “SO2”,“NO2”,“Dust” of the second year is constant.

hk$x = as.matrix(cbind(rep(1,n), (hk_data[,1:3])))
hk$y = hk_data$`Hospital Admission`
setting$type = 0
setting$bw_set = c(0.1, 0.35)
setting$eta = 0.2
setting$lrvmethod = 1
setting$lb  = 10
setting$ub  = 15
hk1 = list()
hk1$x = hk$x[366:730,]
hk1$y = hk$y[366:730]
p1 <- heter_gradient(hk1, setting, mvselect = -2, verbose = T)

## [1] "m 12 tau_n 0.414293094094381"
## [1] 10464.35
##        V1       
##  Min.   : 1405  
##  1st Qu.: 3824  
##  Median : 4853  
##  Mean   : 5203  
##  3rd Qu.: 6214  
##  Max.   :14718

p1

## [1] 0.016