Statistics and time series: API index

Find an operation by its purpose. Entries link to the complete signature and contract.

HMath.Probability

API	Purpose
Distribution	Parameterized probability law.
Bernoulli	Declaration and type contract below.
Binomial	Declaration and type contract below.
NegativeBinomial	Declaration and type contract below.
Geometric	Declaration and type contract below.
Hypergeometric	Declaration and type contract below.
Poisson	Declaration and type contract below.
Categorical	Declaration and type contract below.
DiscreteUniform	Declaration and type contract below.
Uniform	Declaration and type contract below.
Normal	Declaration and type contract below.
LogNormal	Declaration and type contract below.
Exponential	Declaration and type contract below.
Gamma	Declaration and type contract below.
Beta	Declaration and type contract below.
ChiSquare	Declaration and type contract below.
StudentT	Declaration and type contract below.
FisherF	Declaration and type contract below.
Cauchy	Declaration and type contract below.
Laplace	Declaration and type contract below.
Logistic	Declaration and type contract below.
Weibull	Declaration and type contract below.
Pareto	Declaration and type contract below.
Rayleigh	Declaration and type contract below.
Maxwell	Declaration and type contract below.
Gumbel	Declaration and type contract below.
GeneralizedExtremeValue	Declaration and type contract below.
BetaBinomial	Declaration and type contract below.
Skellam	Declaration and type contract below.
VonMises	Declaration and type contract below.
Triangular	Declaration and type contract below.
TruncatedNormal	Declaration and type contract below.
Mixture	Declaration and type contract below.
Empirical	Declaration and type contract below.
GaussianKDE	Declaration and type contract below.
validateDistribution	Check finite parameters, support ordering, probability normalization, and declared per-family reference budgets.
density	Probability mass for discrete families or density for continuous families.
logDensity	Log density or mass; zero probability is negative infinity, while an integrable endpoint singularity is positive infinity.
cdf	P(X<=x).
survival	P(X>x), using direct upper tails for normal, gamma, beta, t, F, binomial and Poisson to avoid cancellation.
quantile	Generalized inverse CDF, p in [0,1]; endpoints return mathematical support bounds, including infinities.
hazard	Density divided by survival.
logLikelihood	Sum of independent observation log probabilities.
moments	Mean and population variance.
entropy	Shannon or differential entropy in nats.
sample	Draw a model sample and updated immutable RNG; specialized gammanormalcount samplers are reused, with inverse-CDF sampling for remaining families.
fitNormal	Normal maximum-likelihood fit; variance divides by n.
fitExponential	Maximum-likelihood rate for nonnegative observations with strictly positive total.
fitBernoulli	Maximum-likelihood probability for nonempty binary observations.
fitMLEGrid	Select the maximum-likelihood model from an explicit finite candidate grid; this is grid search, not continuous parameter optimization.
fitMAPGrid	Select the maximum log-likelihood plus caller-supplied log prior over a finite model grid.
betaBernoulliUpdate	Conjugate Beta prior update from success/failure observations, returning posterior concentrations (alpha,beta).
gammaPoissonUpdate	Conjugate Poisson-rate update; arguments and result use Gamma shaperate, deliberately distinct from the Gamma distribution constructor shapescale.
normalNormalUpdate	Known-variance conjugate normal mean update.
conditionalProbability	Compute P(A|B) from joint P(A intersection B) and strictly positive P(B).
bayes	Normalize prior probabilities times observation likelihoods.
expectation	Reference expectation under a distribution.
goodnessOfFit	Two-sided one-sample Kolmogorov distance against a specified CDF.
gaussianKDE	Construct an equal-weight Gaussian kernel density with strictly positive bandwidth and finite nonempty observations.
multinomialPMF	Multinomial mass for probabilities summing to one and nonnegative count vector; log-gamma arithmetic avoids factorial overflow.
dirichletDensity	Dirichlet density on the strictly positive simplex interior.
multivariateNormalLogDensity	Log density for a finite mean/point and symmetric positive-definite covariance, validated by Cholesky.
sampleMultivariateNormal	Cholesky-transform independent standard normals; returns a vector and updated state.
wishartLogDensity	Wishart log density for real degrees of freedom nu>p-1 and positive-definite p-by-p scale and observation matrices.
sampleWishart	Reference Wishart draw as the sum of nu Gaussian outer products; requires integer nu>=p and nu<=100000.
Markov	Opaque finite row-stochastic transition matrix.
markov	Validate and construct a row-stochastic matrix with 1..1024 states; row sums tolerate absolute error 1e-12.
transition	Advance a normalized state-probability row vector by one Markov step.
stationary	Stationary probabilities by damped power iteration, with caller iteration budget and positive residual tolerance.
HMM	Opaque finite-state categorical-emission hidden Markov model.
hmm	Validate initial probabilities, square transition matrix and equally sized categorical-emission rows.
forward	Scaled forward returns log likelihood, normalized alpha rows and per-time scaling constants.
backward	Scaled backward messages using the same per-time normalizers as forward; terminal message is the all-ones vector.
posteriorStates	Posterior state probabilities at each observation time from normalized alpha-beta products.
viterbi	Most likely state path and its joint log probability, via max-product dynamic programming in log space.
baumWelch	Baum--Welch EM for one observation sequence, pseudocount>=0.

