Calculation of the transition probability matrix for a descrete markov process from an unbalanced panel data.
Used in the marksim package.
Let's assume you have observations of 10 firms and their profits for the last 10 years. Let's also assume that some observations are missing.
>>> import numpy as np
>>> data = list()
>>> for i in range(10): # generate unbalanced panel
... a = np.array(list(map(lambda x: float(x), range(10))))
... a[np.random.randint(0, len(a), size=int(len(a)*0.2))] = np.NaN
... np.random.shuffle(a)
... data.append(a)
>>> array = np.array(data).T
>>> print(array) # randomly shuffled unbalanced panel
[[nan 0. 1. 5. 9. 5. nan 8. 0. 4.]
[ 5. nan 8. 9. 8. 0. 7. 9. 8. 0.]
[ 8. 4. 9. 8. nan 3. 3. 1. 3. 1.]
[ 9. 7. 7. nan 6. 8. 9. nan nan nan]
[nan 2. nan nan 1. 4. 4. 3. nan 6.]
[ 4. 5. 4. 7. 3. 9. 8. 5. 9. 7.]
[ 6. 8. 6. 1. 4. nan 5. 4. 1. 3.]
[ 3. 3. 0. 4. nan 1. 6. 7. 7. 8.]
[ 7. 6. 3. 3. 5. 2. 2. 6. 4. nan]
[ 1. 9. nan 6. 7. 7. nan nan 6. 9.]]
>>> print(array.shape)
(10, 10)The array above represents an unbalanced panel data where for the first firm:
- in the first year we have no data
- in the second year it's profits were 0
- in the second year 1
- etc...
Now let's assume we would like to allocate the profits in each year into 5 bins (think of percentiles when number of bins is 100) and calculate transition probabilities from the observed data.
With the help of this script, we could do the following:
>>> import TPM
>>> tpm = TPM.calculate_tpm(array, n_states=5)
>>> tpm
[[0.14285714 0.42857143 0.28571429 0. 0.14285714]
[0.46153846 0.15384615 0.15384615 0. 0.23076923]
[0.14285714 0.28571429 0.28571429 0.21428571 0.07142857]
[0.25 0.25 0.25 0. 0.25 ]
[0. 0. 0.16666667 0.83333333 0. ]]
>>> print(tpm.shape)
(5, 5)
Each entry in the above matrix is a frequency with which firms jumped from one state to the other.
Note, that TPM here stands simply for a class name under which all functions are collected.
- calculation for the first order markov process
- calculation for the higher order markov processes
- parallelization and vectorization. Some parts in code are written in for loops.
If you are interested in markov processes, here is a relatively old but good overview of python packages. Additionally, discreteMarkovChain looks like an advanced package.
- Vladimir Korzinov - Initial work - vvkorz
MIT License - see the LICENSE.md file for details