Monash

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

Time plots

Time plots

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

Seasonal plots

Seasonal plots

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

Seasonal plots

• 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()

Seasonal polar plots

Seasonal polar plots

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} }

Seasonal subseries plots

Seasonal subseries plots

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

Seasonal subseries plots

• 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()

Lag plots and autocorrelation

Lagged scatterplots

gglagplot(USAccDeaths, lags=9)

Lagged scatterplots

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} }

Autocorrelation

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 $y_{t-k}$.

Autocorrelation

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)

binb documentation built on July 2, 2020, 4:08 a.m.