medium · Quantitative Finance prob-stats
An analyst models the movement of a stock between three regimes: 1 (Growth), 2 (Stagnation), and 3 (Crisis). Regime 3 is absorbing. The transition matrix for the transient regimes is Q = beginpmatrix 0.5 & 0.4 0.1 & 0.8 endpmatrix.
If the fundamental matrix is N = (I - Q)^-1, what is the interpretation of the sum of the entries in the first row of N?
- The expected total time spent in all transient states before absorption, given the process starts in regime 1.
- The long-run share of time the process spends within regime 1 before its first transition into crisis.
- The expected number of direct transitions observed between the Growth and Stagnation states before absorption occurs.
- The probability that the process eventually reaches the absorbing crisis regime 3, given that it starts out in regime 1.
Sign up free to see the explanation and track your rank →
More Quantitative Finance prob-stats practice
- What is the estimated OLS slope hatβ?
- Assuming 252 trading days in a year, what is the annualized historical volatility?
- If the correlation between two assets is ρ = 0.6, what is the R^2 of a linear regression o
- If the slope β is positive, what is the correlation coefficient ρ between x and y?
- What is the defining property of the 'Cumulative Distribution Function' F(x)?
- Which 'standardized moment' should they measure to quantify this?
- What is the probability the stock outperforms given the signal fired?
- Which statistical property describes a time series where the mean, variance, and autocorre