The Temporal Markov Transition Field

Researcher Michael Leznik has introduced the Temporal Markov Transition Field (TMTF), a significant upgrade to a decade-old method for preparing time series data for AI analysis. The original Markov Transition Field (MTF), created by Wang and Oates in 2015, efficiently encodes a time series as a two-dimensional image by mapping transition probabilities between quantile states. However, it uses a single, global transition matrix, which averages all dynamics. This fails catastrophically for non-stationary processes—data where the underlying patterns change over time, like a stock market shifting from a bull to a bear regime. The MTF loses all information about *when* these changes happen, producing a misleading image.

Leznik's TMTF solves this by partitioning the time series into K contiguous chunks and estimating a separate, local transition matrix for each segment. The resulting T x T image contains K horizontal bands of distinct texture, each encoding the dynamics (like persistence, mean reversion, or trending) of its specific time period. This amplitude-agnostic, order-preserving representation is tailor-made as an input channel for convolutional neural networks (CNNs), allowing them to visually identify not just what patterns exist, but crucially, their temporal sequence. The paper formally defines the method, analyzes its bias-variance trade-off, and provides a concrete numerical example showing its superiority for characterizing complex, evolving time series data common in finance, IoT, and climate science.