# STAT 443 Lab 1 Introducing Time Series in R. solution

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## 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 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.

Useful R commands for time series analysis