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Aug
16
comment Measuring momentum as AR(1) process
I'll try and find time to provide an answer to this in the next few days. In the meantime, you might want to edit the question to indicate you are actually talking about autocorrelation in returns, not prices (you had me very confused for a few minutes there).
Aug
13
comment Is R being replaced by Python at quant desks?
It's not far enough along in the development cycle for your needs, but keep an eye out for julia in the future. I've played around with it a bit myself and it has the potential to replace/complement both R and Python for this kind of technical work.
Aug
12
comment Negative high frequency intraday volatility - Zhou estimator
@OrvarKorvar It would be best to avoid describing the Zhou estimator as "Realized Variance". Realized Variance has a specific meaning. It is the sum of squared intraday returns, and hence non-negativity is guaranteed. The Zhou estimator is what you are actually talking about. It is the sum of squared intraday returns plus a covariance correction term. The correction term can, in finite sample, result in a negative overall estimator (as you observe in the question).
Aug
11
comment How to interpret Realized Volatility and TSRV using R
If you are happy with my response, please click the tick mark next to my answer so that the question is marked as answered. Also, feel free to upvote (the up arrow next to my answer). Cheers.
Aug
10
comment Is volatility for the next day forecastable? To any extent?
@mt_christo My PhD was (roughly) in this area :-)
Aug
10
comment Is volatility for the next day forecastable? To any extent?
@mt_christo Standardization is not based on what happened in the near future. I've updated the answer and tried to better explain the test that was performed. Let me know if you're still unsure.
Aug
10
comment Is volatility for the next day forecastable? To any extent?
I've updated my answer. Sorry, it is really long now. But as I initially said, it is a big question. Hopefully it makes for an interesting read.
Aug
10
comment Is volatility for the next day forecastable? To any extent?
This is really three separate questions (see the breakdown in my answer). I don't think the mods actually have the tools to do anything about this, but just in case they do, I've deliberately split my answer into three parts.
Aug
6
comment Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility
Wait, hang on. When you say "trade" do you mean a trade that you personally perform, or do you mean any old trade on the exchange?
Aug
6
comment Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility
Nearly there. Do you also use trade 2 on day 1 in your regression? What about trade 3 on day 1? Or is it always trade 1 on day $t$, $t = 1, ..., T$?
Aug
5
comment Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility
I'm missing something here. Are you using every trade from the day in your regression, or just the first trade? If you're only using the first trade, then how can you ever have more than on observation in your realised volatility? Even if the first trade occurs 60 minutes into the day, this means that every 5-minute return from 0 to 55 minutes will (if you're following the usual rules) be set equal to zero...
Aug
4
comment Is there a considered floor for variation the 1st principal component must explain?
A positive lower bound exists for the smallest eigenvalue of any symmetric positive definite matrix (see here). A positive lower bound for the variation explained by the first principal component immediately follows. I think the only way to reduce the floor to zero would be to take the extreme case where every column of your covariance matrix is linearly dependent, and for any practical work, this is obviously silly.
Aug
4
comment Interpreting and scaling of Realized Variance with sample data
@joesyc I've added an update to the answer to reflect the regression you describe. If you think I've answered the question satisfactorily, don't forget to upvote (click the up arrow next to my answer) and mark the question answered (click the tick mark).
Aug
4
comment Interpreting and scaling of Realized Variance with sample data
Can you please define VWAP?
Jul
31
comment FORECASTING Model AR(1) in an Autoregressive Form The Pi´s Parameters
@diogobastos for an ar1, $\alpha(L)$ and $\pi(L)$ are identical, and forecasting equation only includes one lag (as above). Sorry, on phone so not much detail in this comment.
Jul
31
comment FORECASTING Model AR(1) in an Autoregressive Form The Pi´s Parameters
Hang on, I'll turn this into an answer.
Jul
31
comment FORECASTING Model AR(1) in an Autoregressive Form The Pi´s Parameters
You haven't actually defined $\phi$ or pi in the question, so I can't really answer that question. However, you appear to be using R. So what I can tell you is that the AR1 coefficient estimated by R is the same as the $\phi$ in my previous comment. The intercept estimated by R is not the same as the $\mu$ in my comment. Specifically, R provides estimates in Normal form, which for an AR1 is $(1 - \phi L)(Y_t - c) = \epsilon_t$. So using $\mu$ as defined in my previous comment we have $\mu = c(1 - \phi)$, where $c$ is the intercept estimated output by R. ($L$ is the lag operator)
Jul
29
comment FORECASTING Model AR(1) in an Autoregressive Form The Pi´s Parameters
You state that your model is an AR(1). Therefore it has no MA component. It immediately follows that the first and third form in the linked pdf are equivalent since $\mu(L) = 1$. So if you can do the first form, you can do the third. As near as I can tell, in your description of the third form above, you are confusing the infinite order MA representation of an AR(1) for the actual AR(1). The forecasting equation for an AR(1) is just $\mathbb{E}_t Y_{t+1} = \mu + \phi Y_t$, where $\mu$ is the intercept and $\phi$ is the AR1 coefficient.
Jul
29
comment GARCH model, expectation of volatility?
@ZacharyBlumenfeld Yes, I was a little too hasty to finish my answer. Your concern is a good one. Now that I think about it, I'm also worried about some of the higher moments of $\sigma_t^2$. Existence of these moments is a non-trivial matter. I've adjusted my answer to reflect your concerns. Cheers -colin
Jul
28
comment GARCH model, expectation of volatility?
Okay, so I did some grinding with a Taylor expansion, and interestingly, the first two terms are known irrespective of the distribution of $\epsilon_t$, so we can get a pretty good approximate solution to the question. See my answer for more detail.