01Module 10 - Time Series Mathematics for ML EngineeringOverview of time series mathematics - stationarity, autocorrelation, Fourier analysis, ARIMA, state-space models, Kalman filter, cointegration, and wavelets. Critical for financial ML, IoT, and sequential model design.02Stationarity and Ergodicity - The Prerequisites for Time Series MLEngineering guide to strict and weak stationarity, ergodicity, unit roots, Augmented Dickey-Fuller test, differencing, and why failing to check stationarity breaks ML time series models.03Autocorrelation and Partial AutocorrelationACF and PACF functions, lag plots, correlograms, Ljung-Box test, and identifying ARIMA orders from autocorrelation structure. Essential for time series model selection in ML and forecasting.04Fourier Analysis for ML EngineersDiscrete Fourier Transform, Fast Fourier Transform, power spectrum, frequency-domain features, and Fourier-based positional encodings in transformers. Essential for audio ML, IoT, and sequence model design.05ARIMA ModelsAR, MA, ARMA, ARIMA, and SARIMA models - derivation, parameter estimation, Box-Jenkins methodology, diagnostic checking, and Python implementation with statsmodels. The classical forecasting baseline every ML engineer must know.06State Space Models and the Kalman FilterState space representation, Kalman filter derivation, smoothing, sensor fusion, connection to RNNs and LSTMs, and implementation in Python. The mathematical backbone of optimal sequential estimation.07Cointegration and Granger CausalityCointegration, Johansen test, error correction models, Granger causality, and their applications in pairs trading, causal feature selection, and financial ML. Essential for multi-series time series analysis.08Wavelets and Multiscale AnalysisContinuous and discrete wavelet transforms, mother wavelets, multiresolution analysis, wavelet denoising, and connections to WaveNet and modern audio neural networks. Simultaneous time-frequency analysis beyond Fourier.
