---
title: "Projekt z Ekonometrii finansowej"
author: "Patryk Formela"
output: 
  flexdashboard::flex_dashboard:
    orientation: columns
    #vertical_layout: fill
    #social: menu
    source_code: embed
---

```{r setup, include=FALSE}
library(flexdashboard)
library(dygraphs)
library(xts)
library(pander)
dane <- read.csv(file = 'cw_4_PPP.csv', header = TRUE, sep = ',')
timeseries <- ts(dane, start = (1950), end = (2010), frequency(1))
can <- timeseries[,3]
```

Poziomy
===================================== 

Column {data-width=350}
-----------------------------------------------------------------------

### CANGBP

```{r}
dygraph(timeseries[,16]) %>%
  dySeries(label = "CANGBP")
```


### PCAN

```{r}
dygraph(timeseries[,4])%>%
  dySeries(label = 'PCAN')
```

### PGBP

```{r}
dygraph(timeseries[,12])%>%
  dySeries(label = 'PGBP')
```

Column {data-width=350}
------------------------------------------------------------------------
### LCANGBP

```{r}
dygraph(timeseries[,32])%>%
  dySeries(label = 'LCANGBP')
```

### LPCAN

```{r}
dygraph(timeseries[,20])%>%
  dySeries(label = 'LPCAN')
```

### LPGBP

```{r}
dygraph(timeseries[,28])%>%
  dySeries(label = 'LPGBP')
```



```{r setupe, include=FALSE}
tsdiff <- diff(timeseries, differences = 1)
```

Różnice
===================================== 

Column {data-width=350}
-----------------------------------------------------------------------

### DIFFCANGBP

```{r}
dygraph(tsdiff[,16]) %>%
  dySeries(label = "CANGBP")
```


### DIFFPCAN

```{r}
dygraph(tsdiff[,4])%>%
  dySeries(label = 'PCAN')
```

### DIFFPGBP

```{r}
dygraph(tsdiff[,12])%>%
  dySeries(label = 'PGBP')
```

Column {data-width=350}
------------------------------------------------------------------------
### DIFFLCANGBP

```{r}
dygraph(tsdiff[,32])%>%
  dySeries(label = 'LCANGBP')
```

### DIFFLPCAN

```{r}
dygraph(tsdiff[,20])%>%
  dySeries(label = 'LPCAN')
```

### DIFFLPGBP

```{r}
dygraph(tsdiff[,28])%>%
  dySeries(label = 'LPGBP')
```

```{r setupes, include=FALSE}
fit <- lm(LCANGBP ~ LPCAN + LPGBP, data = tsdiff)
```


Model
=====================================


Column {data-width=600}
------------------------------------------------------------------------
### Model
```{r}
summary(fit)
```

### Model z wartością wyrównaną
```{r, echo= FALSE}
fitedvalues <- fitted(fit)
```

```{r, echo= FALSE}
library(lmtest)
library(nortest)
library(car)
fitedvalues <- fitted(fit)
fitted_sq<- fitedvalues^2
fit2 <- lm(LCANGBP ~ LPCAN + LPGBP + fitted_sq, data = tsdiff)
residu <- residuals(fit)
```

```{r}
summary(fit2)
```

Column {.tabset}
-----------------------------------------------------------------------

### Test normalności

```{r}
sf.test(residu)
```

### Test na heteroskedastyczność

```{r}
bptest(fit)
```

### Test na autokorelację

```{r}
dwtest(fit, alternative = c("greater", "two.sided", "less"), iterations = 15)
```

### Seryjna autokorelacja

```{r}
bgtest(fit, order = 4, type = 'Chisq')
```


### Test na zgodność

```{r}
resettest(fit, power = 2:3, type = 'fitted')
```

### Test liniowych restrykcji

```{r}
linearHypothesis(fit, c('LPCAN = -1', 'LPGBP = 1'), test = 'F')
```

Row
------------------------------------------------------------------------

### Wykres funkcji acf
```{r}
acf(residu, type = 'correlation', plot = TRUE, lag.max = 25)
```

### Wykres funkcji pacf
```{r}
acf(residu, type = 'partial', plot = TRUE, lag.max = 25)
```


VAR, VECM
=====================================

Column{.tabset}
------------------------------------------------------------------------

```{r setap, include= FALSE}
library(tseries)
library(vars)
library(dynlm) #for function `dynlm()`
library(nlWaldTest) # for the `nlWaldtest()` function
library(broom) #for `glance(`) and `tidy()`
library(sandwich)
library(knitr) #for `kable()`
library(forecast) 
```

### ADF tests LPCAN

```{r}
adf.test(timeseries[,'LPCAN'])
```

### ADF tests LPGBP

```{r}
adf.test(timeseries[,'LPGBP'])
```

### ADF tests dLPCAN

```{r}
adf.test(tsdiff[,'LPCAN'])
```

### ADF tests dLPGBP

```{r}
adf.test(tsdiff[,'LPGBP'], k = trunc((length(tsdiff[,1])-1)^(1/3)))
```

### KPSS tests LPCAN

```{r}
kpss.test(timeseries[,'LPCAN'])
```

### KPSS tests LPGBP

```{r}
kpss.test(timeseries[,'LPGBP'])
```

### KPSS tests dLPCAN

```{r}
kpss.test(tsdiff[,'LPCAN'])
```

### KPSS tests dLPGBP

```{r}
kpss.test(tsdiff[,'LPGBP'])
```

### Test kointegracji 1

```{r}
cint1.dyn <- dynlm(LPCAN~LPGBP-1, data=timeseries)
#kable(tidy(cint1.dyn), digits=4)
pander(cint1.dyn)
```
### Test kointegracji 2

```{r}
ehat <- resid(cint1.dyn)
cint2.dyn <- dynlm(d(ehat)~L(ehat)-1)
summary(cint2.dyn)
```


Column {data-width=600}
------------------------------------------------------------------------


### Model VAR
```{r}
library(vars)
Dc <- tsdiff[,'LPCAN']
Dy <- tsdiff[,'LPGBP']
varmat <- as.matrix(cbind(Dc,Dy))
varfit <- VAR(varmat) # `VAR()` from package `vars`
summary(varfit)
```


Źródła:
====================================

### Online

- [ADF, VAR](https://bookdown.org/ccolonescu/RPoE4/vec-and-var-models.html)
- [Restrykcje](https://stats.stackexchange.com/questions/211584/testing-linear-restriction-in-r)
- [Regresja](https://www.statmethods.net/stats/regression.html)