trenddetection

Trenddetection is the process of identifying and characterizing sustained movements in a data series over time, separating genuine directional changes from random fluctuations, seasonality, and noise. It can be applied to univariate series or multivariate data where common trends may exist.

Methods used for trend detection range from statistical tests to modeling approaches. Statistical tests for trend include Mann-Kendall, Spearman’s rho, and seasonal variants. Trend estimation often uses linear regression or robust estimators like Theil-Sen. Smoothing approaches such as moving averages or exponential smoothing help reveal underlying trends. Time-series decomposition (STL) separates trend, seasonal, and residual components. Change point detection methods (CUSUM, Pettitt test, Bayesian) identify abrupt shifts in level or trend. State-space models and Kalman filters provide time-varying trend estimation. In multivariate contexts, cointegration and common-trend extraction identify shared movements. Modeling frameworks include ARIMA with trend terms, exponential smoothing state space (ETS) models, and regression with autoregressive errors. Machine learning methods include neural networks (LSTM, RNN) for nonlinear trends and ensemble methods for trend signals.

Applications of trend detection span finance (price or return trends), economics, climatology and environmental monitoring, epidemiology, marketing and social media analytics, and industrial sensing.

Evaluation and challenges involve data quality, stationarity, and proper handling of seasonality. Risks include overfitting, non-stationarity, structural breaks, and data snooping. Validation uses out-of-sample testing, time-series cross-validation, and backtesting. See also time series analysis, change point detection, trend estimation, and forecast evaluation.