Artificial Intelligence: Hidden Markov Model

A simplified model for the stock market is that it can be in one of three states: Bull Market, Bear Market, or Mild Market. Each day, the market can be observed to be Up, Down, or Unchanged. In a Bull Market, the market is Up 70% of the days, Down 10% of the days, and Unchanged on the other days. In a Bear Market, the market is down 60% of the days, Up 10% of the days, and Unchanged on the other days. In a Mild Market, the market is up 30% of the days, Down 30% of the days, and Unchanged on the other days. Show how the market can be formulated as an HMM. What is the probability of transitioning from every state to every other state? What is the probability of observing each output (Up, Down or Unchanged) in each state? a. b. Use the filtering algorithm to determine the probability of being in each state at time r after observing Up Down Down,for 1-12.3 A simplified model for the stock market is that it can be in one of three states: Bull Market, Bear Market, or Mild Market. Each day, the market can be observed to be Up, Down, or Unchanged. In a Bull Market, the market is Up 70% of the days, Down 10% of the days, and Unchanged on the other days. In a Bear Market, the market is down 60% of the days, Up 10% of the days, and Unchanged on the other days. In a Mild Market, the market is up 30% of the days, Down 30% of the days, and Unchanged on the other days. Show how the market can be formulated as an HMM. What is the probability of transitioning from every state to every other state? What is the probability of observing each output (Up, Down or Unchanged) in each state? a. b. Use the filtering algorithm to determine the probability of being in each state at time r after observing Up Down Down,for 1-12.3