# Introduction to Dynamic Linear Models for Time Series Analysis

## TL;DR

Dynamic linear models (DLM) provide a flexible, hierarchical framework for analyzing diverse time series data, accommodating non-stationarity, missing data, and varying observation accuracy, with efficient estimation methods.

## Contribution

This paper introduces the DLM framework, demonstrating its ability to unify classical models and handle complex real-world time series analysis tasks.

## Key findings

- DLM can model non-stationary processes effectively.
- Efficient estimation via Kalman and MCMC methods is feasible.
- DLM accommodates missing data and irregular sampling.

## Abstract

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be seen as general regression models where the coefficients can vary in time. In addition, they allow for a state space representation and a formulation as hierarchical statistical models, which in turn is the key for efficient estimation by Kalman formulas and by Markov chain Monte Carlo (MCMC) methods. A dynamic linear model can handle non-stationary processes, missing values and non-uniform sampling as well as observations with varying accuracies. This chapter gives an introduction to DLM and shows how to build various useful models for analysing trends and other sources of variability in geodetic time series.