AMS 586: Time Series
Teaching connection: Teaching assistant in Fall 2024, Fall 2025, and Fall 2026.
This page is part of my personal academic record, not an official course website.
Course description
Linear time series models, moving average (MA), autoregressive (AR), ARMA and ARIMA models, estimation and forecasting, interval predictions, forecast errors, stationary processes in the frequency domain, state-space models.
Textbooks and resources
Required textbooks
- Analysis of Financial Time Series by Ruey S. Tsay, 3rd edition, 2010, Wiley
- The Analysis of Time Series: An Introduction with R by Chris Chatfield and Haipeng Xing, 7th edition, 2019, Chapman and Hall/CRC
Supplementary textbook
- Time Series Analysis and Its Applications: With R Examples by Robert H. Shumway and David S. Stoffer, 4th edition, Springer, 2017
Learning outcomes
- Master the concepts of stationary time series:
- Decomposition of time series into trend component, seasonal component, and stationary process;
- Strictly stationary process versus weakly stationary process;
- White noise and Gaussian white noise;
- Autocovariance, mean and variance;
- Autocorrelation function (ACF);
- Partial autocorrelation function (PACF);
- Autoregressive process (AR) – model introduction, condition for stationarity;
- Moving average process (MA) – model introduction, condition for invertibility;
- Autoregressive Moving Average Process (ARMA) – model introduction, conditions for stationarity and invertibility, three representations of ARMA;
- Linear time series models.
- Master statistical inference related to the stationary time series processes (AR, MA and ARMA):
- Computation of the population & sample autocorrelations;
- Computation of the population & sample partial autocorrelations;
- Determination of the order of the AR processes based on PACF;
- Determination of the order of the MA processes based on ACF;
- Identification of the ARMA processes;
- Estimation of AR, MA and ARMA;
- Goodness-of-fit indices: AIC, AICC, BIC;
- Normality test for the residuals;
- Forecast with ARMA models;
- Linear regression with ARMA errors;
- Stationary processes in the frequency domain.
- Master statistical concepts and inference related to the autoregressive integrated moving average processes (ARIMA) & Unit-Root Nonstationarity:
- Random walk;
- Random walk with drift;
- Trend stationary time series;
- ARIMA model and its reduction to ARMA through differencing;
- Unit-root test;
- Seasonal models and seasonal differencing;
- Mastery of related statistical programs using R.
- Demonstrate skills for statistical concepts and inference related to the conditional heteroscedastic models:
- Volatility;
- AutoRegressive Conditional Heteroskedasticity (ARCH) models;
- Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models;
- ARMA-GARCH Models – identification, estimation and forecast;
- Mastery of related statistical programs using R.
- Demonstrate mastery of basic statistical concepts related to nonlinear models:
- Bilinear models;
- Threshold autoregressive (TAR) models;
- Smooth transition AR (STAR) models;
- Markov switching models;
- Nonparametric methods.
- Demonstrate skills for statistical concepts and inference related to the state-space models:
- Local Trend Model;
- Kalman Filter;
- Linear state-space models;
- Model transformation;
- Structural equation modeling;
- Mastery of related statistical programs using R or SAS.