Time Series Analysis

Time series analysis studies data points collected over time to identify trends and predict future values. It’s widely used in data science for forecasting. This article covers components, models, an example, and applications.

Key Components

• Trend: Long-term direction (e.g., \( y_t = \beta t \)).
• Seasonality: Repeating patterns (e.g., sales spikes in December).
• Noise: Random fluctuations (\( \epsilon_t \)).

Decomposed as \( y_t = T_t + S_t + \epsilon_t \).

Forecasting Models

• Moving Average: Smooths data, \( \hat{y}_t = \frac{1}{k} \sum_{i=t-k}^{t-1} y_i \).
• ARIMA: Combines autoregression, differencing, and moving average.

Predicts based on past patterns.

Example Analysis

Data: Monthly sales {Jan: 100, Feb: 110, Mar: 130}:

• Trend: Upward, ~10/month.
• MA (2 periods): Feb = 105, Mar = 120.
• Forecast Apr: ~140.

Simple trend-based prediction.

Applications

Used in:

• Finance: Stock price forecasting.
• Weather: Temperature predictions.
• Retail: Inventory planning.

Drives temporal insights.