# How to use a realized kernel?

I've read that realized kernels are the thing to use for calculating daily volatility from high-frequency data. So I've got minute data, how do I actually use such a kernel? Will it give me minute-ly volatility, do I have to normalize it somehow? Also, what data do I feed it - minute data since the start of the trading day, one day's worth of data, all historical data I have until this point, or something else?

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The use of kernels to estimate volatility using intraday data is "nothing more" than combining:

• kernel smoothing

Thus you have to take care about the "usual pits" of these two approaches.

Intraday volatility estimation. I hope you know the "signature plot" effect. Of course if you use the proper estimation method, it should take care of if, but just in case you should check that you do not suffer from it.

Kernel smoothing. You will have to tune the time scale of your kernel. Of course theoretical papers like Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise do not really have to do it since their results are asymptotic but real life is not. Moreover you may know that since you will have at date $t$ information of previous dates in your estimator $\hat\sigma_t$, if you multiply it by a statistic from the past $X_{t-\delta t}$ you will obtain a "trace" of the correlation between $X$ and $\sigma$ (i.e. somewhere inside $\mathbb{E}(\hat\sigma_t \cdot X_{t-\delta t})$ you have a term in $\mathbb{E}(K(\delta t) \cdot \sigma_{t-\delta t} \cdot X_{t-\delta t})$, where $K$ is your kernel). It may add biais if you use your kernel volatility estimate to build other estimators. And not only for multiplications.

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