Time Series analysis

Overview

A time series is a sequence of observations indexed by time (or by an ordered index that represents time). Time series may be univariate (one variable over time) or multivariate (multiple variables observed jointly).

Key properties that often matter in practice include sampling frequency, missingness/irregular sampling, seasonality, trends, and temporal dependence (autocorrelation).

Core Concepts

• Indexing and sampling: timestamps, frequency, time zones, and alignment across sources
• Components: trend, seasonality, cycles, residual/noise (see decomposition notes)
• Stationarity: whether the series’ distribution changes over time
• Lag/lead structure: autocorrelation, partial autocorrelation, and lag features
• Leakage: train/test splits must respect time order

Common Tasks

• Exploratory time-series analysis (structure, periodicity, regime shifts)
• Forecasting (point forecasts and prediction intervals)
• Classification (including imbalanced time-series classification)
• Anomaly detection (point/contextual/collective anomalies)
• Preprocessing: smoothing, decomposition, imputation, normalization

Practical Workflow (Checklist)

1. Define the problem: target, horizon, granularity, and acceptable latency.
2. Build the dataset: collect, align timestamps, deduplicate, and handle missing data.
3. Establish baselines: naive/seasonal naive, moving average, simple AR/ARIMA.
4. Train and evaluate: rolling or blocked evaluation; avoid feature leakage.
5. Deploy and monitor: drift, data quality checks, alerting, and retraining triggers.

Notation

• Time Series Notation

Related Notes

• Minority oversampling for imbalanced time series classification
• time series forecasting
• Multivariate Time Series
• SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion
• Multivariate Time Series Anomaly Detection
• Assessment of Accuracy Metrics for Time Series Forecasting
• Time Series Analysis vs Forecasting
• Time series ETL (Extract, Transform, Load) Decomposition
• Smoothing Techniques for time series data
• TimesFM
• Large Language Models for Time Series: A Survey
• Deep Learning for multivariate time series data Anomaly Detection
• TimeScaleDB

References

• Time Series Forecasting using Deep Learning (Amazon)