Mathematics of Time Series Forecasting

Where Mathematical Rigor Meets the Art of Predicting the Future Book Description Time series forecasting is one of the most valuable skills an AI/ML professional can possess. Mathematics of Time Series Forecasting transforms the complexity of time-dependent data into a clear, intuitive, and powerful framework for prediction. This book bridges rigorous mathematical foundations with hands-on implementation, allowing readers to truly understand-not just apply the forecasting models. Beginning with the core principles of time series behavior, you will learn how to diagnose stationarity, seasonality, and stochastic patterns that shape real-world datasets. Step-by-step derivations guide you through the mathematics behind ARIMA, SARIMA, Exponential Smoothing, VAR, and other classical models, while practical Python examples demonstrate how these methods are built and validated in practice. The book then moves beyond traditional statistics, exploring machine learning and deep learning techniques-including gradient boosting, neural networks, and LSTMs-that have transformed the forecasting landscape. What you will learn ¿ Build mathematical intuition behind ARIMA, SARIMA, VAR, and LSTM models ¿ Test, transform, and prepare real-world time series for forecasting ¿ Apply statistical, ML, and DL methods with Python step-by-step ¿ Diagnose stationarity, seasonality, and stochastic behavior in data ¿ Model multivariate time series and interpret cross-variable dependencies ¿ Bridge mathematical theory with applied forecasting across domains Who is This Book For? This book is tailored for data scientists, analysts, and engineers with a foundational understanding of statistics, linear algebra, and Python programming. Readers should also be comfortable with basic data manipulation and visualization to fully benefit from the mathematical depth and practical applications of time series forecasting. Table of Contents 1. Introduction to Time Series and Mathematical Foundations 2. Preparing Time Series Data 3. Tests for Stationarity - Part 1 4. Tests for Stationarity - Part 2 5. Tests for Stationarity - Part 3 6. Foundations of Time Series Preparation 7. Statistical Models for Forecasting 8. ML and DL for Timeseries 9. Multivariate Time Series Models Index