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  • Getting started
  • User guide
  • Examples
  • API reference
  • Engine reference
  • Project
  • GitHub
  • PyPI
  • Conda-Forge
  • Codecov

Section Navigation

  • cultivars.engine._core
    • _containers
    • _converters
    • _defaults
    • _estimators
    • _loaders
    • _mappings
    • _matrices
    • _notes
    • _polynomials
    • _protocols
    • _recursions
    • _reparams
    • _rotations
    • _samplers
    • _scales
    • _scores
    • _spectra
    • _transforms
    • _types
    • _validators
    • _wavelets
  • cultivars.engine._internals
    • _assessments
    • _chains
    • _coefficients
    • _covariances
    • _emitters
    • _engines
    • _filters
    • _fits
    • _inferences
    • _layouts
    • _levels
    • _means
    • _mixins
    • _models
    • _moments
    • _objectives
    • _parameters
    • _posteriors
    • _predictors
    • _priors
    • _results
    • _selections
    • _simulators
    • _smoothers
    • _solutions
    • _solvers
    • _specifications
    • _states
    • _substrates
    • _systems
    • _tests
  • cultivars.univariate
    • cultivars.univariate.autoregression
      • AR
      • ARResult
        • ARResult._comparison_label
        • ARResult._from_fit
        • ARResult._summary_table
    • cultivars.univariate.box_jenkins
      • ARIMA
      • ARIMAX
      • ARMA
      • SARIMA
      • SARIMAX
      • ARMAResult
        • ARMAResult._comparison_label
        • ARMAResult._from_fit
        • ARMAResult._invertibility_ma
        • ARMAResult._notes
        • ARMAResult._specification
        • ARMAResult._stationarity_ar
        • ARMAResult._summary_table
    • cultivars.univariate.conditional_variance
      • ARGARCH
      • ARMAEGARCH
      • ARMAFIGARCH
      • ARMAGARCH
      • ARMAGJR
      • EGARCH
      • FIGARCH
      • GARCH
      • GJR
      • ARMAFIGARCHResult
        • ARMAFIGARCHResult._comparison_label
        • ARMAFIGARCHResult._from_fit
        • ARMAFIGARCHResult._summary_table
      • ARMAGARCHResult
        • ARMAGARCHResult._comparison_label
        • ARMAGARCHResult._from_fit
        • ARMAGARCHResult._mean_ma_params
        • ARMAGARCHResult._mean_notes
        • ARMAGARCHResult._summary_table
        • ARMAGARCHResult._variance_label
      • FIGARCHResult
        • FIGARCHResult._comparison_label
        • FIGARCHResult._from_fit
        • FIGARCHResult._summary_table
      • GARCHResult
        • GARCHResult._comparison_label
        • GARCHResult._from_fit
        • GARCHResult._mean_ma_params
        • GARCHResult._summary_table
    • cultivars.univariate.fractional_integration
      • ARFIMA
      • ARFIMAResult
        • ARFIMAResult._comparison_label
        • ARFIMAResult._from_fit
        • ARFIMAResult._summary_table
    • cultivars.univariate.mean_function
      • ARNN
      • TARNN
      • ARNNResult
        • ARNNResult._comparison_label
        • ARNNResult._from_fit
        • ARNNResult._summary_table
      • MeanFunctionEngine
        • MeanFunctionEngine._is_protocol
        • MeanFunctionEngine._is_runtime_protocol
      • TARNNResult
        • TARNNResult._comparison_label
        • TARNNResult._from_fit
        • TARNNResult._series
        • TARNNResult._summary_table
    • cultivars.univariate.regime_switching
      • MarkovSwitchingAR
      • MarkovSwitchingARResult
        • MarkovSwitchingARResult._comparison_label
        • MarkovSwitchingARResult._from_fit
        • MarkovSwitchingARResult._likelihood_ratio_obstacle
        • MarkovSwitchingARResult._series
        • MarkovSwitchingARResult._summary_table
    • cultivars.univariate.smooth_transition
      • ESTAR
      • LSTAR
      • STARResult
        • STARResult._comparison_label
