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I can't directly answer your question about coding for HAR-RV models, but before you do anything with rolling windows I suggest you look at the paper here. Essentially the paper claims that clustering on time series sequences ( i.e. rolling windows ) is useless, so if your HAR-RV model involves clustering in anyway you'll need to think very carefully about ...

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I really like Philip P's work, but frankly I do not believe this paper is his best one. It is understandable you do not catch how to use it: there is no dataset in the paper, and the orders of magnitude of $\sigma dW$ and $\delta_t x$ are so different. My suggestions: some components are missing, $x$ should be a point process, for instance an Hawkes ...

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The simple answer is that when you calculate the value weighted return at time $t$ all you really need is the return during time $t$ and the market-capitalization weight as of $t-1$. You can filter the securities to remove the missing ones (and others that you may remove for other reasons, e.g. too small or price too low), calculate weights based on the ...

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The factor models are based on the following linear regression model: $(R_t - R_f)$ = $\alpha$ + $\beta_{mkt}$*$(R_{mkt} - R_f)$ + $\sum\limits_{i=1}^n {x_{k,t}}$ + $\epsilon_t$ $\alpha$ is the regression model intercept and indicates the portfolio performance in excess to the market excess return and the other factor; It has to be strictly positive and ...

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The R function you have to use is the lm() function. On QuickR you can find a simple and clear tutorial on how to estimate a linear (multiple) regression model generally using the lm(). As further reference, I suggest you to read the Introducing R tutorial about linear model by G. Rodriguez. I did not read the paper you cited, but, anyway, you should ...

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