R Notebook

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Facilitator: CDAM Experts

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Session 8: Time Series Analysis

Learning Objectives:

By the end of this session, you will be able to:

• Understand the structure and components of time series data .

• Decompose time series into trend , seasonality , and residuals .

• Visualize time series data using appropriate plots.

• Analyze autocorrelation and partial autocorrelation.

• Build basic ARIMA models for forecasting.

• Apply time series analysis techniques to real-world datasets.

1. Introduction to Time Series Data

What is a Time Series?

A time series is a sequence of data points indexed in chronological order.

Examples:

• Monthly sales figures

• Daily stock prices

• Hourly temperature readings

• Quarterly GDP values

Getting Started

set a working directory Default location where R looks for files and saves outputs

setwd("~/2025_R_TRAINING") # It tells R where to look for files and where to save files

1. Analyze and Visualize Time Series Data: Load a time series dataset and plot it.

Load and visualize time series data

library(scales)
library(ggplot2)
library(stats)
library(forecast)

Example: Visualize time series data

# Create a sample time series
set.seed(123)  # Ensure reproducibility

# Generate 36 random values (e.g., monthly data for 3 years)
data <- rnorm(36, mean = 100, sd = 10)

# Create a time series object starting from January 2020
ts_data <- ts(data, start = c(2020, 1), frequency = 12)

# Convert the ts object into a data frame
df <- data.frame(
  Date = seq(as.Date("2020-01-01"), by = "month", length.out = length(ts_data)),
  price = as.numeric(ts_data))

# Plot the time series
ggplot(df, aes(x = Date, y = price)) +
  geom_line(color = "blue", size = 1) +  # Line plot
  geom_point(color = "red", size = 2) +  # Optional: Add points
  labs(title = "Time Series Plot using ggplot2",
       x = "Date",
       y = "Price of Goods",
       caption = "Source: CDAM Experts, 2025") +
  scale_x_date(date_labels = "%b %Y", date_breaks = "6 months") +  # Format x-axis
 theme_classic()

2. Decompose Time Series: Use decompose() to separate the trend, seasonality, and residuals.

# Example: Decompose time series
# Create a time series object
ts_data <- ts(df$price, frequency = 12, start = c(2023, 1))

# Decompose the time series
decomposed_data <- decompose(ts_data)

# Plot the decomposition
plot(decomposed_data)

3. Autocorrelation Function (ACF): Use acf() to analyze autocorrelation.

# Example: Autocorrelation function
acf(ts_data, lag.max = 20)

4. Build an ARIMA Model: Fit an ARIMA model using auto.arima() from the forecast package.

# Example: Fit an ARIMA model

# Fit the ARIMA model
arima_model <- auto.arima(ts_data)

# Print the model summary
summary(arima_model)

Series: ts_data 
ARIMA(0,0,0)(1,0,0)[12] with non-zero mean 

Coefficients:
         sar1      mean
      -0.4516  100.2065
s.e.   0.1653    1.0677

sigma^2 = 71.79:  log likelihood = -128.35
AIC=262.7   AICc=263.45   BIC=267.45

Training set error measures:
                    ME    RMSE      MAE        MPE     MAPE      MASE       ACF1
Training set 0.1988831 8.23411 6.774103 -0.5167801 6.841991 0.5137243 0.08037085

# Forecast future values
forecast_values <- forecast(arima_model, h = 6)  # Forecast next 6 periods

# Plot the forecast
plot(forecast_values)

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Homework

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• Work with a Time Series Dataset :

• Load a time series dataset (e.g., stock prices, weather data, or sales data)

• Perform the following tasks:

• Visualize the time series data.

• Decompose the time series into trend, seasonality, and residuals.

• Analyze autocorrelation using ACF.

• Build and evaluate an ARIMA model for forecasting.

Homework Assignment

Exercise A: Import a Time Series Dataset

• Download a public time series dataset(synthetic_TS.csv)

• Load it into R using rio() or read.csv()

• Print first few rows and check structure

Exercise B: Time Series Decomposition

• Convert your data to a ts object

• Decompose it into trend, seasonality, and residuals

• Plot each component

Exercise C: Stationarity Check

• Plot the time series

• Use the ADF test to check for stationarity

• Difference the series if necessary

Exercise D: ACF and PACF Analysis

• Plot ACF and PACF

• Identify possible AR and MA orders for ARIMA

Exercise E: Build an ARIMA Model

• Fit an ARIMA model using auto.arima() or manual specification

• Interpret the model output

• Forecast future values (e.g., next 6–12 periods)

Exercise F: Write a Summary

• Summarize your findings clearly in plain language

• Include:

  • What question you were answering

  • Whether the series was stationary

  • Which model you chose and why

  • What the forecast suggests

Additional Resources

• Official R Documentation for stats : https://stat.ethz.ch/R-manual/R-devel/library/stats/

• Forecasting Principles and Practice (Free Book) by Rob J Hyndman & George Athanasopoulos: https://otexts.com/fpp3/

• Time Series Cheat Sheet : https://posit.co/download/rstudio-cheatsheets

• Introduction to Statistical Learning (ISLR) – Free book with R labs: http://faculty.marshall.usc.edu/gareth-james/ISL/