HMath.Random

API	Purpose
Generator	Algorithm variant.
PCG32	Declaration and type contract below.
Xoshiro256StarStar	Declaration and type contract below.
Xoroshiro128Plus	Declaration and type contract below.
MT19937	Declaration and type contract below.
Philox4x32	Declaration and type contract below.
Threefry2x64	Declaration and type contract below.
ChaCha20	Declaration and type contract below.
RNG	Opaque immutable generator state, including any buffered block outputs.
seedRNG	Deterministically encode a 64-bit seed.
nextWord64	Produce one word and its successor state.
cloneRNG	Copy an immutable state; the copy produces exactly the same future outputs.
splitRNG	Create two deterministic child streams by hashing two successive parent words.
serializeRNG	Serialize full state, including pending block output, with the versioned hmath-rng-1 prefix.
restoreRNG	Parse a versioned full state and validate generator lengths, forbidden zero states, and MT word/index ranges.
uniform	Uniform 53-bit real on [0,1), using the most significant random bits.
uniformOpen	Uniform 52-bit midpoint real on (0,1), safe as input to logarithms.
uniformInt	Unbiased inclusive integer range using 64-bit rejection.
sampleN	Run a checked sampler sequentially, returning values and final state.
normal	Normal sample with finite mean and strictly positive standard deviation.
boxMuller	Standard normal through the polar-coordinate Box--Muller transform, consuming two uniforms.
marsagliaNormal	Standard normal through Marsaglia polar disk rejection, with 10000-proposal budget.
zigguratNormal	Marsaglia--Tsang 128-layer Ziggurat normal generator.
exponential	Exponential sample parameterized by strictly positive rate, via an open-uniform logarithm.
gamma	Gamma shape/scale sample using Marsaglia--Tsang rejection and the shape-augmentation identity below shape one; 10000-proposal budget.
beta	Beta(a,b) as the ratio of independent gamma variates.
poisson	Poisson count by exponential-arrival inversion.
binomial	Binomial count from n independent Bernoulli trials. n<=10000000 and p in [0,1].
weighted	Draw an index in proportion to finite nonnegative weights; max scaling handles subnormal or overflowing totals and zero weights are never selected.
AliasTable	Opaque Walker alias table with normalized acceptance thresholds and alternative indices.
aliasTable	Build a Walker alias table from finite nonnegative weights with positive maximum; max scaling avoids overflow.
aliasSample	Draw an index from an already validated alias table, using one uniform integer and one uniform real.
reservoir	Algorithm R reservoir over a finite stream, retaining k positions uniformly without replacement.
shuffle	Fisher--Yates permutation of list positions.
withReplacement	Draw count values independently from a nonempty finite population, preserving duplicates.
withoutReplacement	Uniform subset in shuffled order.
stratified	One uniform point per equal-width interval of [0,1), in increasing stratum order.
importance	Self-normalized importance estimate from values and nonnegative finite importance weights.
rejection	Accept proposals with the supplied target/envelope probability in [0,1]; the first argument is a hard proposal budget.
inverseTransform	Apply a checked inverse CDF to an open uniform; propagates inverse-domain or nonconvergence errors.
metropolisHastings	Symmetric random-walk Metropolis in log density.
gibbs	A full Gibbs sweep uses caller-supplied exact conditional samplers in coordinate order.
hamiltonianMonteCarlo	Identity-mass HMC with Gaussian momentum, leapfrog count and positive step size, log density and its gradient.
monteCarlo	Uniform-[0,1] Monte Carlo integral and estimated standard error from at least two draws.
halton	Unshifted Halton point, dimensions 1..16 and zero-based nonnegative point index; index zero is the origin.
sobol	Sobol digital net in dimensions 1..8, 32 direction bits.
faure	Faure's Pascal digital transform in the least prime base >= dimension.
latinHypercube	Random n-by-d Latin hypercube in [0,1), with a separate Fisher--Yates stratum permutation per axis; n>0 and 1<=d<=1024.
randomQuality	Mean, population variance, and lag-one correlation; descriptive quality diagnostics, not a cryptographic certification or a replacement for TestU01.
entropySeed	Read eight bytes from the operating system entropy device, little endian.

