Using mlrv to anaylze data

Loading data

Hong Kong circulatory and respiratory data.

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

load("../data/hk_data.RData")
# 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 0.2862"
## [1] "RS"
## [1] "p-value 0.3022"
## [1] "VS"
## [1] "p-value 0.126"
## [1] "KS"
## [1] "p-value 0.4046"

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 0.7034"
## [1] "RS"
## [1] "p-value 0.8002"
## [1] "VS"
## [1] "p-value 0.7702"
## [1] "KS"
## [1] "p-value 0.8612"

Output

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

	KPSS	RS	VS	KS
plug	0.2862	0.3022	0.1260	0.4046
diff	0.7034	0.8002	0.7702	0.8612

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.3.2 by xtable 1.8-4 package
## % Tue Dec 26 10:15:14 2023
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.286 & 0.302 & 0.126 & 0.405 \\ 
##   diff & 0.703 & 0.800 & 0.770 & 0.861 \\ 
##    \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 0.418"
## [1] "RS"
## [1] "p-value 0.3628"
## [1] "VS"
## [1] "p-value 0.1198"
## [1] "KS"
## [1] "p-value 0.569"

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 0.332134206312301"
## [1] "test statistic: 141.654657280933"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   11.78   69.74  142.39  235.86  302.58 3490.68 
## [1] "p-value 0.5018"
## [1] "RS"
## [1] "gcv 0.193398841583897"
## [1] "m 15 tau_n 0.332134206312301"
## [1] "test statistic: 1067.76713443354"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   494.1  1027.5  1232.8  1304.9  1512.1  3531.3 
## [1] "p-value 0.7044"
## [1] "VS"
## [1] "gcv 0.193398841583897"
## [1] "m 8 tau_n 0.332134206312301"
## [1] "test statistic: 103.342038019402"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   6.723  41.592  71.645 104.158 129.037 994.853 
## [1] "p-value 0.336"
## [1] "KS"
## [1] "gcv 0.193398841583897"
## [1] "m 17 tau_n 0.332134206312301"
## [1] "test statistic: 671.676091515897"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   337.2   719.1   920.8  1003.3  1208.8  3178.5 
## [1] "p-value 0.812"

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	0.4180	0.3628	0.1198	0.569
diff	0.5018	0.7044	0.3360	0.812

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.3.2 by xtable 1.8-4 package
## % Tue Dec 26 10:16:38 2023
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.418 & 0.363 & 0.120 & 0.569 \\ 
##   diff & 0.502 & 0.704 & 0.336 & 0.812 \\ 
##    \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 0.1714"
## [1] "RS"
## [1] "p-value 0.123"
## [1] "VS"
## [1] "p-value 0.1156"
## [1] "KS"
## [1] "p-value 0.2482"

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. 
##   18.63  101.76  202.70  335.57  421.49 3033.43 
## [1] "p-value 0.5762"
## [1] "RS"
## [1] "gcv 0.128932561055931"
## [1] "m 17 tau_n 0.382134206312301"
## [1] "test statistic: 998.08124125936"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   652.5  1239.0  1498.5  1569.0  1826.4  3783.7 
## [1] "p-value 0.9314"
## [1] "VS"
## [1] "gcv 0.128932561055931"
## [1] "m 9 tau_n 0.382134206312301"
## [1] "test statistic: 78.0587445148255"
## [1] "Bootstrap distribution"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   12.79   65.05  109.38  154.78  193.22 1514.37 
## [1] "p-value 0.6688"
## [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. 
##   288.9   695.7   912.5   991.8  1194.7  2857.1 
## [1] "p-value 0.7358"

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	0.1714	0.1230	0.1156	0.2482
diff	0.5762	0.9314	0.6688	0.7358

xtable::xtable(pvmatrix, digits = 3)

## % latex table generated in R 4.3.2 by xtable 1.8-4 package
## % Tue Dec 26 10:17:49 2023
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & KPSS & RS & VS & KS \\ 
##   \hline
## plug & 0.171 & 0.123 & 0.116 & 0.248 \\ 
##   diff & 0.576 & 0.931 & 0.669 & 0.736 \\ 
##    \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 11 tau_n 0.414293094094381"
## [1] 10464.35
##        V1       
##  Min.   : 1343  
##  1st Qu.: 3343  
##  Median : 4328  
##  Mean   : 4674  
##  3rd Qu.: 5633  
##  Max.   :13336

p1

## [1] 0.0058