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# Applied Mathematics & Statistics

#### AMS 316, Time Series

Catalog 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. This course is offered as both AMS 316 and AMS 586.

Prerequisite: AMS 311 and AMS 315.

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.

Text: Analysis of Time Series, 6th Edition by Chatfield and Taylor
ISBN# 9781584883173

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;
* Analying 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.