HMath.Statistics

API	Purpose
mean	Arithmetic mean of a finite nonempty list: sum divided by length.
variance	Population variance of a finite nonempty list, dividing squared deviations by n (not n-1).
standardDeviation	Population standard deviation, sqrt of variance.
median	Sort a finite nonempty list and return its middle value, averaging the central pair for even length.

HMath.Statistics.Advanced

API	Purpose
arithmeticMean	Mean of finite nonempty data.
weightedMean	Reliability-weighted mean of observations and nonnegative finite weights; weights must have finite positive total.
geometricMean	exp(mean(log x)) for strictly positive finite observations.
harmonicMean	Reciprocal of the mean reciprocal, for strictly positive finite observations.
rms	Root-mean-square with max scaling to avoid squaring overflow.
trimmedMean	Discard floor(fraction*n) samples from each sorted tail, with fraction in [0,1/2), then average.
winsorizedMean	Replace floor(fraction*n) values at each tail with the nearest retained value, then average.
median	Type-7 50th percentile; averages the central pair for an even sample count.
modes	All values of maximum multiplicity, sorted ascending; exact floating equality defines ties.
quantile	Hyndman--Fan type-7 quantile with linear interpolation and probability p in [0,1].
percentile	Type-7 quantile with percentage in [0,100].
interquartileRange	Type-7 75th percentile minus 25th percentile.
medianAbsoluteDeviation	Median absolute deviation from the median, without the normal consistency multiplier.
dataRange	Maximum minus minimum; arithmetic overflow is an explicit error.
populationVariance	Second population central moment, dividing by n.
sampleVariance	Unbiased sample variance, dividing by n-1; requires at least two observations.
populationSD	Square root of population variance.
sampleSD	Square root of unbiased sample variance.
coefficientOfVariation	Population standard deviation divided by absolute mean; rejects zero mean.
centralMoment	Population central moment of integer order 0..32; nonfinite intermediate/final arithmetic is rejected.
skewness	Uncorrected population third standardized central moment; requires nonconstant observations.
kurtosis	Uncorrected population excess kurtosis, subtracting three; requires nonconstant observations.
covariance	Covariance of two matching finite data vectors; True selects the n-1 sample correction.
correlation	Pearson correlation of matching nonconstant data vectors.
covarianceMatrix	Covariance matrix for variables supplied as columns (each list is one variable).
spearman	Pearson correlation of average tied ranks; matching nonconstant rank vectors required.
kendall	Kendall tau-b with tied-pair correction; quadratic reference implementation.
partialCorrelation	Partial correlation of variable indices i,j conditional on every other supplied column, through the inverse sample covariance.
autocorrelation	Pearson correlation between overlapping lagged segments; zero<=lag<n-1.
crossCorrelation	Pearson correlation of overlapping x_t and y_(t+lag), using their common finite length.
movingAverage	Valid-window moving means; window must lie in [1,n], with no endpoint padding.
exponentialMovingAverage	EMA with alpha in (0,1], initialized at the first observation.
movingVariance	Valid-window population variances with no endpoint padding.
Streaming	Opaque Welford accumulator storing an unbounded Integer count, mean and sum of squared deviations.
emptyStreaming	Zero-count Welford accumulator.
updateStreaming	Add one finite observation by Welford recurrence; nonfinite arithmetic is rejected.
combineStreaming	Chan parallel merge of two Welford accumulators; empty accumulators are identities.
streamingResult	Return count, mean and variance; True uses n-1 correction and requires at least two samples.
histogramND	Histogram edges must increase strictly; intervals are [a,b), with the last interval closed on its right.
entropy	Shannon entropy in nats for normalized nonnegative probabilities, with 0*log(0)=0.
mutualInformation	Mutual information in nats from a rectangular normalized joint-probability table.
