Random Walk models are another familiar example of a Markov Model. The model is said to possess the Markov Property and is "memoryless". A Markov Model is a stochastic state space model involving random transitions between states where the probability of the jump is only dependent upon the current state, rather than any of the previous states. Prior to the discussion on Hidden Markov Models it is necessary to consider the broader concept of a Markov Model. This will be used to assess how algorithmic trading performance varies with and without regime detection. These detection overlays will then be added to a set of quantitative trading strategies via a "risk manager". In subsequent articles the HMM will be applied to various assets to detect regimes. Specific algorithms such as the Forward Algorithm and Viterbi Algorithm that carry out these tasks will not be presented as the focus of the discussion rests firmly in applications of HMM to quant finance, rather than algorithm derivation. The discussion will then focus specifically on the architecture of HMM as an autonomous process, with partially observable information.Īs with previous discussions on other state space models and the Kalman Filter, the inferential concepts of filtering, smoothing and prediction will be outlined. The discussion will begin by introducing the concept of a Markov Model and their associated categorisation, which depends upon the level of autonomy in the system as well as how much information about the system is observed.
#MARKOV MODELS PYTHON TUTORIAL SERIES#
This article series will discuss the mathematical theory behind Hidden Markov Models (HMM) and how they can be applied to the problem of regime detection for quantitative trading purposes. In this instance the hidden, or latent process is the underlying regime state, while the asset returns are the indirect noisy observations that are influenced by these states. These models are well suited to the task as they involve inference on "hidden" generative processes via "noisy" indirect observations correlated to these processes. The modeling task then becomes an attempt to identify when a new regime has occurred and adjust strategy deployment, risk management and position sizing criteria accordingly.Ī principal method for carrying out regime detection is to use a statistical time series technique known as a Hidden Markov Model. This motivates a need to effectively detect and categorise these regimes in order to optimally select deployments of quantitative trading strategies and optimise the parameters within them.
#MARKOV MODELS PYTHON TUTORIAL SERIAL#
In particular it can lead to dynamically-varying correlation, excess kurtosis ("fat tails"), heteroskedasticity (clustering of serial correlation) as well as skewed returns. These various regimes lead to adjustments of asset returns via shifts in their means, variances/volatilities, serial correlation and covariances, which impact the effectiveness of time series methods that rely on stationarity. Such periods are known colloquially as "market regimes" and detecting such changes is a common, albeit difficult process undertaken by quantitative market participants. A consistent challenge for quantitative traders is the frequent behaviour modification of financial markets, often abruptly, due to changing periods of government policy, regulatory environment and other macroeconomic effects.