knitr::opts_chunk$set(echo = TRUE) library(forecast) library(ggplot2) options(width=50)

autoplot(USAccDeaths) + ylab("Total deaths") + xlab("Year")

ggseasonplot(USAccDeaths, year.labels=TRUE, year.labels.left=TRUE) + ylab("Total deaths")

- Data plotted against the individual "seasons" in which the data were observed. (In this case a "season" is a month.)
- Something like a time plot except that the data from each season are overlapped.
- Enables the underlying seasonal pattern to be seen more clearly, and also allows any substantial departures from the seasonal pattern to be easily identified.
- In R:
`ggseasonplot()`

ggseasonplot(USAccDeaths, year.labels=TRUE, polar=TRUE) + ylab("Total deaths")

\only<2>{ \begin{textblock}{4}(8,4) \begin{alertblock}{} Only change is to switch to polar coordinates. \end{alertblock} \end{textblock} }

ggsubseriesplot(USAccDeaths) + ylab("Total deaths")

- Data for each season collected together in time plot as separate time series.
- Enables the underlying seasonal pattern to be seen clearly, and changes in seasonality over time to be visualized.
- In R:
`ggsubseriesplot()`

gglagplot(USAccDeaths, lags=9)

gglagplot(USAccDeaths, lags=9, do.lines=FALSE)

\only<2>{ \begin{textblock}{4}(8.3,3) \begin{block}{} \begin{itemize}\tightlist \item Each graph shows $y_t$ plotted against $y_{t-k}$ for different values of $k$. \item Autocorrelations are correlations associated with these scatterplots. \end{itemize} \end{block} \end{textblock} }

We denote the sample autocovariance at lag $k$ by $c_k$ and the sample autocorrelation at lag $k$ by $r_k$. Then define

\begin{block}{}
\begin{align*}
c_k &= \frac{1}{T}\sum_{t=k+1}^T (y_t-\bar{y})(y_{t-k}-\bar{y}) \[0.cm]
\text{and}\qquad
r_{k} &= c_k/c_0
\end{align*}
\end{block}\pause\small

- $r_1$ indicates how successive values of $y$ relate to each other
- $r_2$ indicates how $y$ values two periods apart relate to each other
- $r_k$ is \textit{almost} the same as the sample correlation between $y_t$ and $y_{t-k}$.

Results for first 9 lags for `USAccDeaths`

data:

USAccDeathsacf <- matrix(acf(c(USAccDeaths), lag.max=9, plot=FALSE)$acf[-1,,1], nrow=1) colnames(USAccDeathsacf) <- paste("$r_",1:9,"$",sep="") knitr::kable(USAccDeathsacf, booktabs=TRUE, align="c", digits=3, format.args=list(nsmall=3))

```
ggAcf(USAccDeaths)
```

**Any scripts or data that you put into this service are public.**

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.