Time Series Analysis Course

Lesson 1 • Components of a Time Series

Decomposes series into trend, seasonality, cyclicality, and irregular noise. Understanding components guides every modeling decision in later chapters.

Lesson 2 • Descriptive Statistics for Time Series

Applies summary statistics—mean, variance, autocorrelation—specifically to temporal data. These metrics reveal structure before any model is fit.

Lesson 3 • What Is a Time Series

Defines time series as ordered observations indexed by time and contrasts them with cross-sectional data. Establishes the conceptual baseline for the entire course.

Lesson 1 • Variance-Stabilizing Transformations

Covers log, Box-Cox, and power transformations to stabilize heteroscedastic variance. Stable variance improves model fit and forecast interval accuracy.

Lesson 2 • Differencing and Detrending

Applies first and seasonal differencing to remove unit roots and deterministic trends. Correct differencing order is critical for ARIMA model specification.

Lesson 3 • Handling Missing Values and Outliers

Addresses imputation strategies and outlier detection specific to temporal data. Clean series reduce bias in stationarity tests and model estimates.

Lesson 4 • Understanding Stationarity

Defines strict and weak stationarity in terms of constant mean, variance, and autocovariance. Stationarity is a prerequisite for most classical time series models.

Lesson 1 • Portmanteau Tests for Autocorrelation

Covers Ljung-Box and Box-Pierce tests to assess whether residual autocorrelation is significant. These tests validate model adequacy after fitting.

Lesson 2 • Cross-Correlation Between Series

Extends correlation analysis to pairs of series to detect leading and lagging relationships. Cross-correlation is foundational for multivariate and transfer function models.

Lesson 3 • Partial Autocorrelation Function

Introduces PACF as the correlation at lag k after removing shorter-lag effects. PACF patterns guide AR order selection in ARIMA modeling.

Lesson 1 • Forecasting with ARIMA

Generates point forecasts and prediction intervals using fitted ARIMA models. Forecast evaluation metrics connect model quality to business value.

Lesson 2 • Diagnostic Checking and Residual Analysis

Validates fitted models by testing residuals for white noise, normality, and homoscedasticity. Passing diagnostics confirms the model captures all systematic structure.

Lesson 3 • ARIMA Model Specification

Guides order selection using ACF, PACF, and information criteria such as AIC and BIC. Correct specification avoids overfitting and underfitting.

Lesson 4 • Parameter Estimation Methods

Covers maximum likelihood and conditional least squares estimation for ARIMA parameters. Estimation method choice affects small-sample performance.

Lesson 1 • Handling Multiple Seasonalities

Addresses series with daily, weekly, and annual cycles simultaneously using TBATS and Fourier terms. Multiple seasonality is common in energy, retail, and web traffic data.

Lesson 2 • Seasonal ARIMA Models

Extends ARIMA with seasonal AR and MA operators to model periodic autocorrelation. SARIMA is the standard approach for monthly and quarterly economic data.

Lesson 3 • STL Decomposition

Introduces Seasonal and Trend decomposition using Loess for robust, flexible seasonal extraction. STL handles changing seasonality better than classical methods.

Lesson 4 • Exponential Smoothing Methods

Covers simple, double, and Holt-Winters exponential smoothing as alternatives to ARIMA. ETS models are intuitive and competitive for short-horizon forecasting.

Lesson 1 • GARCH Extensions

Covers EGARCH, GJR-GARCH, and IGARCH to capture asymmetric and integrated volatility effects. Extensions improve fit for series with leverage effects.

Lesson 2 • GARCH Models

Introduces GARCH(p,q) as a parsimonious extension that includes lagged conditional variances. GARCH(1,1) is the industry standard for financial volatility.

Lesson 3 • ARCH Models

Derives the ARCH(q) model for conditional variance as a function of past squared residuals. ARCH provides the theoretical foundation for all GARCH extensions.

Lesson 4 • Heteroscedasticity in Time Series

Identifies volatility clustering and ARCH effects as departures from constant variance. Recognizing these patterns motivates the GARCH model family.

Lesson 1 • Vector Autoregression Models

Extends AR models to systems of equations where each variable depends on its own and others' lags. VAR captures dynamic feedback among economic and financial variables.

Lesson 2 • Structural VAR Models

Imposes economic theory restrictions on VAR to identify structural shocks. SVAR enables causal inference beyond reduced-form Granger causality.

Lesson 3 • Vector Error Correction Models

Combines short-run VAR dynamics with long-run cointegrating relationships in a VECM. VECM is the correct specification when cointegration is present.

Lesson 4 • Impulse Response and Variance Decomposition

Traces the effect of a shock in one variable through the entire system over time. These tools translate VAR estimates into economically interpretable narratives.

Lesson 1 • Transformer Models for Sequences

Adapts attention-based transformer architectures to time series forecasting tasks. Transformers achieve state-of-the-art results on long-horizon benchmarks.

Lesson 2 • Model Evaluation and Benchmarking

Establishes rigorous evaluation protocols using time-series cross-validation and statistical tests. Proper benchmarking prevents overconfident claims about ML superiority.

Lesson 3 • Feature Engineering for Time Series

Transforms raw time series into supervised learning datasets using lag features and calendar variables. Good feature engineering is the primary driver of ML forecast quality.

Lesson 4 • Recurrent Neural Networks

Introduces LSTM and GRU architectures designed to capture long-range temporal dependencies. RNNs excel on high-frequency and multivariate sequence data.