Because we model log-prices as a Gaussian, the distribution of prices is a log-Normal distribution, whose mean and standard deviation can be derived in closed form from the estimators <a href="https://www.codecogs.com/eqnedit.php?latex=\hat&space;y_{t,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat&space;y_{t,i}" title="\hat y_{t,i}" /></a> and <a href="https://www.codecogs.com/eqnedit.php?latex=\hat\sigma_{t,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat\sigma_{t,i}" title="\hat\sigma_{t,i}" /></a>. We use log-Normal distribution statistics at times <a href="https://www.codecogs.com/eqnedit.php?latex=t=1\dots,T" target="_blank"><img src="https://latex.codecogs.com/gif.latex?t=1\dots,T" title="t=1\dots,T" /></a> to produce the stock estimation plot and at time <a href="https://www.codecogs.com/eqnedit.php?latex=T+1" target="_blank"><img src="https://latex.codecogs.com/gif.latex?T+1" title="T+1" /></a> to fill the prediction table. In order to produce the sector estimation plot, we proceed analogously but with sector-level estimators <a href="https://www.codecogs.com/eqnedit.php?latex=\hat&space;y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat&space;y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" title="\hat y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" /></a> and <a href="https://www.codecogs.com/eqnedit.php?latex=\hat\sigma^s_{t,k}=\log(1+e^{\hat\psi^s_k+|1-\tau_t|})" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat\sigma^s_{t,k}=\log(1+e^{\hat\psi^s_k+|1-\tau_t|})" title="\hat\sigma^s_{t,k}=\log(1+e^{\hat\psi^s_k+|1-\tau_t|})" />.
0 commit comments