Time_Series_Simulation_And_Fitting.Rmd

---
title: "Time Series Simulation and Fitting"
output: html_notebook
---

The xts package is called Extensible Time Series.
Load needed Libraries
```{r}
library(glue)
library(xts)
```
Set parameters for the simulation.
```{r}
l=10000
```
Look at LC_TIME.
```{r}
Sys.getlocale("LC_TIME")
```
A time series contains two pieces, a `Index` containing a date index and `Data`.
Use `read.zoo` to read a file from the zoo package.  The file was downloaded from
`https://raw.githubusercontent.com/cran/zoo/master/vignettes/demo1.txt`
to my project directory `data`.
The format uses the standard date formating codes.
%d
: Numeric day: 13
%b
: Three diget month: Feb
%Y: Four digit year: 2005
sep
: Separator in the text file between the *Time* index and the *Data* value.
```{r}
z <- read.zoo(file.path("data","demo1.txt"),sep = "|", format="%d %b %Y")
glue("The class of z is {class(z)}")
str(z)
```


```{r}
dates <-xts::timeBasedSeq('20060204//m',length=l)
```

Simulate a time series that is observed every day instead of every month using '2006//d'.
```{r}
parameters <- list(  model=list(ar=c(0,0,0,0.8), ma=c(0.5)),   n=l)
y <- ts(do.call(arima.sim,parameters),frequency=4)
fit_y <- arima(y, order=c(0,0,1), seasonal=list(order=c(1,0,0)), include.mean=FALSE)
c(coef(fit_y), sigma2 = fit_y$sigma2)
x <-xts(y,order.by = dates,descr="Simulated xts object")
colnames(x) <- c("rate")
attr(x,'frequency') 

# Fit without the frequency.  Seasonal adjustment will be wrong.
fit_auto <- auto.arima(x)
broom::tidy(fit_auto)
sweep::sw_tidy(fit_auto)
sweep::sw_tidy(x)

attr(x,'frequency') <-4
attr(x,'frequency') 

fit_x    <- arima(x, order=c(0,0,1), seasonal=list(order=c(1,0,0)),include.mean=FALSE)
c(coef(fit_x), sigma2 = fit_x$sigma2)

fit_auto <- auto.arima(x)
broom::tidy(fit_auto)
install.packages('tsdecomp')
library(tsdecomp)
roots.allocation(fit_auto)
```