0

I have a sequential data from time `T1`

to `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).

For `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 `B`

.

My question is: Am I doing something wrong? Am I contradicting the memoryless property of the Markov Chains?