# Tag Info

7

I think it's alive and well. I don't think there's a specific "decoupling" time, but if you look at e.g. Munnix et al. "Statistical causes for the Epps eﬀect in microstructure noise", it seems that the biased correlation is about 60% of the real value for 1 min data and about 90% for 5 min data, so you could say that 5 min is pretty safe, but 1 min is ...

7

Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...

6

Quick summary: Your model should still be well specified, as long as: 1) You do the analysis on a heavily traded asset, e.g. IBM on NYSE, and 2) You use heteroskedasticity-consistent standard errors in your estimation framework, e.g. White's standard errors. I'm going to start the long answer by re-stating the question to make sure I've got it right. Let ...

6

In any finite sample, it is always possible for the Zhou estimator to return a negative number, even though we know the unobservable parameter being estimated is non-negative. This is a well known issue in the academic literature. There are several approaches to dealing with this problem: 1) Ignore it. (I don't like this one). It is particularly nefarious ...

6

From an academic viewpoint you do not have a lot of choices: The Rosenbaum-Robert approach, the price model with uncertainty zones is a model of trades and duration between trades (implicitly). It is worthwhile to try it. You can also use an Hawkes process, it will have the nice effect of capturing clustering effects on trades. if you want to use ...

4

I use Yhang Zhang measure for intraday volatility for timeseries with a rolling 5 or 10 day window. I wrote a C++ and vba implementation which I'm happy to share if you wish. Takes olhc data and gives an 'estimate' of the volatility. For intraday trading (gamma hedging), I found it is a fairly good estimator of the days range. But I would caution on whether ...

3

First, you should use an exponential moving average, since the amount of state you need to keep is much smaller than for a simple moving average. Second the well known estimator of volatility, $$\hat{\sigma} = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2}$$ is not very robust, since the squaring amplifies the contribution of outliers (which is why ...

3

It is all a matter of frequency. For instance if you want to get annual realized volatility you multiply your last expression by $\sqrt{(N*251)}$ or the second to last expression by $\sqrt{(251)}$. In other words, your last expression is the 5-min realized volatility whereas the second to last expression is the daily realized volatility.

3

1) Spurious autocorrelation of non-synchronous trading data was analyzed in this article: http://www.amazon.com/An-econometric-analysis-nonsynchronous-trading/dp/1245789457 During some time intervals a lot of trades occur and during some nothing happens(so prices are stale). So serial correlation of traded prices may be present but this may be due to stale ...

3

I'll address your questions in order: 1a) For TSRV constructed using high frequency returns from NYSE market open to market close on a single day, the output should be numbers on the order of magnitude of 1e-4 to 1e-5. In other words, your numbers look about right. I got these number from calculating TSRV for IBM data myself using Kevin Sheppard's MatLab ...

2

The equivalence you are trying to find can only exist in the framework of static volatility. I think the problem is that in the real world, statistical volatility varies a lot with time; and worse off the relative rate at which it varies increases with smaller time increments. So not only does the answer not apply in real-world markets, an estimation of ...

2

The code you posted is wrong since you do not model the time series behavior of the up/down process (ie if you have 10 up move and consequently 10 down move it is not the same as the opposite ie 10 down and after 10 up..). I would recommend you to use standards Arma Garch models apply on returns instead of modeling the process of up/down. These are (at ...

2

Unfortunately for you (but maybe helpful to others) I can only refer to R packages. The R package high-frequency (link) provides rHYCov. The synchrony package (link) provides a whole plethora of methods for temporal, spatial and spatio-temporal statistics. Furthermore, I would personally advise against HY for its boundary artefacts and instead use ...

1

No, you can't use GBM for this. The underlying assumptions of the GBM/Blackschooles framework is that logreturns are normally distributed. This holds true for daily returns but it can't be assumed for shorter time periods. One explanation I've seen for this (I think in Paul Wilmott Introduces Quantitative Finance) is that the daily returns are the cumulative ...

1

Multiday aggregations are usually moving averages, not OHLC. For example, I might get the 10-day MA; I would not ask for the 10-day high. (Charts might take the latest sample, but that's only for visualization.) As for multiday bars that aren't defined by time, I'm not sure how to interpret something like that. The bars would span multiple days and then cut-...

1

In practice you try to cross the half-spread when your signal is bigger than half-spread so your goal is to find a stable signal that is bigger than half-spread in expectation.

1

Q1.) Is there anything wrong in principle with this simple sampling strategy? I mean sampling is a valid strategy, it just may not be the best. WOuld a VWAP style price be better? Would just an average be better? Typically when no trade has happened you can model the price as the last, average of the bid/ask spread, etc. The price you want depends on ...

1

I agree with Malick in the sense that an ARMA-GARCH is a better model but I would improve the model by doing a ARFIMA-FIGARCH, the FI stands for Fractional Integrated that are used to deal for long memory processes like HF data. When trying to fit the ARMA the normal approach would be to see the ACF and the PACF which will show a lot of dependency (almost ...

1

This is actually a deceptively good question because, as we all know, estimates of variance are extremely sensitive to sampling frequency, sampling intervals, and lags. This is because not all stock prices perfectly adhere to Brownian Motion (i.e., the variance doesn't adhere strongly to the root time rule). It is also not entirely clear from the paper how ...

1

I'll address things in order as I encountered them in the question. First, your formula for RV only makes sense if $X_{t_i}$ is the log-price, not log-return. If this was just a mistype it would probably be best if you edited the question to correct it. If it is not a mistype, let me know, because then you have bigger problems... Answer 0: I have no idea ...

1

If you calculate this estimator point by point, it could very well go negative. But the essence of this estimator is that statistically, it hovers around the realized variance, so it "estimates" the realized variance well. Even though the realized variance is by definition non-negative, the estimated distribution does not have to be. In practice can you ...

1

There are waaaaayyy better estimators than $Var(log(Close_{t+1}/Close_{t}))$. This close-close estimator is unbiased, and has a data efficiency defined as $1$. The Parkinson estimator uses high and low prices only (useful when you don't trust your open and close prices, or don't have them). It has a data efficiency of about $4$. The expected variance from "...

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