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Performance — Lodestar.Stats.TimeSeries

What Lodestar.Stats.TimeSeries costs against the library a reader would otherwise reach for. How to read a row, and what this page leaves out: docs/guides/performance.md.

Stationarity and seasonal decomposition against Cortex.TimeSeries (issue #671)

Full method and what agrees: bench/README.md.

Machine: AMD Ryzen 7 8700G w/ Radeon 780M Graphics, 1 CPU, 16 logical and 8 physical cores (BenchmarkDotNet's own header), Ubuntu 26.04.1 LTS, .NET SDK 10.0.401, .NET 10.0.12 runtime, AVX-512. Window: BenchmarkDotNet 0.14.0, default job, on 2026-09-15. Cortex.TimeSeries 1.1.0. Each pair returned the same statistic before it was timed.

n	function	Lodestar.Stats.TimeSeries	Cortex.TimeSeries	Cortex / Lodestar	Allocated, Lodestar	Allocated, Cortex
200	ADF, lag 4	6.987 μs	15.819 μs	2.26	20.68 KB	16.18 KB
200	KPSS, level	2.219 μs	2.328 μs	1.05	1.69 KB	3.43 KB
200	decomposition, period 12	0.810 μs	1.499 μs	1.85	6.50 KB	8.16 KB
2,000	ADF, lag 4	101.382 μs	181.199 μs	1.79	203.51 KB	142.76 KB
2,000	KPSS, level	59.554 μs	60.223 μs	1.01	15.75 KB	31.55 KB
2,000	decomposition, period 12	8.253 μs	15.391 μs	1.86	62.75 KB	78.48 KB

The augmented Dickey-Fuller test is 1.79× to 2.26× faster than Cortex's. Its lag search fits through OrdinaryLeastSquares.Estimate, which applies the reflections to the response and stops at the coefficients, their standard errors and the residual sum of squares, rather than forming Q explicitly and pricing variance inflation factors and a Student quantile per coefficient to hand back one t statistic. It allocates more than Cortex at 2,000 points: the design and its column-major copy. The p-value stays what the test is for — Cortex's is clamped at 0.01, where MacKinnon's surface gives 1.1e-9 to 9.5e-4 on the regressions checked.

The decomposition is 1.85× faster: the moving average is a running sum over each window's interior rather than a weighted pass over the whole window, O(n) against O(n·period). KPSS is level, with half the allocation; its cost is the lagged products of the long-run variance, which both sides compute.

Lodestar.Stats' serial-correlation diagnostics against Cortex.TimeSeries (issue #617)

Full method, and why the partial autocorrelations of the two libraries differ: bench/README.md.

Machine: the AMD Ryzen 7 8700G named above. Window: one BenchmarkDotNet run, default job, on 2026-09-13, 12 benchmarks, 20 lags throughout.

Method	SampleSize	Mean	Ratio	Allocated
LodestarAutocorrelation	200	18.582 μs	1.00	1,000 B
CortexAutocorrelation	200	7.308 μs	0.39	192 B
LodestarPartialAutocorrelation	200	18.829 μs	1.01	1,192 B
CortexPartialAutocorrelation	200	7.696 μs	0.41	768 B
LodestarLjungBox	200	8.407 μs	0.45	720 B
CortexLjungBox	200	7.375 μs	0.40	224 B
LodestarAutocorrelation	2,000	88.121 μs	1.00	1,000 B
CortexAutocorrelation	2,000	76.709 μs	0.87	192 B
LodestarPartialAutocorrelation	2,000	88.041 μs	1.00	1,192 B
CortexPartialAutocorrelation	2,000	77.123 μs	0.88	768 B
LodestarLjungBox	2,000	77.513 μs	0.88	720 B
CortexLjungBox	2,000	76.915 μs	0.87	224 B

The gap is one function call. Lodestar's ACF and PACF are 11.3 and 11.1 μs slower at 200 points and 11.4 and 10.9 μs slower at 2,000 — constant while the series grows tenfold, which a kernel difference could not be. Both compute the confidence band Cortex.TimeSeries does not, through one NormalQuantile call, and the Ljung-Box pair, which has no band, is 1.14× at 200 points and level at 2,000. Subtracting the 11.5 μs quantile leaves 7.1 μs against Cortex's 7.3 at 200 points and 76.6 μs against 76.7 at 2,000. The allocation difference is the band and the result record that carries it, and #709 confirmed it by removing that cost: without the bisection the pairs are level.

The vector autoregression against statsmodels (issue #786)

Full method and what agrees: bench/README.md. Nothing in .NET estimates a VAR, so the incumbent is statsmodels 0.15.0 through compare-var. Machine: the AMD Ryzen 7 8700G named above, on 2026-09-16; one run of each side. A two-variable series at lag 2, milliseconds per fit, best of five.

n	VectorAutoregression.Fit	statsmodels, wall / cpu	ratio, wall
1,000	0.042 ms	1.263 / 1.263 ms	30.23
10,000	0.485 ms	8.565 / 8.564 ms	17.65
100,000	5.391 ms	79.616 / 79.609 ms	14.77

What the fit costs by shape, from VectorAutoregressionBenchmarks, BenchmarkDotNet 0.14.0 default job:

observations	variables	lags	mean	Allocated
500	2	1	14.76 μs	60.53 KB
500	2	4	49.28 μs	132.84 KB
500	5	1	72.24 μs	206.76 KB
500	5	4	422.41 μs	590.05 KB
5,000	2	1	244.97 μs	587.95 KB
5,000	2	4	829.14 μs	1,293.21 KB
5,000	5	1	911.36 μs	2,000.01 KB
5,000	5	4	4,701.02 μs	5,548.08 KB

Both axes multiply: a system of K variables at lag p fits K least squares over a design of 1 + K·p columns.