AMS 316, Introduction to Time Series Analysis

Catalog Description: Trend and seasonal components of time series models, autoregressive and moving average (ARMA) models, Box-Jenkins methodology, Portmanteau test, unit-root, generalized autoregressive conditionally heteroskedasticity (GARCH) models, exponential GARCH, stochastic volatility models. This course is offered as both AMS 316 and AMS 586.

Prerequisite: AMS 311 and AMS 315

SBC: SBS+

AMS 315 and 316 satisfy the Validation by Educational Experience program. For more details about actuarial preparation at Stony Brook see Actuarial Program and the Society of Actuaries.

Textbook:

"The Analysis of Time Series, An Introduction with R" by Chris Chatfield and Haipeng Xing, 7th edition, 2019, Chapman & Hall/CRC; ISBN: 9781498795630

THIS COURSE IS OFFERED IN THE FALL SEMESTER ONLY.

Week 1.	Introduction and examples
Week 2.	Simple descriptive techniques, trend, seasonality, the correlogram
Week 3.	Linear time series models and examples
Week 4.	moving average (MA), autoregressive (AR) and examples
Week 5.	ARMA model and examples
Week 6.	ARIMA model and examples
Week 7.	Data analysis with time series models
Week 8.	Estimation and examples
Week 9.	Model identification and fitting
Week 10.	Interval predictions and examples
Week 11.	Forecasting, forecast errors and examples
Week 12.	Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis.
Week 13.	State-space models: Dynamic linear models and the Kalman filter

Learning Outcomes for AMS 316, Time Series Analysis

1.) Review topics from the prerequisite course (AMS311 and AMS315).
* Basic probability concepts- mean, variance, covariance, density, distribution;
* Basic probability distributions- binomial, Poisson, normal, chi-square);
   * Probability theorems- law of large number, central limit theorem;
   *Statistical procedures- least-square, maximum likelihood;
   * Statistical concepts (hypothesis testing, confidence intervals).

2.) Demonstrate skill using the following methods:
   * Identifying the trend and seasonal effects from a time series;
   * Identifying the order of an ARMA time series;
   * Analyzing the time series using ARMA models;
   * Predicting future observations based on the principle of minimizing mean squared errors.

3.) Develop proficiency using intermediate level statistical procedures.
* Calculation of autocorrelation functions for different types of time series models (AR, MA, ARMA)
* Select the order of AR, MA, and ARMA models
* Compute the prediction of AR, MA, and ARMA series.

4.) Review scientific studies that use the techniques introduced in class.
* Analyze some current US economic time series and interpret the result.
* Reference to advanced studies of the topic.

5.) Introduce some statistical software related to the topic and apply it to analyze real time series.
* One data project using statistical software and the models introduced in class.