The goal of mlrv is to provide plug-in and debiased difference-based long-run covariance matrix estimation for time series regression. Two applications of hypothesis testing are also provided. The first one is for testing for structural stability in coefficient functions. The second one is aimed at detecting long memory in time series regression.

You can install the development version of mlrv from GitHub with:

This is a basic example which shows you how to solve a common problem: test if the coefficient function of “SO2”,“NO2”,“Dust” of the second year is constant using debiased difference-based estimator for the long-run covariance matrix function.

```
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()
setting = list(B = 5000, gcv = 1, neighbour = 1)
setting$lb = floor(20/7*n^(4/15)) - setting$neighbour
setting$ub = max(floor(24/7*n^(4/15))+ setting$neighbour,
setting$lb+2*setting$neighbour+1)
## basic example code
```

```
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$lrvmethod = 1 #using debiased difference-based estimator
setting$lb = 10
setting$ub = 50
hk1 = list()
hk1$x = hk$x[366:730,]
hk1$y = hk$y[366:730]
p1 <- heter_gradient(hk1, setting, mvselect = -2, verbose = T)
#> [1] "m 26 tau_n 0.374190823993618"
#> [1] 10464.35
#> V1
#> Min. : 2669
#> 1st Qu.: 5462
#> Median : 6844
#> Mean : 7288
#> 3rd Qu.: 8721
#> Max. :19621
p1
#> [1] 0.1092
```

One can also use another scheme of MV selection based on the volatility of the estimator by setting mvselect = -1.