Time Series Analysis in R

Time series analysis is a statistical technique used to understand how data points evolve over time. In R programming, time series analysis can be efficiently performed using the ts() function, which helps organize data with associated time stamps. This method is widely applied in business and research to analyze trends and make forecasts, such as sales trends, inventory management, stock market prices, population growth, and more.

Creating Time Series Data in R

The core function to create time series objects in R is:

objectName <- ts(data, start, end, frequency)

Parameters:

• data: A numeric vector containing the observed values.
• start: The time of the first observation.
• end: The time of the last observation (optional).
• frequency: The number of observations per unit time (e.g., 12 for monthly data, 4 for quarterly).

Note: For more detailed information about the ts() function, you can run help("ts") in the R console.

Example: COVID-19 Weekly Cases Time Series

Consider weekly COVID-19 positive cases from January 22, 2020, to April 15, 2020. The following R code creates a time series object and plots the data: We define a vector x containing weekly COVID-19 positive cases. Then load the lubridate library to help work with date formats and ceate a time series object mts starting from January 22, 2020, with weekly frequency. Then we plot the time series data with appropriate axis labels and a title.

install.packages("lubridate")
library(lubridate)

x <- c(580, 7813, 28266, 59287, 75700,
       87820, 95314, 126214, 218843, 471497,
       936851, 1508725, 2072113)

mts <- ts(x, start = decimal_date(ymd("2020-01-22")), frequency = 365.25 / 7)

plot(mts, xlab = "Weekly Data", ylab = "Total Positive Cases",
     main = "COVID-19 Pandemic", col.main = "darkgreen")

Output:

Multivariate Time Series Analysis

Multivariate time series analysis allows simultaneous visualization of multiple related time series. For example, tracking both total COVID-19 positive cases and deaths weekly , we define two numeric vectors: positiveCases and deaths representing weekly COVID-19 data. Then we load lubridate for date handling and combine both vectors into a multivariate time series object mts. Then we plot the multivariate time series with labels and title.

library(lubridate)

positiveCases <- c(580, 7813, 28266, 59287,
                   75700, 87820, 95314, 126214,
                   218843, 471497, 936851,
                   1508725, 2072113)

deaths <- c(17, 270, 565, 1261, 2126, 2800,
            3285, 4628, 8951, 21283, 47210,
            88480, 138475)

mts <- ts(cbind(positiveCases, deaths),
          start = decimal_date(ymd("2020-01-22")),
          frequency = 365.25 / 7)

plot(mts, xlab = "Weekly Data", main = "COVID-19 Cases", col.main = "darkgreen")

Output:

Time Series Forecasting in R

Forecasting future values of a time series is an essential aspect of analysis. The forecast package in R provides tools to build predictive models. Here, we use the automated ARIMA model to forecast future COVID-19 cases . Here we load lubridate for date processing and forecast for forecasting functions. Then we create a time series object mts with weekly frequency starting January 22, 2020. Then we fit an ARIMA model automatically using auto.arima() and generate forecasts for the next 5 weeks. Then we plot both the historical and forecasted data.

install.packages("forecast")
library(lubridate)
library(forecast)

x <- c(580, 7813, 28266, 59287, 75700,
       87820, 95314, 126214, 218843,
       471497, 936851, 1508725, 2072113)


mts <- ts(x, start = decimal_date(ymd("2020-01-22")), frequency = 365.25 / 7)

fit <- auto.arima(mts)

forecasted_values <- forecast(fit, 5)

print(forecasted_values)

plot(forecasted_values, xlab = "Weekly Data", ylab = "Total Positive Cases",
     main = "COVID-19 Pandemic", col.main = "darkgreen")

Output:

Plotting the result

In this article, we explored how to perform time series analysis in R, including creating univariate and multivariate time series, visualizing data, and applying forecasting models using ARIMA. These techniques provide valuable insights and predictions for time-dependent data across various fields.