1. Introduction to Time Series#
This chapter lays the foundation for understanding time series analysis, one of the most important skills in modern data science. You will explore the fundamental concepts, discover where to find quality data, and learn specialized techniques for building accurate predictive models.
In this chapter, you will learn the following topics:
What are Time Series? Time series data represents measurements or observations recorded sequentially over time. This section introduces the fundamental concepts, definitions, and characteristics that define time series data, along with real-world examples across various domains. You will explore applications in finance (stock prices, exchange rates), climate science (temperature, precipitation records), biomedical fields (heart rate monitoring, brain activity), and many other areas where understanding temporal patterns is essential. By the end of this section, you will understand how time series differs from other data types and why specialized analytical techniques are necessary to extract meaningful insights from sequential data.
Best Sources for Public Datasets: Now that you understand what time series data is, the next question is where to find quality data to work with. Access to high-quality data is crucial for learning, research, and practical applications in time series analysis. This section provides a comprehensive guide to discovering and accessing reliable public datasets from government agencies, academic institutions, and research organizations. You will learn about major data repositories in the United States and Canada, including federal and state/provincial resources, as well as international data sources. The section covers strategies for identifying appropriate datasets for your projects, understanding data formats and accessibility, and best practices for downloading and organizing data for analysis.
Time Series Cross-Validation: Building accurate predictive models with time series data requires special attention to how we evaluate model performance. This section explores cross-validation techniques specifically designed for time series analysis, highlighting the critical differences between traditional machine learning cross-validation and time series cross-validation methods. You will learn about various windowing approaches such as rolling windows, expanding windows, and time series split strategies that maintain the temporal ordering of data. The section emphasizes why standard cross-validation can lead to unrealistic performance estimates and demonstrates how proper time series cross-validation ensures that your models generalize well to future unseen data while respecting the temporal integrity of your dataset.
Time Series Graphics emphasizes that time series analysis begins with visualization, moving beyond simple line plots to employ specialized graphic techniques essential for understanding the data’s structure, features, and anomalies before applying any sophisticated models. This section teaches you how to plot raw time series levels to immediately identify trends, seasonality, and structural breaks; how to visualize rate-of-change data (e.g., Year-over-Year growth) to highlight volatility and cyclical behavior often masked in raw level plots; and how to create heatmaps to analyze patterns of change across different time periods. The section provides concrete, real-world examples by demonstrating how to fetch and visualize official data from major sources, including the U.S. Bureau of Labor Statistics (BLS), Environment and Climate Change Canada, and S&P/Case-Shiller Home Price Indices.
ACF and PACF: Visual Diagnostics for Time Series: Understanding the internal structure of time series data is fundamental to building effective forecasting models. This section introduces two powerful diagnostic tools—the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF)—that reveal how observations in a time series depend on their past values. You will learn to interpret ACF plots to identify seasonality, trends, and overall dependence structure, and to use PACF plots to isolate direct lag relationships and determine the appropriate order of autoregressive models. Through real-world examples—including monthly temperature data exhibiting strong seasonal cycles and synthetic stock returns showing white noise behavior—you will develop intuition for recognizing these patterns and applying them to guide model selection. The section also explains the practical considerations for choosing the number of lags to examine and demonstrates how ACF and PACF analysis connects to model building, residual diagnostics, and proper time series cross-validation, establishing these tools as essential components of your time series analysis workflow.
Beyond their roles in model specification, ACF and PACF analyses serve as diagnostic checks throughout the modeling lifecycle. After fitting a forecasting model (such as an ARIMA or exponential smoothing model), examining the ACF of residuals reveals whether the model has adequately captured the temporal structure in the data. Ideally, residuals should resemble white noise—exhibiting no significant autocorrelation at any lag, indicating that the model has extracted all predictable information. If residual plots show lingering autocorrelation, this signals model misspecification and suggests the need for additional lags, seasonal terms, or alternative modeling approaches. Furthermore, when working with multivariate time series or comparing relationships between two series (as in cross-correlation analysis), ACF and PACF help clarify whether observed associations result from direct lead-lag relationships or confounding through shared external drivers like seasonality. By mastering the interpretation of these visual diagnostics, practitioners gain the ability to transition seamlessly from exploratory analysis to model validation, ensuring that final predictions rest on solid statistical foundations and genuine understanding of the data-generating process.