MA413: Time Series & Random Process in Linear Systems

Learning Outcomes

• Time-series fundamentals: Explain components (trend/seasonality/irregular) and perform decomposition and detrending/seasonal adjustment.
• Stationarity & correlograms: Diagnose (weak) stationarity; compute/interpret ACF and PACF; select probability models for stationary series.
• Nonstationary processes: Describe homogeneous nonstationary series; use differencing/integration; relate simple and integrated models.
• ARIMA estimation: Fit AR/MA/ARMA/ARIMA via method of moments and maximum likelihood; interpret parameter estimates.
• Diagnostics & testing: Conduct hypothesis tests, residual diagnostics, and goodness-of-fit checks to validate models.
• Forecasting: Fit AR/MA/ARMA/ARIMA via method of moments and maximum likelihood; interpret parameter estimates.
• ARIMA estimation: Construct and evaluate forecasts from ARIMA-family models, including interval prediction.

Takeaways

This intensive three-week summer course pushed me to quickly grasp core time-series concepts—from stationarity tests and ARIMA estimation to spectral and volatility modelling. The fast pace was challenging, but it forced me to consolidate key ideas efficiently. Our group project, applying ARIMA, GARCH, and VAR models to stock market data, made the theory tangible: I saw how model diagnostics, forecasting accuracy, and volatility estimation play out in real-world financial contexts. Beyond the math, I learned the importance of structured validation and careful model interpretation when working under tight time constraints.