Simulate from and fit a discrete-time autoregressive log stochastic volatility model. Run with python xarsv.py.
Sample output:
#obs: 1000000
mu phi sigma
true -0.500000 0.900000 0.400000
fit -0.497048 0.910509 0.377125
mean std skew kurtosis min max
vol 0.865088 0.417543 1.540771 4.381076 0.068404 6.841719
log(vol) -0.249821 0.458181 -0.004259 0.003998 -2.682318 1.923039
returns 0.000676 0.961069 0.016876 4.004919 -13.000362 17.599214
returns/vol 0.000224 1.001080 0.002882 -0.004051 -4.770352 4.496121
mu phi sigma
true -0.500000 0.900000 0.400000
fit -0.498815 0.916295 0.365594
mean std skew kurtosis min max
vol 0.865183 0.420412 1.564852 4.576003 0.088911 5.967455
log(vol) -0.250893 0.460690 -0.002258 -0.001021 -2.420119 1.786320
returns -0.000413 0.962733 0.015700 3.903745 -10.188885 11.650475
returns/vol -0.001248 1.000968 -0.002871 0.001489 -4.787957 4.829210
mu phi sigma
true -0.500000 0.900000 0.400000
fit -0.503347 0.889827 0.422405
mean std skew kurtosis min max
vol 0.865523 0.419989 1.544392 4.325622 0.075386 5.731296
log(vol) -0.250369 0.460482 -0.003971 -0.003401 -2.585135 1.745942
returns 0.000182 0.960359 0.004223 3.915706 -12.880456 11.390660
returns/vol -0.000037 0.998975 -0.000440 -0.000098 -4.861752 5.047978