        • STARResult._from_fit
        • STARResult._summary_table
        • STARResult._transition_params
        • STARResult._weight_at
    • cultivars.univariate.stochastic_volatility
      • SV
      • UCSV
      • SVPosterior
        • SVPosterior._convergence_label
        • SVPosterior._from_chain
        • SVPosterior._from_gibbs
        • SVPosterior._replication_notes
        • SVPosterior._series
        • SVPosterior._spec_label
        • SVPosterior._summary_table
      • SVResult
        • SVResult._params
        • SVResult._comparison_label
        • SVResult._from_fit
        • SVResult._series
        • SVResult._summary_table
      • UCSVPosterior
        • UCSVPosterior._from_fit
        • UCSVPosterior._series
        • UCSVPosterior._summary_table
    • cultivars.univariate.threshold
      • SETAR
      • TAR
      • SETARResult
        • SETARResult._comparison_label
        • SETARResult._from_fit
        • SETARResult._summary_table
        • SETARResult._weight_at
    • cultivars.univariate.unobserved_components
      • UnobservedComponents
      • UnobservedComponentsResult
        • UnobservedComponentsResult._smoothed_state
        • UnobservedComponentsResult._smoothed_state_cov
        • UnobservedComponentsResult._slices
        • UnobservedComponentsResult._params
        • UnobservedComponentsResult._comparison_label
        • UnobservedComponentsResult._component
        • UnobservedComponentsResult._component_std
        • UnobservedComponentsResult._from_fit
        • UnobservedComponentsResult._series
        • UnobservedComponentsResult._summary_table
  • cultivars.multivariate
    • cultivars.multivariate.large_dim
      • cultivars.multivariate.large_dim.bayesian
        • BVAR
        • BVARResult
      • cultivars.multivariate.large_dim.dynamic_factor
        • DFM
        • DFMResult
      • cultivars.multivariate.large_dim.factor_augmented
        • FAVAR
        • FAVARResult
      • cultivars.multivariate.large_dim.factor_volatility
        • FactorSV
        • FactorSVResult
      • cultivars.multivariate.large_dim.gibbs
        • GibbsBVAR
        • GibbsBVARResult
      • cultivars.multivariate.large_dim.graphical
        • GraphicalVAR
        • GraphicalVARResult
      • cultivars.multivariate.large_dim.hierarchical
        • HierarchicalBVAR
        • HierarchicalBVARResult
      • cultivars.multivariate.large_dim.sparse
        • SparseVAR
        • SparseVARResult
      • cultivars.multivariate.large_dim.spillover
        • Spillover
        • SpilloverResult
      • cultivars.multivariate.large_dim.student
        • StudentBVAR
        • StudentBVARResult
      • cultivars.multivariate.large_dim.volatility
        • BVARSV
        • BVARSVResult
    • cultivars.multivariate.nonlinear
      • cultivars.multivariate.nonlinear.functional_coefficient
        • FunctionalCoefficientVAR
        • FunctionalCoefficientVARResult
      • cultivars.multivariate.nonlinear.quantile
        • QVAR
        • QVARResult
      • cultivars.multivariate.nonlinear.smooth_transition
        • STVAR
        • STVARResult
      • cultivars.multivariate.nonlinear.threshold
        • TVAR
        • TVARResult
      • cultivars.multivariate.nonlinear.time_varying
        • TVPSVAR
        • TVPVAR
        • TVPVARSV
        • TVPSVARResult
        • TVPVARResult
        • TVPVARSVResult
    • cultivars.multivariate.reduced_form
      • cultivars.multivariate.reduced_form.closed_global
        • GVAR
        • GVARResult
      • cultivars.multivariate.reduced_form.error_correction
        • VECM
        • VECMX
        • VECMResult
        • VECMXResult
      • cultivars.multivariate.reduced_form.functional
        • FunctionalVAR
        • FunctionalVARResult
