R - Time Series Analysis

Modern Time Series Analysis in R

A time series is a sequence of data points indexed in time order. Common examples include daily stock prices, monthly sales data, or hourly temperature readings. R is exceptionally powerful for time series analysis, offering both classic and modern frameworks.

We will start with the classic ts object, which is fundamental to R. Then, we’ll introduce the modern tsibble framework, which integrates seamlessly with the tidyverse for more flexible and robust analysis.

The Classic Approach: ts() Objects

The ts() function creates a time-series object, which is a vector or matrix with additional attributes for time.

Syntax

ts(data, start = 1, end = numeric(), frequency = 1, ...)

• data: A vector or matrix of the observations.
• start: The time of the first observation. Can be a single number or a vector like c(year, period) (e.g., c(2020, 1) for January 2020).
• frequency: The number of observations per unit of time. This is a critical parameter: 1 for annual, 4 for quarterly, 12 for monthly, 52 for weekly.

Example: Monthly Rainfall Data

Let’s create a time series object for monthly rainfall data starting from January 2022 and visualize it.

# Load modern libraries for plotting
library(ggplot2)

# Sample monthly rainfall data
rainfall_data <- c(799, 1174, 865, 1334, 635, 918, 685, 998, 784, 985, 882, 1071)

# Create a time series object for monthly data starting in Jan 2022
rainfall_ts <- ts(rainfall_data, start = c(2022, 1), frequency = 12)

# Print the object to see its structure
print(rainfall_ts)

# Visualize the time series
# The autoplot() function from ggplot2 is smart and works well with ts objects
autoplot(rainfall_ts) +
  labs(
    title = "Monthly Rainfall (2022)",
    x = "Time",
    y = "Rainfall (mm)"
  ) +
  theme_minimal()

When you print rainfall_ts, you get a nicely formatted output showing the data aligned by month and year:

         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct    Nov    Dec
2022     799   1175    865   1335    635    918    685    999    784    985    883   1071

The autoplot() command generates a clean line chart, which is the standard way to visualize a time series.

The Modern Approach: tsibble

For complex analyses, the tsibble package provides a modern, tidy data structure for time series. A tsibble is a special kind of data frame (tibble) that requires an index (the time variable) and optional key (variables that define unique time series).

# You may need to install these packages first
# install.packages("tsibble")
# install.packages("dplyr")

library(tsibble)
library(dplyr)

# Create two series for different cities
rainfall_city_A <- c(799, 1174, 865, 1334, 635, 918, 685, 998, 784, 985, 882, 1071)
rainfall_city_B <- c(655, 1306, 1323, 1172, 562, 824, 822, 1265, 799, 1105, 1106, 1337)

# Create a data frame (tibble)
rainfall_df <- tibble(
  Month = yearmonth(seq(from = as.Date("2022-01-01"), by = "month", length.out = 12)),
  City_A = rainfall_city_A,
  City_B = rainfall_city_B
)

# Pivot to a long format, which is the 'tidy' way
rainfall_long <- rainfall_df %>%
  pivot_longer(cols = c(City_A, City_B), names_to = "City", values_to = "Rainfall")

# Convert to a tsibble, specifying the time index and the key
rainfall_tsibble <- as_tsibble(rainfall_long, index = Month, key = City)

print(rainfall_tsibble)

The tsibble object clearly shows its structure:

# A tsibble: 24 x 3 [1M]
# Key:       City [2]
   Month   City   Rainfall
   <mth>   <chr>     <dbl>
 1 2022 Jan City_A      799
 2 2022 Feb City_A     1175
 3 2022 Mar City_A      865
# ... with 21 more rows

Visualizing Multiple Time Series

Visualizing a tsibble with ggplot2 is natural and powerful. You can easily create facets or color by the key variable.

# Plotting the tsibble automatically handles grouping by the key
ggplot(rainfall_tsibble, aes(x = Month, y = Rainfall, color = City)) +
  geom_line() +
  labs(
    title = "Monthly Rainfall Comparison",
    subtitle = "Data for City A vs. City B",
    x = "Time",
    y = "Rainfall (mm)"
  ) +
  theme_minimal()

Next Steps: Analysis and Forecasting

• Decomposition: Break down a time series into its trend, seasonal, and random components using functions like decompose() (base R) or the more advanced STL() from the feasts package.
• Forecasting: Predict future values. The fable package provides a modern tidy interface for popular models like ETS (Error, Trend, Seasonality) and ARIMA (AutoRegressive Integrated Moving Average).
• Best Practices: Always visualize your data first. Check for missing values and outliers. Understand the underlying frequency of your data to choose the right model.
• Resources: The online book Forecasting: Principles and Practice (3rd ed) is the definitive resource for modern time series analysis in R using the tsibble ecosystem.