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 for Fall 2024:
"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.
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Week 1. |
Introduction and examples |
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Week 2. |
Simple descriptive techniques, trend, seasonality, the correlogram |
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Week 3. |
Linear time series models and examples |
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Week 4. |
moving average (MA), autoregressive (AR) and examples |
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Week 5. |
ARMA model and examples |
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Week 6. |
ARIMA model and examples |
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Week 7. |
Data analysis with time series models |
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Week 8. |
Estimation and examples |
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Week 9. |
Model identification and fitting |
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Week 10. |
Interval predictions and examples |
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Week 11. |
Forecasting, forecast errors and examples |
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Week 12. |
Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis. |
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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.