CT6 Ch12 Markov purely indeterministic

[Bharti Singla]

Hii all
What is the difference between a 'purely indeterministic process' and a process posesses 'markov property' in time series?
On the top of page8 of this chapter, it is written that 'when we talk of a "stationary time series process", we shall mean a weakly stationary purely indeterministic process'. And purely indeterministic process is if the value of X1,......,Xn is less useful to predict the value of XN as N→∞. But we actually use some past data in time series to predict future values. So, how can be every stationary series is purely indeterministic?
And how it is different from Markov property?
Please anyone clarify.
Thanks

 

[John Lee]

If it has a white noise term then it will be purely indeterministic as white noise is random and therefore unpredictable - so the further you go into the future the more new white noise terms are added and so the weaker the deterministic part is.

Markov means that the formula only depends on the last value of Xt.

So:

\(X_t = 0.8X_{t-1} + e_t\) is Markov and purely indeterministic

markov since Xt only depends on the previous X and indeterministic as it has a white noise term.

 

[Bharti Singla]

Okay,thankyou sir.