Re: [Gretl-devel] [Gretl-users] multivariate lrvar?

On Mon, 16 Apr 2018, Sven Schreiber wrote: Hm, I see. I personally would prefer redefining the $\Gamma$ matrices. I'd go from <LaTeX> Rather, one computes the sandwich filling by summation as % \[ \hat{\Sigma} = \hat{\Gamma}(0) + \sum_{j=1}^p w_j \left(\hat{\Gamma}(j) + \hat{\Gamma}'(j) \right) \] % where the $k \times k$ sample autocovariance matrix $\hat{\Gamma}(j)$, for $j \geq 0$, is given by \[ \hat{\Gamma}(j) = \frac{1}{T} \sum_{t=j+1}^T \hat{u}_t \hat{u}_{t-j}\, X'_t\, X_{t-j} \] and $w_j$ is the weight given to the autocovariance at lag $j > 0$. </LaTeX> to <LaTeX> Rather, one computes the sandwich filling by summation as % \[ \hat{\Sigma} = \hat{\Gamma}(0) + \sum_{j=1}^p w_j \left(\hat{\Gamma}(j) + \hat{\Gamma}'(j) \right) \] % where the $k \times k$ matrix $\hat{\Gamma}(j)$, for $j \geq 0$, is proportional (by a factor $T$) to the sample autocovariance matrix, and is given by \[ \hat{\Gamma}(j) = \sum_{t=j+1}^T \hat{u}_t \hat{u}_{t-j}\, X'_t\, X_{t-j}, \] where $w_j$ is the weight given to the autocovariance at lag $j > 0$. </LaTeX> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------