klDivergence	KL(P||Q) in nats, including positive infinity when Q is zero on positive P mass.
jsDivergence	Equal-mixture Jensen--Shannon divergence in nats, bounded by log 2.
zScores	Standardize with population standard deviation; constant samples are rejected.
standardError	Unbiased sample standard deviation divided by sqrt n, requiring n>=2.
confidenceInterval	Two-sided Student-t confidence interval for a normal population mean with unknown variance; confidence level in (0,1).
bootstrap	Seeded nonparametric resampling with replacement.
jackknife	Leave-one-out bias-corrected statistic and jackknife standard error; requires n>=2.
TestResult	Test statistic, p value clamped to [0,1] after numerical checks, and applicable degrees of freedom.
TestResult	Declaration and type contract below.
testStatistic	Computed statistic for the selected hypothesis test.
pValue	Reported tail probability, clamped to [0,1]; interpret using the test's documented alternative hypothesis.
degreesOfFreedom	Distribution degrees-of-freedom parameters in test-specific order (for example numerator then denominator for F tests).
oneSampleT	Two-sided one-sample Student t test against a finite null mean; assumes independent normal observations.
twoSampleT	Two-sided pooled t test when True, Welch unequal-variance test when False; each group requires n>=2 and positive combined variation.
pairedT	Two-sided one-sample t test on paired differences; matching group lengths required.
zTest	Two-sided one-sample normal z test with known strictly positive population standard deviation.
chiSquareTest	Pearson goodness-of-fit chi-square statistic for observed and positive expected counts; first argument is number of fitted nuisance parameters.
varianceFTest	Two-sided normal-population variance-ratio F test, requiring positive sample variances.
anova	One-way fixed-effects F test on independent normal groups with common variance; each group requires n>=2.
welchAnova	Welch one-way heteroscedastic F test with Satterthwaite denominator degrees of freedom.
kruskalWallis	Tie-corrected Kruskal--Wallis H statistic with chi-square asymptotic calibration.
mannWhitney	Mann--Whitney U for the first sample; two-sided tie-corrected normal approximation with continuity correction.
wilcoxon	Wilcoxon signed-rank test for differences, dropping zeros and using average absolute tied ranks and continuity-corrected normal calibration.
kolmogorovSmirnov	Two-sided KS statistic and asymptotic p value against a fully specified continuous distribution.
shapiroWilk	Royston's AS R94 coefficients and normal-tail approximation, n=3..5000, uncensored samples.
andersonDarling	Anderson--Darling normality test after fitting the sample mean and unbiased sample standard deviation.
levene	One-way ANOVA on absolute deviations; True chooses group medians (Brown--Forsythe), False chooses means.
bartlett	Bartlett homogeneity-of-variance test, appropriate for normal samples; positive group variances required.
fisherExact	Two-sided Fisher exact test on nonnegative 2-by-2 counts (a,b;c,d).
permutationTest	Seeded two-sided random-label permutation p value for a caller statistic, with the (b+1)/(B+1) correction.
bonferroni	Bonferroni-adjusted p values in original order, capped at one.
benjaminiHochberg	Monotone Benjamini--Hochberg FDR-adjusted p values in original order.
cohensD	Difference of sample means divided by pooled unbiased standard deviation.
etaSquared	One-way ANOVA explained sum of squares divided by total sum of squares.
normalTestPower	Exact power under a known-variance two-sided one-sample normal z-test.
normalSampleSize	Smallest integer n whose exact known-variance two-sided normal-test power meets the target; hard budget n<=100000000.
tukeyOutliers	Zero-based indices outside [Q1-kIQR,Q3+kIQR], with positive multiplier k and type-7 quartiles.
grubbs	Two-sided single-outlier Grubbs test, returning candidate index, G statistic and rejection decision at alpha; normality assumption required.
masked	Keep True-mask observations, then validate retained values.
huberLocation	Huber M location by iteratively reweighted means, scaled by 1.4826*MAD; zero MAD returns the median.

