Mathematics of Time Series Forecasting

Where Mathematical Rigor Meets the Art of Predicting the Future

Key Features
● Get a free one-month digital subscription to www.avaskillshelf.com
● Step-by-step mathematical derivations for time series intuition.
● Clean, transform, decompose, and engineer time series with rigor.
● Master ARIMA, SARIMA, Exponential Smoothing, and VAR models.
● Apply ML and LSTM deep learning with intuitive Python examples.

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.

Thus, whether you are forecasting financial markets, demand patterns, sensor data, or macroeconomic indicators, this book equips you with the mathematical insight and practical tools to build accurate, reliable, and interpretable forecasting systems.

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.

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

About the Author
Dr. Sulekha AloorRavi is a data science and analytics leader specializing in time series forecasting, Artificial Intelligence (AI), and quantitative modeling. With a doctorate in AI, she has built AI-driven investment and decision systems in global financial services. An author and educator, she bridges mathematics, statistics, and machine learning to make advanced forecasting practical and accessible.

About the Technical Reviewer
Dileep Vuppaladhadiam is an accomplished leader in the field of Artificial Intelligence and Machine Learning (AI/ML) with a remarkable 18-year track record of shaping the industry. His expertise spans a wide spectrum of domains, including solution design, data architecture, data engineering, data science, and the practical application of artificial intelligence and machine learning technologies.

Throughout his career, Dileep has played a pivotal role in deploying cutting-edge AI/ML-based applications, employing rigorous data science methodologies to empower data-driven decision-making. His achievements include the successful implementation of numerous AI/ML solutions, both on-premises and in cloud environments, delivering substantial business value.

Dileep's academic journey is equally impressive, encompassing accounting, economics, finance, business administration, data science, artificial intelligence, business analytics, and business intelligence. His commitment to education extends beyond his own studies, as he has also served as a dedicated coach, mentor, and faculty member, inspiring and guiding countless aspiring data scientists.

His professional footprint spans diverse sectors, including Manufacturing and Industrial, Information Technology, Banking, Finance, Retail, Travel and Tourism, as well as Consulting. Dileep has had the privilege of leading Research and Development, Technical Consultancy, and Support teams, bringing innovative solutions to renowned organizations such as IBM, Capgemini, Barclays, HSBC, HomeCredit, Mindtree, and Infosys.

Currently, he holds the prestigious position of Vice President at Wells Fargo, where he plays a pivotal role in guiding the global enterprise towards achieving unparalleled business value. Dileep’s focus centers on harnessing the power of robust and scalable data engineering and data science approaches tailored to the modern business landscape.