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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

Autocorrelation and Model Identification

After addressing time series components and stationarity, the focus shifts to understanding the internal correlation structure of the data. How does a value at time $t$ relate to values at previous times like $t-1$ , $t-2$ , and so on? Answering this is essential for selecting appropriate forecasting models.

This chapter introduces the primary tools for analyzing this temporal dependence:

Autocorrelation Function (ACF): Learn how it measures the correlation between a time series and its lagged versions.
Partial Autocorrelation Function (PACF): Understand how it measures the correlation between a time series and a lagged version after removing the influence of intermediate lags.
Plotting and Interpretation: See how to generate ACF and PACF plots using Python libraries and learn standard patterns that suggest specific model types (like AR or MA models).

By the end of this chapter, you will be able to compute and interpret ACF and PACF plots to help identify potential candidate models for your stationary time series data.

Sections

3.1 Autocorrelation Function (ACF)
3.2 Partial Autocorrelation Function (PACF)
3.3 Plotting ACF and PACF in Python
3.4 Interpreting ACF/PACF for Model Selection
3.5 Hands-on Practice: ACF/PACF Plotting and Interpretation

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