HMath.TimeSeries

API	Purpose
difference	Apply (1-B^lag)^order.
autocorrelation	Biased covariance divided by lag-zero covariance, global sample mean.
resample	Linear samples require brackets (or an exact timestamp).
crossCorrelation	Corr(x_t,y_(t+lag)), global means and full lag-zero energy normalization.
Series	Opaque, validated timestamps paired with optional observations.
series	Preserve order and missing values; reject duplicate or nonfinite times.
regularSeries	Sample times start+i*step.
observations	Extract time-ordered (timestamp,Maybe value) observations from a validated Series.
seriesValues	Complete-data conversion never silently drops a missing observation.
isRegular	Relative spacing tolerance; fewer than three observations are regular.
Alignment	Time-series timestamp join policy: Inner intersection or Outer union,with missing values explicit.
Inner	Declaration and type contract below.
Outer	Declaration and type contract below.
LeftAligned	Declaration and type contract below.
align	Exact timestamp equality.
Fill	Missing-value strategy selecting forward fill,backward fill,or linear interpolation under the checked boundary rules.
ForwardFill	Declaration and type contract below.
BackwardFill	Declaration and type contract below.
LinearFill	Declaration and type contract below.
fillMissing	Directional filling leaves the unavailable leading/trailing end missing.
Resampling	Series resampling policy selecting bin means,last-bin values,or linear point samples.
LinearSamples	Declaration and type contract below.
BinMean	Declaration and type contract below.
BinLast	Declaration and type contract below.
Rolling	Rolling-window statistic selector for mean,variance,standard deviation,minimum,or maximum.
MovingMean	Declaration and type contract below.
MovingVariance	Declaration and type contract below.
MovingSD	Declaration and type contract below.
MovingMinimum	Declaration and type contract below.
MovingMaximum	Declaration and type contract below.
rolling	Full trailing windows only; variance is population variance (ddof=0).
exponentialAverage	Recursive EMA, initialized at the first observation; 0<alpha<=1.
weightedAverage	Nonnegative chronological weights: first weight multiplies oldest sample.
cumulativeReturns	Cumulative simple return relative to the first strictly positive price.
logarithmicReturns	Consecutive log returns, using log prices to avoid ratio overflow.
durbinLevinson	Levinson recursion for a positive definite Toeplitz covariance.
yuleWalker	Biased sample autocovariances with centered data; returns mean separately.
partialAutocorrelation	Given maximum lag then samples, compute ACF and Durbin-Levinson partial correlations, returning lag zero (1) followed by requested PACF lags.

