In Our Last Chapter, We have discussed about Stochastic Modeling in Stock Market.
The Markov Model is a type of stochastic model, while the Markov Chain represents a stochastic process.
A Markov Model is a statistical model used to predict a sequence of unknown variables based on the Markov property. It’s an extension of the concept of Markov Chains to more complex scenarios.
State Space (S): The set of all possible states which represent possible conditions or positions a system can be in.
Markov Models are diverse and adaptable, suitable for various scenarios and data types. Here, we focus on four of the most commonly used models, each distinct in its approach and application.
Although these are the msot common variations, Here are some additional types:
These models and chains are foundational to understanding many processes and systems in fields ranging from computer science to finance to biology. They provide a mathematical framework for dealing with stochastic processes and making predictions in the face of uncertainty
In a Hidden Markov Model (HMM), there’s an additional feature called emission probabilities.
Unlike a basic Markov Model or Markov Chain where states are observable, in HMMs, the states are hidden or unobservable. However, each hidden state emits an observable symbol (or output) with a certain probability.
Emission probabilities define the likelihood of each hidden state producing a particular observable symbol.
For example, consider a simplified weather model where the actual weather (sunny, rainy) is hidden, but you can observe people carrying umbrellas or not.
The emission probabilities might define the likelihood of observing someone with an umbrella given it’s rainy or sunny.
The power of Markov models lies in their simplicity and the analytical approach they offer. By focusing on current states and their probable transitions, they provide a framework for understanding complex systems without the need for extensive historical data analysis.