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I have a $T \times N$ matrix of asset returns, where $T$ = number of periods, and $N$ = number of assets. Calculating the covariance matrix of this set of returns is simple. How do I calculate the Newey-West-adjusted covariance matrix with lag = $k$?

Since each off-diagonal element within the covariance matrix is simply $cov(r_i, r_j)$, i.e. the covariance between the returns of asset $i$ and $j$, and in the standard OLS setting, $r_{i,t} = \beta_0 + \beta_1r_{j,t} + \epsilon_t$ yields the solution for $\beta_1 = \displaystyle\frac{cov(r_i, r_j)}{var(r_j)}$, I assume there's some relationship between the unadjusted $\beta_1$ and the Newey-West adjusted version?

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  • $\begingroup$ "...unadjusted β1 and the Newey-West adjusted version?"---There's no "Newey-West adjusted version" of beta or beta hat. "How do I calculate the Newey-West-adjusted covariance matrix with lag = k?"---replace the residual ACF's in the scalar version of Newey-West by their matrix (N by N, in this case) version appropriately. $\endgroup$ – Michael Oct 1 '20 at 12:49

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