What Is Markov Analysis?
Markov analysis is a method used to forecast the value of a variable whose predicted value is influenced only by its current state, not by any prior activity. In essence, it predicts a random variable based solely upon the current circumstances surrounding the variable.
The technique is named after Russian mathematician Andrei Andreyevich Markov, who pioneered the study of stochastic processes, which are processes that involve the operation of chance. He first used this method to predict the movements of gas particles trapped in a container. Markov analysis is often used for predicting behaviors and decisions within large groups of people.
- Markov analysis is a method used to forecast the value of a variable whose predicted value is influenced only by its current state, not by any prior activity.
- The primary advantages of Markov analysis are simplicity and out-of-sample forecasting accuracy.
- Markov analysis is not very useful for explaining events, and it cannot be the true model of the underlying situation in most cases.
- Markov analysis is useful for financial speculators, especially momentum investors.
Understanding Markov Analysis
The Markov analysis process involves defining the likelihood of a future action given the current state of a variable. Once the probabilities of future actions at each state are determined, a decision tree can be drawn. Then, the likelihood of a result can be calculated, given the current state of a variable. Markov analysis has several applications in the business world. It is often used to predict the number of defective pieces that will come off an assembly line, given the operating status of the machines on the line.
It can also be used to predict the proportion of a company's accounts receivable that will become bad debts. Some stock price and option price forecasting methods also incorporate Markov analysis. Lastly, companies often use it to forecast future brand loyalty of current customers and the outcome of these consumer decisions on a company's market share.
Advantages of Markov Analysis
The primary benefits of Markov analysis are simplicity and out-of-sample forecasting accuracy. Simple models, such as those used for Markov analysis, are often better at making predictions than more complicated models. This result is well-known in econometrics.
Disadvantages of Markov Analysis
Markov analysis is not very useful for explaining events, and it cannot be the true model of the underlying situation in most cases. Yes, it is relatively easy to estimate conditional probabilities based on the current state. However, that often tells one little about why something happened.
In engineering, it is quite clear that knowing the probability that a machine will break down does not explain why it broke down. More importantly, a machine does not really break down based on a probability that is a function of whether or not it broke down today. In reality, a machine might break down because its gears need to be lubricated more frequently.
In finance, Markov analysis faces the same limitations that it has in engineering, but fixing problems is complicated by our relative lack of knowledge about financial markets. Markov analysis is much more useful for estimating the portion of debts that will default than it is for screening out bad credit risks in the first place.
Markov analysis is a valuable tool for making predictions, but it does not provide explanations.
An Example of Markov Analysis
Markov analysis can be used by stock speculators. Suppose that a momentum investor estimates that a favorite stock has a 60% chance of beating the market tomorrow if it does so today. This estimate involves only the current state, so it meets the key limit of Markov analysis. Markov analysis also allows the speculator to estimate that the probability the stock will outperform the market for both of the next two days is 0.6 * 0.6 = 0.36 or 36%, given the stock beat the market today. By using leverage and pyramiding, speculators attempt to amplify the potential profits from this type of Markov analysis.