Fundamentals of Time Series

This section introduces the core principles of working with chronological data in Python. It covers how trends, seasonality, cycles, and random components interact and shows how to index, plot, and subset time-series data. Learners see how decomposition separates a series into interpretable parts (trend, seasonality, irregular), and discover the importance of stationarity—using differencing, autocorrelation plots, and tests like Dickey-Fuller to confirm whether the data is ready for reliable forecasting.

INTRODUCTION TO TIME SERIES ANALYSIS

Learning Objectives

• Define what a time series is and explain its distinguishing features

• Identify and describe the main components (trend, seasonality, cyclic, irregular)

• Understand basic operations in Python for creating, plotting, and subsetting time-series objects

• Recognize differences between regular and irregular time series

Indicative Content

• Definition and Nature of Time Series

  • Chronologically ordered data, examples (annual, monthly, daily)

• Components of Time Series

  • Trend, seasonality, cyclic fluctuations, irregular variation

• Time Series in Python

  • Creating date-based indices

  • Visualizing data over time

  • Subsetting time-based slices

• Irregular Time Series

  • Handling and resampling data that isn’t uniformly spaced

TIME SERIES DECOMPOSITION

Learning Objectives

• Differentiate between additive and multiplicative models

• Apply moving averages to smooth time series data

• Decompose a time series into trend, seasonal, and residual components

• Perform and interpret seasonal adjustments

Indicative Content

• Additive vs. Multiplicative Models

  • \(Y_t = T_t + S_t + R_t\) vs. \(Y_t = T_t \times S_t \times R_t\)

• Moving Averages

  • Filtering out short-term noise

  • Choosing period length (monthly, quarterly, etc.)

• Classical Decomposition

  • Trend, seasonal indices, and irregular components

• Seasonal Adjustment

  • Removing seasonal effects to reveal the underlying trend

STATIONARITY OF TIME SERIES (PART 1 & PART 2)

Learning Objectives

• Define stationarity and explain its role in time series forecasting

• Recognize non-stationary patterns and understand unit roots

• Use differencing and de-trending to stabilize mean and variance

• Validate stationarity with ACF/PACF plots and the Dickey-Fuller test

Indicative Content

• Stationary vs. Non-Stationary Processes

  • White noise vs. random walk, constant mean/variance

• Importance of Stationarity

  • Avoiding spurious regression

  • Reliable forecasting models

• Identification Methods

  • Visual checks for trend/drift

  • Slow decay in ACF as a sign of non-stationarity

• Differencing & De-trending

  • Stabilizing the series (first-order, second-order)

• Dickey-Fuller Test

  • Hypothesis of unit root, interpreting p-values

• Partial Autocorrelation (PACF)

  • Understanding AR processes and clarifying model orders

TOOLS AND METHODOLOGIES (FUNDAMENTALS)

• Basic Python Data Handling

  • Data manipulation libraries (e.g., pandas) for date/time indexing

  • Plotting time-series data over intervals

• Decomposition & Stationarity

  • Moving averages for smoothing

  • Separating trend, seasonality, and residual

  • Autocorrelation-based checks (ACF/PACF)

  • Dickey-Fuller tests for detecting unit roots

• Key Concepts

  • Additive vs. multiplicative decomposition

  • Differencing for stationarity

  • Why stationarity is crucial for accurate forecasting