tidsseriestudier

Tidsseriestudier, or time series analysis, is a field of statistics and econometrics focused on data observed sequentially in time. The goal is to describe temporal dynamics, quantify dependence over time, and forecast future values. Analyses can be univariate (one series) or multivariate (several series interacting).

Core models include autoregressive (AR) and moving-average (MA) components, combined as ARMA or ARIMA when non-stationarity is present. Seasonal patterns lead to SARIMA models. In multivariate settings, vector autoregression (VAR) captures interdependencies. State-space models and Kalman filtering provide flexible frameworks for irregular or noisy data. For financial data, volatility models like GARCH may be used.

Estimation relies on maximum likelihood or Bayesian methods; model selection uses AIC/BIC and cross-validation. Diagnostics check residuals for autocorrelation (Ljung-Box) and for stationarity. Forecast evaluation uses out-of-sample tests and error metrics.

Data typically require evenly spaced observations to avoid irregular-time complications; missing data can be interpolated or modeled with state-space approaches. Applications span economics, finance, meteorology, epidemiology, engineering, and manufacturing, including forecasting, anomaly detection, and process monitoring.

Challenges include non-stationarity, structural breaks, nonlinearities, and model misspecification. Adequate data length, domain knowledge, and careful interpretation are important to avoid overfitting and misinterpretation.