R Time Series Analysis — Analyzing Temporal Data

Learning Objectives

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

• Create and manipulate time series objects
• Decompose time series into trend, seasonal, and residual components
• Apply smoothing methods (moving averages, exponential smoothing)
• Build ARIMA models for forecasting
• Evaluate forecast accuracy

Creating Time Series Objects

# ts() — base R time series
ts_data <- ts(mtcars$mpg, start = 1974, frequency = 1)
print(ts_data)

# Monthly data
monthly <- ts(1:24, start = c(2022, 1), frequency = 12)

# Quarterly data
quarterly <- ts(1:8, start = c(2022, 1), frequency = 4)

# Plot
plot(monthly, main = "Monthly Time Series")

Decomposition

# Load AirPassengers dataset
data("AirPassengers")

# Classical decomposition
decomp <- decompose(AirPassengers, type = "multiplicative")
plot(decomp)

# STL decomposition (more robust)
library(forecast)
stl_decomp <- stl(AirPassengers, s.window = "periodic")
plot(stl_decomp)

# Seasonal plot
ggseasonplot(AirPassengers)
ggsubseriesplot(AirPassengers)

Smoothing Methods

Moving Averages

library(forecast)

# Simple moving average
ma(AirPassengers, order = 12)

# Weighted moving average
weighted.mean(tail(AirPassengers, 12), 1:12/sum(1:12))

# Plot
plot(AirPassengers, main = "AirPassengers with Moving Average")
lines(ma(AirPassengers, 12), col = "red", lwd = 2)

Exponential Smoothing

# Simple exponential smoothing
model_ses <- ses(AirPassengers, h = 12)
plot(model_ses)

# Holt's method (trend)
model_holt <- holt(AirPassengers, h = 12)
plot(model_holt)

# Holt-Winters (trend + seasonality)
model_hw <- hw(AirPassengers, h = 12, seasonal = "multiplicative")
plot(model_hw)

ARIMA Models

Auto ARIMA

library(forecast)

# Automatic ARIMA selection
model <- auto.arima(AirPassengers)
summary(model)

# Forecast
fc <- forecast(model, h = 24)
plot(fc)

# Accuracy
accuracy(model)

Manual ARIMA

# Specify ARIMA order
model <- Arima(AirPassengers, order = c(2, 1, 1), seasonal = c(1, 1, 1))
summary(model)

# Check residuals
checkresiduals(model)

Forecasting

library(forecast)

# ARIMA forecast
model <- auto.arima(AirPassengers)
fc <- forecast(model, h = 12)

# ETS (Error, Trend, Seasonal) model
model_ets <- ets(AirPassengers)
fc_ets <- forecast(model_ets, h = 12)

# Compare
plot(fc)
lines(fc_ets$mean, col = "red")

# Accuracy metrics
accuracy(fc)

Stationarity

library(tseries)

# Augmented Dickey-Fuller test
adf.test(AirPassengers)

# KPSS test
kpss.test(AphAssengers)

# Differencing to achieve stationarity
diff_data <- diff(AirPassengers, differences = 1)
plot(diff_data)

# ACF and PACF
par(mfrow = c(2, 1))
acf(AirPassengers, main = "ACF")
pacf(AirPassengers, main = "PACF")
par(mfrow = c(1, 1))

Practical Examples

Example 1: Stock Price Forecasting

library(quantmod)

# Get stock data
getSymbols("AAPL", src = "yahoo", from = "2020-01-01")

# Use closing prices
prices <- Cl(AAPL)

# Forecast
model <- auto.arima(prices)
fc <- forecast(model, h = 30)
plot(fc, main = "AAPL Stock Price Forecast")

Example 2: Sales Forecasting

# Monthly sales data
set.seed(42)
sales <- ts(cumsum(rnorm(120, 100, 20)) + sin(1:120/12 * 2 * pi) * 500,
            start = c(2014, 1), frequency = 12)

# Decompose
decomp <- stl(sales, s.window = "periodic")
plot(decomp)

# Forecast
model <- auto.arima(sales)
fc <- forecast(model, h = 24)
plot(fc)

Practice Exercises

Exercise 1: US Gas Consumption

Forecast US gas consumption using the WWWusage dataset.

Solution

library(forecast)

# Load data
data("WWWusage")

# Plot
plot(WWWusage, main = "WWW Usage")

# Auto ARIMA
model <- auto.arima(WWWusage)
summary(model)

# Forecast
fc <- forecast(model, h = 10)
plot(fc)

# Accuracy
accuracy(model)

Key Takeaways

• ts() creates time series objects with start, frequency
• Decomposition separates trend, seasonal, and residual components
• Moving averages smooth short-term fluctuations
• Exponential smoothing gives more weight to recent observations
• ARIMA models handle non-stationary data with differencing
• auto.arima() automatically selects best model
• Always check residuals for white noise
• Use forecast() to predict future values

Next: Learn about R Machine Learning with caret — predictive modeling.