Using mlrv to anaylze data

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 0.2886"
## [1] "RS"
## [1] "p-value 0.2792"
## [1] "VS"
## [1] "p-value 0.1458"
## [1] "KS"
## [1] "p-value 0.4296"

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 0.516"
## [1] "RS"
## [1] "p-value 0.8568"
## [1] "VS"
## [1] "p-value 0.5028"
## [1] "KS"
## [1] "p-value 0.8134"

Output

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

	KPSS	RS	VS	KS
plug	0.2886	0.2792	0.1458	0.4296
diff	0.5160	0.8568	0.5028	0.8134

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.6.0 by xtable 1.8-8 package
## % Thu Apr  2 16:13:34 2026
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.289 & 0.279 & 0.146 & 0.430 \\ 
##   diff & 0.516 & 0.857 & 0.503 & 0.813 \\ 
##    \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 0.4406"
## [1] "RS"
## [1] "p-value 0.3938"
## [1] "VS"
## [1] "p-value 0.1212"
## [1] "KS"
## [1] "p-value 0.5818"

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: 141.654657280933"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   11.29   71.65  135.17  221.78  280.41 2459.83 
## [1] "p-value 0.483"
## [1] "RS"
## [1] "gcv 0.193398841583897"
## [1] "m 17 tau_n 0.382134206312301"
## [1] "test statistic: 1067.76713443354"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   568.1  1067.8  1277.4  1336.0  1551.1  2908.2 
## [1] "p-value 0.75"
## [1] "VS"
## [1] "gcv 0.193398841583897"
## [1] "m 15 tau_n 0.382134206312301"
## [1] "test statistic: 103.342038019402"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   14.22   65.84  109.81  153.69  193.18 1254.33 
## [1] "p-value 0.5286"
## [1] "KS"
## [1] "gcv 0.193398841583897"
## [1] "m 8 tau_n 0.382134206312301"
## [1] "test statistic: 671.676091515897"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   223.4   558.0   723.3   787.2   950.5  2761.9 
## [1] "p-value 0.5712"

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	0.4406	0.3938	0.1212	0.5818
diff	0.4830	0.7500	0.5286	0.5712

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.6.0 by xtable 1.8-8 package
## % Thu Apr  2 16:14:16 2026
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.441 & 0.394 & 0.121 & 0.582 \\ 
##   diff & 0.483 & 0.750 & 0.529 & 0.571 \\ 
##    \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 0.1644"
## [1] "RS"
## [1] "p-value 0.1564"
## [1] "VS"
## [1] "p-value 0.1166"
## [1] "KS"
## [1] "p-value 0.2656"

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 9 tau_n 0.382134206312301"
## [1] "test statistic: 166.543448031107"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   15.19  103.87  201.95  323.50  409.03 3972.71 
## [1] "p-value 0.5742"
## [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. 
##     454    1001    1221    1284    1507    3716 
## [1] "p-value 0.7526"
## [1] "VS"
## [1] "gcv 0.128932561055931"
## [1] "m 15 tau_n 0.382134206312301"
## [1] "test statistic: 78.0587445148255"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   18.49  100.50  172.31  242.58  301.05 2240.43 
## [1] "p-value 0.843"
## [1] "KS"
## [1] "gcv 0.128932561055931"
## [1] "m 17 tau_n 0.332134206312301"
## [1] "test statistic: 709.345279801765"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   378.5   820.3  1064.2  1151.7  1398.4  3816.3 
## [1] "p-value 0.8596"

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	0.1644	0.1564	0.1166	0.2656
diff	0.5742	0.7526	0.8430	0.8596

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.6.0 by xtable 1.8-8 package
## % Thu Apr  2 16:14:51 2026
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.164 & 0.156 & 0.117 & 0.266 \\ 
##   diff & 0.574 & 0.753 & 0.843 & 0.860 \\ 
##    \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 13 tau_n 0.414293094094381"
## [1] 10464.35
##        V1       
##  Min.   : 1843  
##  1st Qu.: 3990  
##  Median : 5110  
##  Mean   : 5467  
##  3rd Qu.: 6622  
##  Max.   :14819

p1

## [1] 0.0178