      • cultivars.multivariate.reduced_form.mixed_frequency
        • MFVAR
        • MIDASVAR
        • MFVARResult
        • MIDASVARResult
      • cultivars.multivariate.reduced_form.moving_average
        • VARMA
        • VARMAResult
      • cultivars.multivariate.reduced_form.panel
        • PanelVAR
        • PanelVARResult
      • cultivars.multivariate.reduced_form.term_structure
        • DynamicNelsonSiegel
        • DynamicNelsonSiegelResult
        • TimeVaryingNelsonSiegel
        • TimeVaryingNelsonSiegelResult
      • cultivars.multivariate.reduced_form.vector_autoregression
        • VAR
        • VARX
        • CoefficientInference
        • ConditionalLevels
        • VARResult
        • VARXResult
    • cultivars.multivariate.regime_switching
      • cultivars.multivariate.regime_switching.markov_switching
        • MarkovSwitchingDFM
        • MarkovSwitchingDFMResult
        • MarkovSwitchingSVAR
        • MarkovSwitchingSVARResult
        • MarkovSwitchingVAR
        • MarkovSwitchingVARResult
        • RegimeSystemResult
    • cultivars.multivariate.structural
      • cultivars.multivariate.structural.external_instruments
        • ProxySVAR
      • cultivars.multivariate.structural.factor_augmented
        • FactorAugmentedSVAR
        • FactorAugmentedSVARResult
      • cultivars.multivariate.structural.heteroskedacity
        • HeteroskedasticSVAR
      • cultivars.multivariate.structural.non_gaussian
        • NonGaussianSVAR
      • cultivars.multivariate.structural.perturbation
        • PerturbationDSGE
        • PerturbationDSGEPosterior
        • PerturbationDSGEResult
        • PerturbationDSGESolution
        • PerturbationModelSpecification
      • cultivars.multivariate.structural.set_identification
        • SetIdentifiedSVAR
        • SetIdentifiedSVARResult
      • cultivars.multivariate.structural.sign_restrictions
        • NarrativeSignRestrictedSVAR
        • SignRestrictedSVAR
        • SignRestrictedSVARResult
      • cultivars.multivariate.structural.stochastic_volatility
        • LongMemorySV
        • LongMemorySVResult
        • StochasticVolatilitySVAR
        • StochasticVolatilitySVARResult
      • cultivars.multivariate.structural.zero_restrictions
        • LongRunSVAR
        • MixedSVAR
        • RecursiveSVAR
        • SVARResult
        • ShortRunSVAR
  • cultivars.state_space
    • cultivars.state_space.linear_gaussian
      • DurbinKoopmanSmootherResult
      • KalmanFilterResult
      • LinearGaussianSSM
        • LinearGaussianSSM._at
        • LinearGaussianSSM._default_initial_cov
        • LinearGaussianSSM._forward
        • LinearGaussianSSM._from_arma
        • LinearGaussianSSM._from_nelson_siegel_system
        • LinearGaussianSSM._from_structural_system
        • LinearGaussianSSM._prepare_data
        • LinearGaussianSSM._simulate_forward
        • LinearGaussianSSM._validate_matrix
        • LinearGaussianSSM._validate_vector
    • cultivars.state_space.nonlinear
      • NonlinearSSM
        • NonlinearSSM._draw_states
        • NonlinearSSM._gaussian_update
        • NonlinearSSM._jacobian
        • NonlinearSSM._lag_stack_state_space
        • NonlinearSSM._measure
        • NonlinearSSM._predict
        • NonlinearSSM._prepare
        • NonlinearSSM._refuse_hooks
        • NonlinearSSM._rts_backward
        • NonlinearSSM._sigma_points
        • NonlinearSSM._smoother_gain
        • NonlinearSSM._systematic_resample
        • NonlinearSSM._unscented_weights
      • ParticleFilterResult
      • ParticleSmootherResult
      • RtsSmootherResult
    • cultivars.state_space.regime_switching
      • HamiltonFilterResult
      • KimFilterResult
      • KimSmootherResult
      • MarkovSwitchingSSM
        • MarkovSwitchingSSM._ar
