The simplest Markov model is the [[Markov chain]]. It models the state of a system with a [[random variable]] that changes through time.<ref name=":0" /> In this context, the Markov property suggests that the distribution for this variable depends only on the distribution of a previous state. An example use of a Markov chain is [[Markov chain Monte Carlo|Markov chain Monte Carlo]], which uses the Markov property to prove that a particular method for performing a [[random walk]] will sample from the [[joint distribution]].
==Hidden Markov model==
Line 57:
==Markov-chain forecasting models==
Markov-chains have been used as a forecasting methods for several topics, for example price trends<ref name="SLS">{{cite journal |first1=E.G. |last1=de Souza e Silva |first2=L.F.L. |last2=Legey |first3=E.A. |last3=de Souza e Silva |url=https://www.sciencedirect.com/science/article/pii/S0140988310001271 |title=Forecasting oil price trends using wavelets and hidden Markov models |journal=Energy Economics |volume=32 |year=2010}}</ref>, wind power<ref name="CGLT">{{cite journal |first1=A |last1=Carpinone |first2=M |last2=Giorgio |first3=R. |last3=Langella |first4=A. |last4=Testa |url=https://www.sciencedirect.com/science/article/pii/S0378779614004714 |title=Markov chain modeling for very-short-term wind power forecasting |journal=Electric Power Systems Research |volume=122 |year=2015}}</ref> and solar irradiance<ref name="MMW">{{cite journal |first1=J. |last1=Munkhammar |first2=D.W. |last2=van der Meer |first3=J. |last3=Widén |url=https://www.sciencedirect.com/science/article/pii/S0038092X19303469 |title=Probabilistic forecasting of high-resolution clear-sky index time-series using a Markov-chain mixture distribution model |journal= Solar Energy |volume=184 |year=2019}}</ref>. The Markov-chain forecasting models utilize a variety of different settings, from discretizing the time-series<ref name="CGLT" /> to hidden Markov-models combined with wavelets<ref name="SLS" /> and the Markov-chain mixture distribution model (MCM)<ref name="MMW" />.