HMath.TimeSeries.Core

API	Purpose
Series	Opaque, validated timestamps paired with optional observations.
series	Preserve order and missing values; reject duplicate or nonfinite times.
regularSeries	Sample times start+i*step.
observations	Extract time-ordered (timestamp,Maybe value) observations from a validated Series.
seriesValues	Complete-data conversion never silently drops a missing observation.
isRegular	Relative spacing tolerance; fewer than three observations are regular.
Alignment	Time-series timestamp join policy: Inner intersection or Outer union,with missing values explicit.
Inner	Declaration and type contract below.
Outer	Declaration and type contract below.
LeftAligned	Declaration and type contract below.
align	Exact timestamp equality.
Fill	Missing-value strategy selecting forward fill,backward fill,or linear interpolation under the checked boundary rules.
ForwardFill	Declaration and type contract below.
BackwardFill	Declaration and type contract below.
LinearFill	Declaration and type contract below.
fillMissing	Directional filling leaves the unavailable leading/trailing end missing.
Resampling	Series resampling policy selecting bin means,last-bin values,or linear point samples.
LinearSamples	Declaration and type contract below.
BinMean	Declaration and type contract below.
BinLast	Declaration and type contract below.
resample	Linear samples require brackets (or an exact timestamp).
Rolling	Rolling-window statistic selector for mean,variance,standard deviation,minimum,or maximum.
MovingMean	Declaration and type contract below.
MovingVariance	Declaration and type contract below.
MovingSD	Declaration and type contract below.
MovingMinimum	Declaration and type contract below.
MovingMaximum	Declaration and type contract below.
rolling	Full trailing windows only; variance is population variance (ddof=0).
exponentialAverage	Recursive EMA, initialized at the first observation; 0<alpha<=1.
weightedAverage	Nonnegative chronological weights: first weight multiplies oldest sample.
cumulativeReturns	Cumulative simple return relative to the first strictly positive price.
logarithmicReturns	Consecutive log returns, using log prices to avoid ratio overflow.
difference	Apply (1-B^lag)^order.
autocorrelation	Biased covariance divided by lag-zero covariance, global sample mean.
crossCorrelation	Corr(x_t,y_(t+lag)), global means and full lag-zero energy normalization.
durbinLevinson	Levinson recursion for a positive definite Toeplitz covariance.
yuleWalker	Biased sample autocovariances with centered data; returns mean separately.
partialAutocorrelation	Given maximum lag then samples, compute ACF and Durbin-Levinson partial correlations, returning lag zero (1) followed by requested PACF lags.
finite	Test whether Double is neither NaN nor infinite.
require	Given predicate then message, return Right () or time-series-prefixed Left InvalidArgument.
checked	Return list unchanged when every sample is finite; otherwise return Left NonFiniteResult.
validate	Given minimum sample count then list, require length between that minimum and 16384 and all finite values.
average	Unchecked arithmetic average using per-term division by list length; empty list returns zero by empty sum.

HMath.TimeSeries.Diagnostics

API	Purpose
Deterministic	Stationarity-test deterministic terms: level-only or linear-trend specification.
Level	Declaration and type contract below.
LinearTrend	Declaration and type contract below.
Stationarity	Significance level paired with critical value.
Stationarity	Declaration and type contract below.
stationarityStatistic	Computed ADF/KPSS stationarity test statistic.
stationarityCriticalValues	Significance-level and critical-value pairs for the selected test/deterministic specification.
stationarityObservations	Number of effective observations used by the test.
stationarityNull	Human-readable null hypothesis, which differs between ADF and KPSS.
augmentedDickeyFuller	OLS of delta x_t on x_(t-1), an intercept, optional trend, and explicitly supplied lagged differences.
kpss	KPSS leveltrend stationarity with an explicit BartlettNewey--West lag bandwidth.
changePoints	Exact quadratic dynamic programming for piecewise-constant least squares, minimizing total within-segment SSE plus penalty per change.
cusum	Two-sided Page CUSUM with supplied baseline mean/SD.
anomalies	Median/MAD outliers, using the normal-consistency factor 1.4826022185.
DTWResult	Dynamic-time-warping accumulated distance and original-series zero-based alignment path.
DTWResult	Declaration and type contract below.
dtwDistance	Accumulated dynamic-time-warping path cost.
dtwPath	Optimal alignment as zero-based index pairs from the two input series.
dynamicTimeWarping	Absolute local cost; Sakoe--Chiba radius must include both endpoints.
spectrum	One-sided unwindowed periodogram density.
ForecastMetric	Prediction-error metric selector; scale/zero-denominator preconditions are checked by the metric function.
MAE	Declaration and type contract below.
MSE	Declaration and type contract below.
RMSE	Declaration and type contract below.
MAPE	Declaration and type contract below.
SMAPE	Declaration and type contract below.
MASE	Declaration and type contract below.
forecastError	MAPE and sMAPE are percentages; zero/zero sMAPE contributes zero.