        • MarkovSwitchingSSM._c
        • MarkovSwitchingSSM._k
        • MarkovSwitchingSSM._p
        • MarkovSwitchingSSM._pi0
        • MarkovSwitchingSSM._sigma2
        • MarkovSwitchingSSM._transition
      • RegimeSwitchingLinearSSM
  • cultivars.bayes
    • cultivars.bayes.chains
      • ConvergenceTest
        • ConvergenceTest._failing
        • ConvergenceTest._assess
    • cultivars.bayes.checks
      • PredictiveCheckTest
        • PredictiveCheckTest._flags
    • cultivars.bayes.combination
      • MarginalLikelihoodSelection
      • ModelCombinationSelection
    • cultivars.bayes.evidence
      • MarginalLikelihoodSelection
    • cultivars.bayes.priors
      • DirichletLaplacePrior
        • DirichletLaplacePrior._check
        • DirichletLaplacePrior._draw_scales
        • DirichletLaplacePrior._initial_scales
        • DirichletLaplacePrior._label
        • DirichletLaplacePrior._scale_variance
        • DirichletLaplacePrior._tracked
        • DirichletLaplacePrior._tracked_label
      • DummyInitialObservationPrior
        • DummyInitialObservationPrior._check
        • DummyInitialObservationPrior._label
      • HorseshoePrior
        • HorseshoePrior._check
        • HorseshoePrior._draw_scales
        • HorseshoePrior._initial_scales
        • HorseshoePrior._label
        • HorseshoePrior._scale_variance
        • HorseshoePrior._tracked
        • HorseshoePrior._tracked_label
      • IndependentNormalWishartPrior
        • IndependentNormalWishartPrior._label
        • IndependentNormalWishartPrior._minnesota
      • MinnesotaPrior
        • MinnesotaPrior._check
        • MinnesotaPrior._label
        • MinnesotaPrior._persistence
      • NoPrior
        • NoPrior._components
        • NoPrior._label
      • NormalGammaPrior
        • NormalGammaPrior._check
        • NormalGammaPrior._draw_scales
        • NormalGammaPrior._initial_scales
        • NormalGammaPrior._label
        • NormalGammaPrior._scale_variance
        • NormalGammaPrior._tracked
        • NormalGammaPrior._tracked_label
      • NormalInverseWishartPrior
        • NormalInverseWishartPrior._label
        • NormalInverseWishartPrior._minnesota
      • Prior
        • Prior._components
        • Prior._label
      • PriorContext
        • PriorContext._lead
      • RandomWalkVolatilityPrior
        • RandomWalkVolatilityPrior._label
      • SpikeAndSlabPrior
        • SpikeAndSlabPrior._check
        • SpikeAndSlabPrior._draw_scales
        • SpikeAndSlabPrior._initial_scales
        • SpikeAndSlabPrior._label
        • SpikeAndSlabPrior._scale_variance
        • SpikeAndSlabPrior._tracked
        • SpikeAndSlabPrior._tracked_label
      • SumOfCoefficientsPrior
        • SumOfCoefficientsPrior._check
        • SumOfCoefficientsPrior._label
      • VolatilityPrior
        • VolatilityPrior._label
  • cultivars.diagnostics
    • cultivars.diagnostics.breaks
      • BreakTest
        • BreakTest._metadata
        • BreakTest._notes
        • BreakTest._repr_fields
        • BreakTest._title
        • BreakTest._verdict
      • MultipleBreakTest
    • cultivars.diagnostics.cointegration
      • JohansenRankTest
    • cultivars.diagnostics.hypothesis
      • ChiSquaredTest
        • ChiSquaredTest._label
        • ChiSquaredTest._summary_table
        • ChiSquaredTest._title
      • HypothesisTest
        • HypothesisTest._pvalue_text
        • HypothesisTest._repr_html_
        • HypothesisTest._summary_table
      • LikelihoodRatioTest
        • LikelihoodRatioTest._label
        • LikelihoodRatioTest._title
      • TabulatedTest
        • TabulatedTest._metadata
        • TabulatedTest._notes
        • TabulatedTest._repr_fields
        • TabulatedTest._row
        • TabulatedTest._summary_table
        • TabulatedTest._title
