ar_1_simulation_2.Rmd

---
title: "R Notebook"
runtime: shiny
output: html_notebook
---

$x_t = \delta +\phi_1 x_{t-1} + \omega_t$
$\omega_t \sim N(0,\sigma^2)$

MA(1)
$x_t = \mu + \omega_t + \phi_1 \omega_{t-1}$
ARIMA   Auto Regression  Differences   Moving average

Start by loading useful libraries.
xts seems to be the time series library many people are currently using.
https://cran.r-project.org/web/packages/xts/vignettes/xts.pdf
lubridate is the tidyverse package for dates.
quantmod lets you get financial data as well as do other things.
https://github.com/joshuaulrich/quantmod
tidyquant is the tidyverse frontend and makes quantmod easier.


google "Core Functions in tidyquant"
```{r}
# load packages ####
# if you do not have these packages - install.packages('package name')
library(tidyquant)
library(quantmod)
library(dplyr)
library(tidyverse)
library(ggplot2)
library(lubridate)
library(xts)
```


It is possible to simulate a time series.  This will help you recognize what they look like.
Here an AR(1) model with correlation of 0.9 is simulated.
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2013/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ar=c(0.99)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
pacf(t)
acf(t)
```

How  about a AR(2)
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2003/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ar=c(0.6,0.3)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
pacf(t)
acf(t)
```
How  about a AR(3)
Try changing the parameters so the add up to more than 1.
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2012/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ar=c(0.5,0.1,0.1)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
acf(t)
pacf(t)

```
Here is a MA(1)
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2003/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ma=c(0.5)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
pacf(t)
acf(t)
```
Here is a MA(2)
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2003/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ma=c(0.6,.5)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
acf(t)
pacf(t)
```
Here is a MA(3)
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2003/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ma=c(0.6,.5,0.9)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
acf(t)
pacf(t)
```
Here is an ARIMA(1,0,1)
Seems impossible to figure diagnose from the plots.
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2013/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ma=0.6,ar=.8),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
acf(t)
pacf(t)
```
Here is an ARIMA(2,0,2)
Seems impossible to figure diagnose from the plots.
```{r}
date <- seq.Date(as.Date("2001/01/01"),as.Date("2003/01/01"),"days")
l <- length(date)
y <-arima.sim(model=list(ma=c(0.6,0.2),ar=c(.8,.1)),n=l)
d <- data.frame(date=date,y=y)
t <- xts(d[,-1],order.by = d[,1])
plot(t)
acf(t)
pacf(t)
```


```{r}
install.packages('XLConnect')
install.packages('XLConnectJars')
install.packages('rJava')
library(XLConnectJars)
library(XLConnect)
tidyquant::tq_index_options()
tq_index("SP500")
```


```{r}
oil <- tidyquant::tq_get("DCOILWTICO", get = "economic.data")
oil
class(oil)
plot(oil)
oil %>% na.omit() %>% pacf
```


Plot using ggplot.
```{r}
oil %>% na.omit() %>% 
  ggplot(aes(x=date,y=price)) +
  geom_point(shape=20)
```
Here is the LA Rain data.
```{r}
data(larain,package='TSA')
larain <- as.xts(larain)
names(larain)
acf(larain)
pacf(larain)
plot(larain)
```

Oil and gold.
https://blog.exploratory.io/introduction-to-tidyquant-quantitative-financial-analysis-for-tidyverse-habitats-e5f72a023ce2
```{r}
oil <- tq_get("DCOILWTICO", get = "economic.data")
names(oil)
dim(oil)
str(oil)
head(oil)
oil %>% na.omit() %>% pacf

gold <- tq_get("GOLDAMGBD228NLBM", get = "economic.data")
plot(gold)

gold %>% na.omit() %>% pacf
```