HMath.TimeSeries.Models

API	Purpose
Smoothing	Exponential smoothing: Simple alpha; Holt alpha beta; HoltWinters period alpha beta gamma.
Simple	Declaration and type contract below.
Holt	Declaration and type contract below.
HoltWinters	Declaration and type contract below.
smoothForecast	Fitted one-step means and future means.
Decomposition	Additive reconstruction is trend+seasonal+remainder at every input index.
Decomposition	Declaration and type contract below.
trendComponent	Estimated trend values aligned with original observations.
seasonalComponent	Estimated seasonal values aligned with original observations.
remainderComponent	Residual values after subtracting trend and seasonality.
decompose	Classical additive decomposition with local linear trend smoothing and centered phase means.
STLConfig	Seasonal period,odd LOESS windows,and inner/robust iteration counts for STL decomposition.
STLConfig	Declaration and type contract below.
stlPeriod	Positive seasonal cycle length in observations.
stlSeasonalWindow	Odd LOESS window for seasonal subseries.
stlTrendWindow	Odd LOESS window for trend smoothing.
stlLowPassWindow	Odd low-pass LOESS smoothing window.
stlInnerIterations	Number of STL seasonal/trend backfitting passes.
stlRobustIterations	Number of robust outer reweighting passes; zero disables robust reweighting.
stl	Cleveland-style STL reference backfitting: smooth seasonal subseries by degree-one tricube LOESS with one-cycle extrapolation; remove a period, period, three-point moving-average low-pass followed by LOESS, then smooth the deseasonalized trend.
defaultSTLConfig	Given seasonal period, construct STL options with seasonal window 7, odd trend window above 2*period, odd low-pass window at/above period, two inner iterations and no robust outer iterations. stl validates the resulting configuration.
ARModel	Intercept followed by lag coefficients; observations stored chronologically.
fitAR	Given AR order then finite chronological samples, fit intercept and lag coefficients by checked OLS.
arCoefficients	Return AR intercept followed by lag-1 through lag-p coefficients.
forecastAR	Given horizon in [0,16384] then fitted AR model, recursively forecast future samples from latest observations.
SARIMAOrder	Ordinary (p,d,q),seasonal (P,D,Q),and cycle period s. fitSARIMA validates supported order/sample budgets.
SARIMAOrder	Declaration and type contract below.
arOrder	Ordinary autoregressive order p.
differenceOrder	Ordinary differencing order d.
maOrder	Ordinary moving-average order q.
seasonalAROrder	Seasonal autoregressive order P.
seasonalDifferenceOrder	Seasonal differencing order D.
seasonalMAOrder	Seasonal moving-average order Q.
seasonalPeriod	Seasonal cycle length s used to place seasonal polynomial lags.
ARIMAModel	Opaque fitted ARIMA/SARIMA state with differencing,parameters,innovation residuals,and original history for forecasting.
fitARIMA	Given optimization options,p,d,q,then finite chronological series, fit nonseasonal ARIMA through fitSARIMA with seasonal orders zero.
fitMA	Given optimization options,MA order q,then samples, fit ARIMA(0,0,q).
fitARMA	Given optimization options,AR order p,MA order q,then samples, fit ARIMA(p,0,q).
fitSARIMA	Parameters are intercept, ordinary AR, ordinary MA, seasonal AR, seasonal MA.
arimaParameters	Return fitted intercept,ordinary AR,ordinary MA,seasonal AR,seasonal MA parameters in that order.
arimaResiduals	Return fitted innovation residuals in chronological order, on the model's differenced process.
arimaInnovationVariance	Return fitted innovation-variance estimate stored in an ARIMA/SARIMA model.
forecastARIMA	Given horizon in [0,16384] then fitted ARIMA/SARIMA model, forecast recursively with future innovations set to zero and undo ordinary/seasonal differencing.
VARModel	Opaque fitted vector autoregression with intercept/lag coefficients and chronological multivariate history.
fitVAR	Given lag order then chronological multivariate rows, fit response-wise OLS with intercept and lag-major features.
varCoefficients	Rows are response components, columns are intercept then lag-major predictors.
forecastVAR	Given horizon then VAR model, recursively return future multivariate observation rows.
kalmanSeries	Reuse the checked Joseph-form linear Kalman update for each complete observation.