• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

weakly stationary purely indeterministic process

N

nageshmcl

Member
Hi,

I didn't understand this concept even by looking at the given examples Q12.4.
Can anyone help me in step by step? Thanks in advance.

Regards,
Nageswar.
 
My response is just the broad strokes.

There are two conditions to be met. We therefore prove/disprove weak stationarity by seeing if these conditions are met.

1. The expectation is constant.(E(Xt) = constant)

This is normally proved by showing that the expectation does not depend on t. It may be an expression but it must be the same for all Xt.

2. The covariance of Xt and Xs must depend on t-s (the lag) only. This part is normally a bit tricky for time series since the Xt might be defined including Xs. Practice eventually gives u a hang of whats happening.

Incidentally I used another textbook for this part to get the basics in place. That part of the acted might be a bit daunting because of the trig functions that they use but they are just doing the above. Indeed this is quite mathematical so get dirty and master the manipulations!!

All the best.
 
Hi,

Thanks for your response. I am unable to catch the timeseries concepts with the given explanation in the material. Can you please give the name of the book to get the fundas on this. And please explain this concept with the egs given in Question 12.4.

Given Yt be a sequence of iid ~ N(0,1), Which of the following are stationary time series?

(i) Xt = sin(wt+U), where U ~ U[0,2Pie]
(ii) Xt = sin(wt+Yt)
How (i) is not purely indeterministic and how it differs from (ii)
(iv) Xt= Yt-1 + Yt - How it is purely indeterministic?

Thanks & Regards,
Nageswar.
 
(iv) Response

Ok Forgive my notation lapses.

iv) A time series is purely indeterministic if the information u have at a certain time becomes increasingly useless in helping u determine the value of the time series at a later time as the time increases since u got the info.

In this case Xt is defined by Yt and Yt-1 ie info at this step and the one before. All other info before that doesn't matter since the Yts are independent. In other words the info u have now at time t won't help u at time t+2 since Xt+2 depends on Yt+2 and Yt+1, info u don't have now since the Yts are independent.
 
(i) and (ii)

Though these expessions look similar they are not at all.

For (i) Xt = sin(wt +U) at t = 0 Xo = sin(U) (U being a constant) therefore this means that if we know the info at the first instance any future Xt can be known. This makes the function deterministic.

For (ii) Xt = sin(wt + Yt) at no time can info of a certain Xt help u with any other Xt since the Yts are independant. They r therefore purely indeterministic.
 
You must log in or register to reply here.
Back
Top