-
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.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
CS2B Sept 2020 Q1ix
- Thread starter Laura
- Start date
Hello
In Section 2.3 of Chapter 14, the asymptotic results are given for the estimators of autocorrelations of an MA(q) process for lags larger than q. Here we have an MA(1) process and so this result holds for the estimator of rho_2 as 2 > q = 1.
For the AR(1) model, we have to use the fact that the estimator is consistent meaning that the asymptotic mean is given by the true value (ie we just need to work out the lag 2 autocorrelation).
Hope this helps!
Andy
In Section 2.3 of Chapter 14, the asymptotic results are given for the estimators of autocorrelations of an MA(q) process for lags larger than q. Here we have an MA(1) process and so this result holds for the estimator of rho_2 as 2 > q = 1.
For the AR(1) model, we have to use the fact that the estimator is consistent meaning that the asymptotic mean is given by the true value (ie we just need to work out the lag 2 autocorrelation).
Hope this helps!
Andy
Thanks Andy!Hello
In Section 2.3 of Chapter 14, the asymptotic results are given for the estimators of autocorrelations of an MA(q) process for lags larger than q. Here we have an MA(1) process and so this result holds for the estimator of rho_2 as 2 > q = 1.
For the AR(1) model, we have to use the fact that the estimator is consistent meaning that the asymptotic mean is given by the true value (ie we just need to work out the lag 2 autocorrelation).
Hope this helps!
Andy
I understand the variance portion now.
However, not too sure about the theoretical mean for both the AR and MA process. Where can I find the formula for the theoretical mean for these processes in the course notes?
Thanks!
Great! For the MA process we can again use the asymptotic result, which states the asymptotic mean is 0.
For the AR process we use the fact that the estimator is consistent, meaning the asymptotic mean is given by the true value, here \( \rho_2 \). We can work this out in R using the ARMAacf function. From a paper A perspective, calculation of \( \gamma_k \) and \( \rho_k \) for an AR(1) process are covered in Section 3 of Chapter 13.
Hope this helps
Andy
For the AR process we use the fact that the estimator is consistent, meaning the asymptotic mean is given by the true value, here \( \rho_2 \). We can work this out in R using the ARMAacf function. From a paper A perspective, calculation of \( \gamma_k \) and \( \rho_k \) for an AR(1) process are covered in Section 3 of Chapter 13.
Hope this helps
Andy
Priyanka Malhotra
Active Member
Hi Andy, Could you please help me understand the explanation for mean and variance of AR process, I am not able to understand why have we considered "asymptotic mean is given by the true value" and variance of AR process is not given in examiners report.
Thanks in advance!
Thanks in advance!
Hi Priyanka
Rho^~(2) is a consistent estimator, which means that the asymptotic mean of the estimator is the true value, rho(2). There is no general result presented in the Core Reading for the asymptotic distribution of rho^~(k) for an AR process, hence why the variance is not mentioned.
Hope this helps!
Andy
Rho^~(2) is a consistent estimator, which means that the asymptotic mean of the estimator is the true value, rho(2). There is no general result presented in the Core Reading for the asymptotic distribution of rho^~(k) for an AR process, hence why the variance is not mentioned.
Hope this helps!
Andy
Priyanka Malhotra
Active Member
Hi, thank you so much! could you please point the section in core reading which states this about AR process?
Hi Priyanka
Are you referring to the result about the estimators being consistent? I don't believe that is explicitly mentioned in the Core Reading, at least I can't find it. It is something we mention in our notes at the bottom of page 20 in Chapter 14 (2022 version).
Andy
Are you referring to the result about the estimators being consistent? I don't believe that is explicitly mentioned in the Core Reading, at least I can't find it. It is something we mention in our notes at the bottom of page 20 in Chapter 14 (2022 version).
Andy