# Objectives

This course aims to give students a clear overview of the basic concepts of time series analysis that are applicable in commonly-found analytical cases in the social sciences, political science, and other fields. Students will learn several important tools to provide trend analytics and forecasting based on past data and time series. Students will be able then to apply the tools and techniques of time series analysis to complex problems to reach effective solutions.

# Prerequisites:

ECON 117, ECON 135, MATH 120, S&DS 238, MATH 241, MATH 222, MATH 225, S&DS 312, S&DS 410,  or permission from the instructor. The ability to work directly with data (basic proficiency in R and Python). Familiarity with probability, statistical inference, regression, and model specification.

However, this course can be  beneficial for Ph.D. students with no solid math background who need to learn how to analyze their time series data for their research.  This course can also be attended as an auditing class.

# Course Description:

This course is composed of three parts. In the first chapter, I will give examples of time series and how we can manage time series data using R and Python. The next three chapters are more theoretical. I will present the notions of stationary processes, linear filtering, ARMA processes, and linear predictions. In the second part of the course, I will introduce non-stationary processes such as ARIMA and SARIMA processes. I will provide methods for estimating models with real data, with an emphasis on efficient model selection procedures and forecasting. The final third of the class will be devoted to other techniques for times series analysis such as exponential smoothing based methods.

Throughout the course, I will make use of several types of real world data.  All of the examples given will be shown how to be performed at the same time in R and Python.

# Main References

This is a restricted list of various interesting and useful books that will be implemented during the course. You will need to consult them occasionally.

# Tentative Course Outline:

• Introduction to Time Series:
• First examples, definitions of trends, seasonality and noise
• Stationary processes, definition and examples, autocovariance, autocorrelation.
• Linear Filtering:
• Definitions and the Theorem of Filtering
• Convolutions and compositions, causal processes
• ARMA Processes:
• The ARMA Equation, Moving Average and Autoregressive processes
• Solving the ARMA equation
• Applications and Examples
• Linear Prediction: Yule-Walker Equations, Levinson-Durbin Algorithm, Partial autocorrelations

• Non-stationary Processes:
• ARIMA and SARIMA processes, simulations and examples
• Model selection and case studies
• Exponential Smoothing Based Methods:
• Time series smoothing, first and second order smoothing
• Modeling higher-order exponential smoothing

# Course Policy:

Project (20%) [reading paper or analyzing original time-series data],

Midterm  (30%, Oct 14),  Final (50%, Dec 16) [Solving problems].

## Course:

I will confirm your enrollment for the course, then you will be able to see the course page.

## Class Policy

Regular attendance is essential and expected.

It's highly recommended

• to show up for the class with your laptop,
• to install RStudio, Anaconda and the required packages (see above),
• to install MikTeX or MacTeX.