Concordia University - Time Series and Forecasting (STAT 460)

STAT 460: Time Series and Forecasting, builds on concepts from STAT 360 to introduce students to advanced time series analysis and forecasting techniques. The course covers essential time series components, including trend, seasonal, and irregular variations, as well as methods for estimating and removing these components. Using techniques such as multiple regression analysis, exponential smoothing, and decomposition (both additive and multiplicative), students learn to forecast seasonal patterns and manage various time series complexities. Additionally, foundational concepts like stationary models and the autocorrelation function provide tools for analyzing time series data and enhancing predictive accuracy.

Key methodologies in the course include ARMA (AutoRegressive Moving Average) models, the Box-Jenkins methodology, and spectral analysis. Students gain proficiency in ARMA processes (p, q), focusing on autocorrelation and partial autocorrelation functions for precise model selection and validation. They further explore spectral densities, the periodogram, and time-invariant filters to analyze frequency components of time series data. By the end of the course, students can perform preliminary and maximum likelihood estimations, apply diagnostic checks, and choose optimal model orders for effective forecasting in real-world contexts.