I have a sequential data from time
T6. The rows contain the sequence of states for 50 customers. There are only 3 states in my data. For example, it looks like this:
T1 T2 T3 T4 T5 T6 Cust1 C B C A A C
My transition matrix
X looks like this:
A B C A 0.3 0.6 0.1 B 0.5 0.2 0.3 C 0.7 0.1 0.2
Now, we see that at time
T6 the state is at
C which corresponds to
c=[0 0 1] vector.
I am now predicting
T7 by doing the matrix multiplication:
c * X which gives me
[0.7 0.1 0.2]. Based on this, I decide that the state at
T7 would be
A (highest prob. value).
T8, I use the result of the probability vector I got above and do
[0.7 0.1 0.2]*X = [0.4 0.44 0.14] and decide that the state is
My question is: Am I doing something wrong? Am I contradicting the memoryless property of the Markov Chains?