---
title: "Remove extreme values in a time series signal with Hector"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Remove extreme values in a time series signal with Hector}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

```


```{r}
# libraries
library(simts)
library(gmwmx)
```

```{r, eval=T, echo=T, message=F}
phase =     0.45
amplitude = 2.5
sigma2_wn =       15
sigma2_powerlaw = 10
d =               0.4
bias =            0
trend =           5/365.25
cosU =            amplitude*cos(phase)
sinU =            amplitude*sin(phase)

# generate model
N = c(1, 7.5, 10, 15, 20)*365

# consider 2 year of data
n = N[1]
model_i = WN(sigma2 = sigma2_wn) 

# define time at which there are jumps
jump_vec =  c(100, 200)
jump_height = c(10, 20)

# define myseed
myseed=123

# set seed
set.seed(myseed)

# generate residuals
eps = simts::gen_gts(model = model_i, n= n)

# add trend, gaps and sin
A = gmwmx::create_A_matrix(1:length(eps), jump_vec, n_seasonal =  1)

# define beta
x_0 = c(bias, trend, jump_height,  cosU,  sinU)

# create time series
yy = A %*% x_0 + eps
```




We plot the generated time series
```{r}
plot(yy)
```

We add extreme values in the signal
```{r}
n_outliers = 30
set.seed(123)
id_outliers=sample(150:350, size = n_outliers)
val_outliers = rnorm(n = n_outliers, mean = max(yy)+10, sd = 5)
yy[id_outliers] = val_outliers
```


We plot the corrupted time series
```{r}
plot(yy)
```

We create a `gnssts` object 
```{r, eval=T}
# save signal in temp
gnssts_obj = create.gnssts(t = 1:length(yy), y = yy, jumps = jump_vec)
```

We remove extreme values from the signal using `removeoutliers` function of `Hector` available by calling `remove_outliers_hector()`
```{r, echo=T, eval=F, fig.height=8, fig.width=6, fig.align='center'}
clean_yy = remove_outliers_hector(x=gnssts_obj, n_seasonal = 1)
```

```{r, eval=T, echo=F}
file_path_clean_yy_remove_outliers_hector = system.file("extdata", "clean_yy.rda", package = "gmwmx", mustWork = T)
load(file_path_clean_yy_remove_outliers_hector)
```

We can compare the original and the signal with detected extreme values removed from the signal:

```{r, echo=F}
oldpar <- par(no.readonly = TRUE) 
```


```{r}
par(mfrow=c(1,2))
plot(yy)
plot(clean_yy$t, clean_yy$y, type = "l", xlab="Time", ylab = "Observation")
```

```{r, echo=F}
par(oldpar)
```