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Introduction

This report presents solutions for the time series analysis questions. Each question includes R code, outputs, and explanatory notes.

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Question 1: Gold, Wool Yarn, and Gas Time Series

Part 1a: Use autoplot() to Plot Each Series

library(fpp2)

## Warning: package 'fpp2' was built under R version 4.1.3

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## -- Attaching packages ---------------------------------------------- fpp2 2.5 --

## v ggplot2   3.5.1      v fma       2.5   
## v forecast  8.23.0     v expsmooth 2.3

## Warning: package 'fma' was built under R version 4.1.3

## Warning: package 'expsmooth' was built under R version 4.1.3

## 

# Frequency of each series
frequency(gold)     # Typically 1 (daily data)

## [1] 1

frequency(woolyrnq) # Quarterly data, frequency = 4

## [1] 4

frequency(gas)      # Monthly data, frequency = 12

## [1] 12

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Part 1b: Find the Frequency of Each Series

# Use autoplot() to plot each series
autoplot(gold) + ggtitle("Gold Prices")

# Use autoplot() to plot each series
autoplot(woolyrnq) + ggtitle("Wool Yarn Production")

# Use autoplot() to plot each series
autoplot(gas) + ggtitle("Gas Production")

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Part 1c: Use which.max() to Find the Outlier in the gold Series

# Find the observation with the maximum value in the gold series
which.max(gold)

## [1] 770

outlier_index <- which.max(gold)
outlier_index

## [1] 770

gold[770]

## [1] 593.7

outlier_value <- gold[outlier_index]
outlier_value

## [1] 593.7

# Print the result
cat("The outlier is at index:", outlier_index, "with value:", outlier_value, "\n")

## The outlier is at index: 770 with value: 593.7

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