# More on Time-Varying Volatility in NGH4

It looks like incorporating the last 12 months of daily NGH4 prices helps bring the recent volatility into focus.  Estimating the Markov regime-switching AR model over the last 12 months (on daily log returns) affords:

$r_{ng,t} = \begin{cases} 0.0006 -0.0429r_{ng,t-1}+ e_{S1,t}, \:\:\:\:\:\:\:\: e_{S1} \sim N(0,0.0122) \\ 0.0040+0.55185r_{ng,t-1}+e_{S2,t}, \:\:\:\:\:\:\: e_{S2} \sim N(0,0.0309) \end{cases}$

with the transition matrix:

$P=\left[ \begin{array} 0.92 \;\;&\;\; 0.50 \\ { } & { } \\ 0.08 \;\;&\;\; 0.50 \end{array}\right]$

This gives annualized volatilities of 19.47% in the low vol state, and 49.08% in the high vol state.  Weighting these volatilities by filtered state probability gives:

and NGH4 over the same period is: