In [3]:

    

#this is where we do markov chain exercises

#we need a way to draw from discrete distributions so we do this

using QuantEcon

#just a qucik test
psi = [0.1, 0.9]
d = DiscreteRV(psi)
rand(d,5)


    

    
Out[3]:





5-element Array{Int64,1}:
 1
 2
 2
 1
 1

In [10]:

    

function mc_sample_path(P; init=1, sample_size=1000)
    #P is our stochastic matrix. Our initial state is init, our sample_size i
    #is the number of time steps the chain should run
    X = Array{Int64}(sample_size) # we allocate our array
    X[1] = init # our initial state. 
    #X is the array of all our states
    
    #we convert our P into a distibution for each row
    n = size(P)[1]
    P_dist = [DiscreteRV(vec(P[i,:])) for i in 1:n]
    
    #we now generate the sample path
    for t in 1:(sample_size-1)
        X[t+1]= rand(P_dist[X[t]])
    end
    return X
end
#so we've got to figure out how this works in the small scale ideally.
#it's mostly the matrix operations which I don't get atm... argh
# at least it doesn't have to be vectorised so differential equatiosn and MCs
# work out okay which is good! so we can do loops and simulatoins efficiently
# which is it's main advantageover python tbh


    

    




WARNING: Method definition mc_sample_path(Any) in module Main at In[8]:4 overwritten at In[10]:4.
WARNING: Method definition #mc_sample_path(Array{Any, 1}, Main.#mc_sample_path, Any) in module Main overwritten.






    
Out[10]:





mc_sample_path (generic function with 3 methods)

In [14]:

    

#we now try it out on a simple matrix

P = [0.4 0.6; 0.2 0.8]
X = mc_sample_path(P, sample_size = 10);
print("done")
println(X)


    

    




done[1,1,2,2,2,1,2,2,2,2]

In [16]:

    

#we now simulate fora long time to see the chain and get the mean
Y =mc_sample_path(P, sample_size=100000)
println(mean(X .==1))


    

    




0.3

In [17]:

    

# we can lso use quant econ directly to handle our markov chain
# whic hprobably has the same rough function, but vastly better as it's a library
# functoin which makes sense adn is cool

mc = MarkovChain(P)
X = simulate(mc, 100000)
mean(X .==1)


    

    
Out[17]:




0.25024

In [ ]: