Time Series Analytics

Volume I of a complete graduate course in time series analytics. Foundations and Linear Models in eighteen rigorous chapters, with theorems, full proofs, and runnable Python on real markets.

This is the textbook the author wished he had when first standing in front of a quantitative graduate audience. The literature splits, awkwardly, into rigorous monographs that assume more probability theory than most applied students bring; econometrics texts that move past foundations to applications; and software-first introductions that get students producing forecasts but unable to defend a single line of the underlying derivation. Time Series Analytics: Theory and Python Practice sits in a different middle. Every chapter combines formal theory with working code.

Volume I covers:

• Foundations (Chapters 1-8): stochastic processes; classical decomposition and STL; smoothing filters and exponential smoothing; the autocorrelation function; portmanteau tests for noise; variance-stabilising transformations.
• Linear models (Chapters 9-18): the Wold decomposition; backshift-operator calculus; the MA, AR, ARMA, ARIMA, and SARIMA families with full Box-Jenkins identification; transfer-function models; and two end-of-volume Python applications on Indian-equity data (MRF Limited daily ARIMA; NIFTY 50 monthly SARIMA).

What makes this different:

• Two theorems per chapter, with full proofs in the Brockwell-Davis tradition. No "as the reader can show".
• Two worked examples per chapter: one synthetic so the student can verify by hand, one drawn from a real Indian-equity series - NIFTY 50, NIFTY Bank, MRF, Reliance Industries.
• Five graded discussion questions per chapter, with full worked solutions in the back-matter Solutions Appendix.
• Pinned numerical results. Every empirical claim is pinned to the exact output of a seeded Python run. Reproduce with np.random.seed(42).

For graduate students in statistics, financial engineering, applied mathematics, and quantitative economics - and for the practitioner who wants both the theory and the working code in a single self-contained text.

Prerequisites: probability through the central limit theorem; linear algebra including Cholesky decomposition; idiomatic NumPy and pandas. No prior exposure to statsmodels, arch, or yfinance is assumed.

Volume II (sold separately) covers Estimation, Forecasting and Diagnostics; Multivariate and Volatility Models (VAR, Granger causality, IRFs, cointegration, ARCH/GARCH/EGARCH/GJR-GARCH and Value-at-Risk); and four end-to-end Python projects on Bitcoin volatility and a Gold-Bitcoin VAR.

Approximately 495 pages • 18 chapters • 90 worked discussion-question solutions • dataset whitelist (NIFTY 50, NIFTY Bank, MRF, Reliance) • full reproducibility under np.random.seed(42).