---
title: "Using mlrv to anaylze data"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Using mlrv to anaylze data}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
Data analysis in the paper of Bai and Wu (2023b).

### Loading data 
Hong Kong circulatory and respiratory data. 

```{r setup}
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


```{r}
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.
```{r}
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
}
```

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

```{r}

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
}



```

#### Output
```{r}
rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")
xtable::xtable(pvmatrix, digits = 3)
```

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

```{r}
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
}
```


- 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. 

```{r}
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
}

```

- Results of shift = 1.2
```{r}
rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")
xtable::xtable(pvmatrix, digits = 3)
```


- Shift = 0.8  with plug-in estimator. 

```{r}
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
}
```

- Shift = 0.8 with the debias difference-based estimator. 
```{r}
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
}
```


- Results of shift = 0.8
```{r}
rownames(pvmatrix) = c("plug","diff")
colnames(pvmatrix) = c("KPSS","RS","VS","KS")
knitr::kable(pvmatrix,type="latex")
xtable::xtable(pvmatrix, digits = 3)
```

### Test for structure stability
Test if the coefficient function of "SO2","NO2","Dust" of the second year is constant. 

```{r}
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)
p1
```