## Description

## Sample Autocorrelation Function.

Objectives of the lab:

• Learn to read time series data into R.

• Create a time series object using package ts.

• Perform basic manipulations on time series.

• Plot a time series and identify its main features.

• Plot a sample autocorrelation function and interpret its behaviour.

• Creating a reproducible report using R Markdown.

Getting started

• Open RStudio

• Create a new R script: File → New File → R Script

• Set working directory: Session → Set Working Directory → . . .

• Install (via Tools → Install Packages) and load necessary package(s)

library(tseries)

• To use the “Help” facility in R, enter help(function) or just ?function, which

will produce the help page for the R command/object function.

1. In this question, you will learn how to read in data into R, define a time series object

and plot time series.

(a) (Reading in data) Datasets can be read into R by one of several methods,

the most common being read.table() and read.csv()

• The dataset “LakeLevels.csv” contains the daily depths (in meters) of a

lake from 2007 to 2011 inclusive. Read the data into R using read.csv().

Use the command <- to assign your dataset to a named object, dat say.

To look at the data, you can use commands head() and tail().

Try head(dat,10) to view the first 10 rows of the data.

• Objects in R are each of a prescribed “class”, this determining characteristics of the object and how functions will act on the object. Your object is

a so–called “dataframe”, which is similar to a matrix except it allows for

different columns to be of different class and uses a different vocabulary

for its manipulation.

The command names() can be used on a data frame to obtain a list of the

vectors contained in the data frame. The call object$name extracts the

vector name from the data frame object.

• Create a plot of your dataframe dat. How does this plot differ from one

you would like for these data?

(b) (Creating a time series object) Time series objects in R are of either ts or

zoo class. We will initially learn how to work with the ts object.

• To determine whether the dataframe you have created is of class ts, the

command is.ts() can be used.

• Objects can be coerced into being time series objects using ts command.

Read the help page on the command ts.

• Create a time series object x containing the lake level data, correctly specifying arguments start and either end or frequency.

(c) (Plotting time series) Using command plot(), make a plot of your time

series object, giving your plot a suitable title and labels for the axes using the

main, xlab, and ylab arguments. How does your new plot differ from your

first plot?

Comment on the features of this time series.

2. In this question, you will explore the sample autocorrelation function (acf) for a

white noise process.

(a) Use the rnorm() function to create 200 independent observations from the

standard normal distribution. Create an object for your data {xt}t=1,2,…,200

and coerce it into class ts.

(b) Plot your simulated time series {xt}. How many of your observations are

outside the range ±2? How many would you expect to be outside ±2?

(c) Use the function acf() to create the sample autocorrelation function for your

time series. Comment on the features of the sample acf here.

You can now prepare a lab report using R Markdown by either creating a new R Markdown file (File → New File → R Markdown) or using the provided R Markdown template.

Knit your file to either PDF or HTML and upload as your lab submission.

Useful R commands for time series analysis

• read.csv()

• ts()

• window()

• start()

• end()

• time()

• diff()

• lag()

• lag.plot()

• head()

• tail()

• class()

• str()