---
title: "STAT 436 / 536 - Lecture 2: Time Series Intro"
date: August 29, 2018
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(warning = FALSE)
library(datasets)
library(ggplot2)
library(dplyr)
```

### Time Series Basics

- So what is a time series? 
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- *Time series models*,
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- What is the purpose of time series analyses?
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- What are the defining features of time series data?
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### R Overview
- R will be used frequently in this class. All assignments, labs, and take home exams should be completed using R Markdown to create reproducible reports. \vfill
- We will also spend time creating dynamic graphics and use R Shiny. \vfill
- For more details on some useful R packages see [https://www.rstudio.com/resources/cheatsheets/](https://www.rstudio.com/resources/cheatsheets/).
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##### Time Series Objects
- R allows objects to be defined as a time series class using the `ts()` command. The time series object contains
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```{r}
library(datasets)
data(AirPassengers)
str(AirPassengers)
```

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##### Plotting in R
Many time series objects can be directly plotted using the `ggfortify` package.
```{r, message = F, fig.align='center', fig.width=6, fig.height=4}
library(ggplot2)
library(ggfortify)
autoplot(AirPassengers) + ylim(0,650) +  
  labs(title="Monthly Airline Passenger Count", y="Number of Passengers(thousands)", x= 'Year') 
```
 
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##### Simulating discrete-time stochastic process
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```{r, message = F, fig.align='center', fig.width=6, fig.height=4}
set.seed(08182018)
maxT <- 100
y = rep(0, T)
evolution.var <- 1

# Simulate Data
for (time.pt in 2:maxT){
  y[time.pt] <- y[time.pt - 1] + rnorm(1, 0, evolution.var)
}

# Plot Data
y.dat <- data.frame(response = y, time = 1:maxT)
ggplot(data=y.dat, aes( x=time, y =response)) + geom_line() + geom_point() 
```

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##### Advanced R: with Baltimore Tow

For this example we will work through some basic commands to create a time series plot using a dataset containing information on vehicle towed in Baltimore, Maryland.


1. Download the dataset
```{r}
library(readr)
tow <- read_csv('http://math.montana.edu/ahoegh/teaching/stat408/datasets/BaltimoreTowing.csv')
```

2. Modify the data variable to be usable format

```{r}
library(dplyr)
```

3. Create an figure to display time series aspect of the dataset
```{r}
library(ggplot2)

```