I am reading about HAR models for realised variance and they all seem to use WLS or OLS to calculate the parameters. Now I understand how that works if you just use say the 10 years of AAPL intraday history. However, if you're doing this for a univariate model on many stocks (like it seems the authors do to create stable parameter estimates) how is this done?

Do I just put say TSLA's stock at the bottom of the dataframe containing AAPL's and let it do the error minimisation and continue to just add n more stocks to this dataframe to get more and more robust estimates?

Edit re Pleb's request:
<https://www.sciencedirect.com/science/article/abs/pii/S0304407615002584>
Page 7

> 
> We complement our analysis of the aggregate market with additional
> results for the 27 Dow Jones Constituents as of September 20, 2013
> that traded continuously from the start to the end of our sample. Data
> on these individual stocks comes from the TAQ database. Our sample
> starts on April 21, 1997, one thousand trading days (the length of our
> estimation window) before the final decimalization of NASDAQ on April
> 9,
> 2001. The sample for the S&P 500 ends on August 30, 2013, while the sample for the individual stocks ends on December 31, 2013, yielding a
> total of 3096 observations for the S&P 500 and **3202 observations for
> the DJIA constituents**. The first 1000 days are only used to estimate
> the models, so that the in-sample estimation results and the rolling
> out-of-sample forecasts are all based on the same samples.
> 
> 
> 

To me this reads like they're bundling all of this data together into a 1,000 day training set and then doing the OLS on that. They don't give different model parameters for an S&P model and a DJIA Model, or one for each of the DJIA constituents they analysed.