STATISTICS

Course Credits: 3 Units

Prerequisites: Stat 129

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STAT 145 - Introduction to Time Series Analysis and Forecasting

Course Description

A time series is a sequence of data points that is often recorded through equally spaced time intervals. Some examples are stock prices, foreign exchange rates, daily infections, and monthly sales. In this course, we will deal with statistical models specifically used for time series datasets. These methods aim to understand the underlying mechanisms causing trend or systemic patterns in the data over time, and ultimately, to provide forecasts of future observations. These forecasts provide a key role in the decision making process of various disciplines such as financial markets, weather patterns, and epidemiolocal studies.

Course Learning Outcomes

By the end of this course, the student must be able to:

  1. Demonstrate awareness of the different concepts of time series analysis and forecasting.
  2. Differentiate the various time series models.
  3. Perform time series analysis with diagnostic checking and proper model selection technique using statistical software.
  4. Communicate results of time series models to stakeholders to explain various conceptual and real-world datasets.
Course Outline

UNIT 1. Introduction

  1. Introduction to Time Series
  2. Objectives of Time Analysis
  3. Simple Time Series Models

UNIT 2. Fundamental Concepts

  1. Stochastic Process
  2. Autocovariance and Autocorrelation
  3. Partial Autocorrelation Function
  4. Estimating the Mean and Autocovariance
  5. Sample Autocorrelation Function
  6. Sample Partial Autocorrelation
  7. Moving Average Representation of Time Series
  8. Autoregressive Representation of Time Series

UNIT 3. Stationary Processes

  1. First-Order Autoregressive Process
  2. Second-Order Autoregressive Process
  3. The General AR(p) Process
  4. First-Order Moving Average Process
  5. Second-Order Moving Average Process
  6. The General MA(q) Process
  7. Autoregressive Moving Average ARMA(p, q) Process
  8. The ARMA(1,1) Process

UNIT 4. Nonstationary and Seasonal Time Series Models

  1. Nonstationarity in the Mean
  2. Stochastic Trend Models and Differencing
  3. Autoregressive Integrated Moving Average ARIMA(p, d, q) Model
  4. Nonstationarity in the Variance and Autocovariance
  5. Seasonal ARIMA Models

UNIT 5. Forecasting

  1. Minimum Mean Square Error Forecast
  2. ARIMA Forecast as Weighted Average of Past Observations
  3. Computation of Forecasts

UNIT 6. Building ARIMA Models

  1. Steps in Model Building
  2. Unit Root Tests
  3. Information Criterion
  4. Validation Techniques
  5. Example: Air Passengers Data

UNIT 7. Advance Methods in Time Series Analysis

  1. Transfer Function Model
  2. Bootstrapping and Bagging
  3. Random Forest for Time Series