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 0.3314"
## [1] "RS"
## [1] "p-value 0.2872"
## [1] "VS"
## [1] "p-value 0.0944"
## [1] "KS"
## [1] "p-value 0.337"

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 0.6868"
## [1] "RS"
## [1] "p-value 0.8878"
## [1] "VS"
## [1] "p-value 0.498"
## [1] "KS"
## [1] "p-value 0.8652"

Output

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

	KPSS	RS	VS	KS
plug	0.3314	0.2872	0.0944	0.3370
diff	0.6868	0.8878	0.4980	0.8652

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Fri Nov 29 08:54:08 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.331 & 0.287 & 0.094 & 0.337 \\ 
##   diff & 0.687 & 0.888 & 0.498 & 0.865 \\ 
##    \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 0.4324"
## [1] "RS"
## [1] "p-value 0.4052"
## [1] "VS"
## [1] "p-value 0.1078"
## [1] "KS"
## [1] "p-value 0.56"

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. 
##   10.85   69.15  134.49  225.72  283.47 2114.91 
## [1] "p-value 0.4828"
## [1] "RS"
## [1] "gcv 0.193398841583897"
## [1] "m 18 tau_n 0.382134206312301"
## [1] "test statistic: 1067.76713443354"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   597.4  1118.9  1332.1  1395.1  1609.6  3395.6 
## [1] "p-value 0.8044"
## [1] "VS"
## [1] "gcv 0.193398841583897"
## [1] "m 17 tau_n 0.332134206312301"
## [1] "test statistic: 103.342038019402"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.81   70.69  109.98  151.99  189.32 1059.14 
## [1] "p-value 0.536"
## [1] "KS"
## [1] "gcv 0.193398841583897"
## [1] "m 17 tau_n 0.332134206312301"
## [1] "test statistic: 671.676091515896"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   341.5   715.8   923.3  1000.5  1210.7  2932.0 
## [1] "p-value 0.8074"

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	0.4324	0.4052	0.1078	0.5600
diff	0.4828	0.8044	0.5360	0.8074

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Fri Nov 29 08:54:41 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.432 & 0.405 & 0.108 & 0.560 \\ 
##   diff & 0.483 & 0.804 & 0.536 & 0.807 \\ 
##    \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 0.233"
## [1] "RS"
## [1] "p-value 0.1844"
## [1] "VS"
## [1] "p-value 0.1264"
## [1] "KS"
## [1] "p-value 0.273"

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. 
##   11.68  102.67  196.68  326.02  409.87 3222.47 
## [1] "p-value 0.5664"
## [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. 
##   487.8   998.0  1213.0  1271.1  1487.2  3555.3 
## [1] "p-value 0.7498"
## [1] "VS"
## [1] "gcv 0.128932561055931"
## [1] "m 18 tau_n 0.332134206312301"
## [1] "test statistic: 78.0587445148257"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   26.40   94.77  156.45  208.72  259.30 1743.69 
## [1] "p-value 0.8364"
## [1] "KS"
## [1] "gcv 0.128932561055931"
## [1] "m 9 tau_n 0.332134206312301"
## [1] "test statistic: 709.345279801765"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   296.3   695.1   903.6   982.6  1202.1  3561.7 
## [1] "p-value 0.7346"

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	0.2330	0.1844	0.1264	0.2730
diff	0.5664	0.7498	0.8364	0.7346

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.4.2 by xtable 1.8-4 package
## % Fri Nov 29 08:55:09 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.233 & 0.184 & 0.126 & 0.273 \\ 
##   diff & 0.566 & 0.750 & 0.836 & 0.735 \\ 
##    \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 0.364293094094381"
## [1] 10464.35
##        V1       
##  Min.   : 1790  
##  1st Qu.: 3772  
##  Median : 4860  
##  Mean   : 5235  
##  3rd Qu.: 6315  
##  Max.   :14624

p1

## [1] 0.0154