Performance

Timings in milliseconds, minimum over repeats, on one core of a 12-core x86-64 machine with OpenBLAS; from bench/bench_python.py (ssfortran and statsmodels both called from Python):

case	ssfortran	statsmodels
log likelihood, local level, n = 100,000	5.0	41
smoother, local level, n = 100,000	79	284
fit, level and trigonometric seasonal, n = 1000	114	528
1000 local level fits, n = 100, fit_many	201	7185
1000 local level fits, n = 100, one by one	1150	7185
fit, local level as a Python MLEModel	11	23

example/bench.f90 and bench/bench_statsmodels.py compare the Fortran core with statsmodels’ Cython filter directly.

Where the time goes

• The likelihood. Estimation evaluates the log likelihood without storing the filter output. In time-invariant models the steady-state shortcut (DK §4.3.4) then reduces a step to a few matrix-vector products.

• The gradient. The analytic score costs one filter and smoother pass, against 2k likelihood evaluations for central differences.

• Small matrices. State space models are small: m and p are often below 10. At that size the per-call cost of BLAS dominates, so the library uses inline loops below a size threshold.

• Many series. fit_many() fits independent models on OpenMP threads without the GIL. Set OPENBLAS_NUM_THREADS=1 so BLAS does not start threads of its own.

• Python models. An MLEModel calls Python at every evaluation; a MappedModel does not.

See Performance for the details.