Foundations of Time Series: Stationarity and Recurrence

To build accurate forecasting models, you must first understand the underlying behavior of your data over time. Many predictive models fail because they assume a stability that simply is not present in real-world datasets. This course guides you through the foundational mathematics of time series analysis, focusing on stationarity and recurrence. You will transition from theoretical definitions to practical statistical tests, learning how to analyze and prepare raw temporal data for modern forecasting pipelines. What you'll learn: - Understand the fundamental definitions of time series components, including trends, seasonality, and noise. - Differentiate between weak (covariance) stationarity and strong stationarity with clear mathematical logic. - Identify recurrence patterns and understand how they impact long-term predictability. - Apply statistical tests such as the Augmented Dickey-Fuller (ADF) and KPSS tests to diagnose non-stationary data. - Transform non-stationary datasets using differencing, logarithmic scaling, and detrending techniques. - Analyze autocorrelation and partial autocorrelation functions to validate stationary behavior. You will start by exploring core terminology and the mathematical definitions of stationary processes. From there, the text-only lessons walk you through diagnostic testing and data transformation techniques, ensuring you can confidently prepare data for any forecasting model. This course is designed for beginner data analysts, aspiring data scientists, and quantitative enthusiasts. No advanced background in time series is required, though a basic familiarity with algebra and statistics is helpful. Start reading today to master the essential mathematical foundations of time series forecasting.