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Time Series Analysis and Forecasting

Chapter 1: Introduction to Time Series Data

Characteristics of Time Series Data

Components: Trend, Seasonality, Cyclical, Irregular

Loading and Handling Time Series in Pandas

Time Shifting, Lagging, and Rolling Windows

Visualizing Time Series Data

Hands-on Practice: Loading and Plotting Data

Chapter 2: Time Series Decomposition and Stationarity

Understanding Stationarity

Methods for Time Series Decomposition

Implementing Decomposition in Python

Testing for Stationarity: Visual Inspection

Statistical Tests for Stationarity (ADF Test)

Achieving Stationarity: Differencing

Hands-on Practice: Decomposition and Stationarity Tests

Chapter 3: Autocorrelation and Model Identification

Autocorrelation Function (ACF)

Partial Autocorrelation Function (PACF)

Plotting ACF and PACF in Python

Interpreting ACF/PACF for Model Selection

Hands-on Practice: ACF/PACF Plotting and Interpretation

Chapter 4: ARIMA Models for Forecasting

Autoregressive (AR) Models

Moving Average (MA) Models

Combining AR and MA: ARMA Models

Introducing Integration: ARIMA Models

Selecting ARIMA Order (p, d, q)

Fitting ARIMA Models in Python (statsmodels)

Model Diagnostics and Residual Analysis

Forecasting with ARIMA Models

Hands-on Practice: Building an ARIMA Model

Chapter 5: Handling Seasonality with SARIMA

Limitations of ARIMA with Seasonal Data

Introduction to Seasonal ARIMA (SARIMA)

Identifying Seasonal Components (ACF/PACF)

Selecting SARIMA Order (p, d, q)(P, D, Q)m

Fitting SARIMA Models in Python

Diagnosing SARIMA Models

Forecasting with SARIMA

Hands-on Practice: Building a SARIMA Model

Chapter 6: Model Evaluation and Selection

Need for Model Evaluation

Train-Test Split for Time Series

Common Evaluation Metrics (MAE, MSE, RMSE, MAPE)

Information Criteria (AIC, BIC)

Comparing Forecasts from Different Models

Visualizing Forecast Performance

Hands-on Practice: Evaluating Forecasts

Introduction to Time Series Data

Time series data, sequences of observations ordered by time, appears frequently in various domains, from finance and economics to weather patterns and sensor readings. Unlike standard cross-sectional data, the temporal ordering is a key feature, meaning observations $y_t$ are often dependent on previous values such as $y_{t-1}$ .

This chapter introduces the foundational concepts needed to work with this type of data. We will cover:

Identifying the unique characteristics and components like trend and seasonality often present in time series.
Using the Pandas library in Python to effectively load, handle, and manipulate time-indexed data.
Techniques such as time shifting, calculating lags, and applying rolling window operations.
Basic methods for visualizing time series data to gain initial insights into its structure.

By the end of this chapter, you will be equipped with the basic tools to start exploring and preparing time series datasets for analysis.

Sections

1.1 Characteristics of Time Series Data
1.2 Components: Trend, Seasonality, Cyclical, Irregular
1.3 Loading and Handling Time Series in Pandas
1.4 Time Shifting, Lagging, and Rolling Windows
1.5 Visualizing Time Series Data
1.6 Hands-on Practice: Loading and Plotting Data

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