Course Structure

In this course, we’ll explore the fundamental concepts of univariate time series analysis using Python. Throughout the course, we’ll cover the following topics:

The basics of time series

We’ll start by introducing the basics of time series analysis. We’ll learn about stochastic processes, which are mathematical models that describe the evolution of a system over time. We’ll explore concepts such as recurrence, which refers to the repetition of patterns in a time series. Understanding stationarity is crucial, as it allows us to make assumptions about the behavior of the data over time. Then, we’ll discuss white noise, a fundamental concept in time series analysis, and random walks, which are stochastic processes often used to model stock prices.

Exploring data

Once we have grasped the foundations, we’ll dive into the crucial task of exploring time series data. Exploratory data analysis is an essential step in understanding the characteristics and properties of a time series. We will learn about the moments of a time series, which describe its statistical properties such as mean, variance, skewness, and kurtosis. We’ll explore various visualization techniques, including density plots, histograms, and Q-Q plots, which allow us to assess the distributional properties of the data. Additionally, we’ll discuss how to perform normality tests to check if the data follows a specific distribution.

The properties of time series

Next, we will delve into the unique properties of time series data. Unlike cross-sectional or panel data, time series data exhibits specific characteristics that require special attention. We will explore the concept of integration, which measures the degree of differencing required to make a time series stationary. To identify the presence of integration, we will explore tests such as the Dickey-Fuller test and others. Autocorrelation, another key concept, measures the relationship between observations at different time points. We will also examine trends, seasons, and cycles, which are fundamental components of many time series.

ARIMA models

Moving forward, we’ll delve into Autoregressive Integrated Moving Average (ARIMA) models, one of the most widely used approaches in time series modeling. We’ll start by examining moving average and autoregressive models individually, which serve as building blocks for more advanced models. We’ll then combine these concepts to form ARMA and ARIMA models. The seasonal ARIMA (SARIMA) model will help us handle seasonal patterns in the data.

On prediction

Prediction is a significant aspect of time series analysis. In this category, we will discuss how to make accurate forecasts. We’ll learn about different prediction loss functions and evaluation metrics to assess the performance of our models. We’ll then explore concepts such as point forecasts, which provide the expected value of future observations. Finally, we’ll talk about confidence intervals, which quantify the uncertainty associated with those forecasts.

Choosing, fitting, and evaluating models

In this final category, we’ll go through the process of choosing, fitting, and evaluating time series models. Model selection plays a crucial role in obtaining accurate predictions. We’ll discuss various tools that help us choose the optimal ARIMA model for our data. We’ll learn about goodness-of-fit measures and diagnostic checks to assess the adequacy of the chosen model. Moreover, we’ll also cover techniques for splitting time series data into training and testing sets, enabling us to perform out-of-sample forecasting and evaluate the performance of our models on unseen data.