دانلود کتاب ریاضیات پیش‌بینی سری‌های زمانی

Time is the most intricate dimension of data. Every transaction, temperature reading, market movement, or sensor output is a snapshot in time. This book, Mathematics of Time Series Forecasting, is written for those who wish to decode that story. The book blends mathematical theory with computational practice, aiming to help readers not only build forecasting models but also understand the science that makes them work. The book bridges classical statistics and modern artificial intelligence, showing how timeless mathematical principles still underpin even the most advanced forecasting architectures. It introduces readers to the continuum between stochastic processes, ARIMA-family models, and deep learning networks, with each concept supported by mathematical derivations and real-world Python implementations. The goal is to empower professionals, researchers, and learners to model uncertainty with precision and interpretability. Hence, whether you are a data scientist, financial analyst, engineer, or researcher, this book will guide you through the complete forecasting journey, from mathematical intuition to practical implementation. Each chapter is structured to balance theory, intuition, and application, ensuring that readers build both conceptual clarity and coding proficiency. Chapter 1 lays the mathematical foundation of time series analysis by introducing stochastic processes, which model uncertainty and temporal dependence. It explores discrete and continuous processes such as Markov Chains, Poisson Processes, Brownian Motion, and Random Walks, providing the conceptual bridge between probability theory and real-world forecasting applications. Chapter 2 explains the concept of stationarity, its types, and its critical role in forecasting accuracy. Readers will learn to identify and handle nonstationary behavior through detrending, differencing, and transformations that make the data suitable for model training. Chapter 3 introduces the first set of statistical tests to verify whether a time series is stationary. Covering visual inspection, the K-S Test, and the Dickey-Fuller family, it demonstrates how to interpret test results, and translate them into practical pre-processing actions for forecasting models. Chapter 4 introduces more powerful and complementary statistical tests such as the Phillips-Perron, KPSS, DF-GLS, and Ng-Perron tests. These approaches offer refined detection of non-stationarity, addressing autocorrelation, heteroskedasticity, and structural complexity in real-world datasets. Chapter 5 explores advanced econometric tools including the Schmidt- Phillips, Variance Ratio, Zivot-Andrews, and Leybourne-McCabe tests. Each test is discussed with mathematical rigor, and demonstrated through examples to handle structural breaks and complex stochastic behavior. Chapter 6 covers data parsing, indexing, resampling, handling irregularities, detrending, deseasonalizing, and variance-stabilizing transformations, forming the essential pre-modelling pipeline for any forecasting task. Chapter 7 introduces the core forecasting architectures such as AR, MA, ARMA, ARIMA, SARIMA, and Exponential Smoothing models. It details their mathematical formulations, assumptions, and implementation in Python, building the foundation for all future model comparisons and enhancements. Chapter 8 presents Machine Learning (ML) methods such as Decision Trees, Random Forests, and XGBoost, along with deep learning architectures like LSTMs. It emphasizes reframing time series problems into supervised learning format, and illustrates how these models capture non-linear and long-term dependencies. Chapter 9 extends forecasting to multivariate systems where multiple timedependent variables interact dynamically. It covers Vector Autoregression (VAR), Vector Error Correction Models (VECM), and deep learning-based Multivariate LSTMs, showing how to model complex interdependencies across variables for higher predictive accuracy. Thus, writing this book has been a journey of translating years of applied learning, mathematical exploration, and practical experimentation into a structured guide for professionals and students, alike. Hence, whether you are decoding financial markets, optimizing energy systems, or uncovering behavioural trends, may these chapters empower you to see patterns in time not as randomness, but as rhythm. Every dataset tells a story as this book is an invitation to understand and forecast it with clarity, rigor, and creativity!