        • TabulatedTest._verdict
      • WaldTest
        • WaldTest._label
        • WaldTest._title
    • cultivars.diagnostics.long_memory
      • LongMemoryEstimate
        • LongMemoryEstimate._record
        • LongMemoryEstimate._summary_table
    • cultivars.diagnostics.nonlinearity
      • BDSTest
        • BDSTest._row
        • BDSTest._summary_table
      • LinearityTest
        • LinearityTest._row
        • LinearityTest._summary_table
    • cultivars.diagnostics.seasonality
      • SeasonalUnitRootTest
        • SeasonalUnitRootTest._metadata
        • SeasonalUnitRootTest._notes
        • SeasonalUnitRootTest._title
    • cultivars.diagnostics.unit_roots
      • UnitRootTest
        • UnitRootTest._metadata
        • UnitRootTest._repr_fields
  • cultivars.forecast
    • cultivars.forecast.backtest
      • Backtest
        • Backtest._endog
        • Backtest._fit
        • Backtest._horizons
        • Backtest._names
        • Backtest._predict
        • Backtest._scheme
        • Backtest._start
        • Backtest._step
        • Backtest._univariate
        • Backtest._window
        • Backtest._forecast
        • Backtest._window_at
      • BacktestResult
        • BacktestResult._density_losses
        • BacktestResult._horizon_index
        • BacktestResult._series_index
        • BacktestResult._summary_table
    • cultivars.forecast.calibration
      • Calibration
        • Calibration._names
        • Calibration._paths
        • Calibration._realized
      • CalibrationResult
        • CalibrationResult._index
        • CalibrationResult._summary_table
    • cultivars.forecast.comparison
      • ClarkWestTest
        • ClarkWestTest._summary_table
      • EncompassingTest
        • EncompassingTest._summary_table
      • ForecastComparison
        • ForecastComparison._losses_a
        • ForecastComparison._losses_b
      • ForecastComparisonResult
        • ForecastComparisonResult._summary_table
      • GiacominiWhiteTest
        • GiacominiWhiteTest._summary_table
      • MincerZarnowitzTest
        • MincerZarnowitzTest._summary_table
    • cultivars.forecast.conditional
      • ConditionalForecastResult
        • ConditionalForecastResult._summary_table
    • cultivars.forecast.confidence_set
      • ModelConfidenceSetSelection
    • cultivars.forecast.fan
    • cultivars.forecast.scoring
      • DensityScore
        • DensityScore._names
        • DensityScore._paths
        • DensityScore._realized
        • DensityScore._kernel_log_score
      • DensityScoreResult
        • DensityScoreResult._summary_table
  • cultivars.spectral
    • cultivars.spectral.band_pass
      • BandPassResult
        • BandPassResult._summary_table
      • BaxterKingFilter
        • BaxterKingFilter._high
        • BaxterKingFilter._low
        • BaxterKingFilter._truncation
      • ChristianoFitzgeraldFilter
        • ChristianoFitzgeraldFilter._high
        • ChristianoFitzgeraldFilter._low
    • cultivars.spectral.causality
      • ConditionalSpectralCausality
        • ConditionalSpectralCausality._cause_index
        • ConditionalSpectralCausality._n_frequencies
        • ConditionalSpectralCausality._restricted
        • ConditionalSpectralCausality._result
      • ConditionalSpectralCausalityResult
        • ConditionalSpectralCausalityResult._index
        • ConditionalSpectralCausalityResult._summary_table
      • SpectralCausality
        • SpectralCausality._n_frequencies
        • SpectralCausality._result
      • SpectralCausalityResult
        • SpectralCausalityResult._index
        • SpectralCausalityResult._summary_table
    • cultivars.spectral.cycles
      • TurningPoints
        • TurningPoints._min_cycle
        • TurningPoints._min_phase
        • TurningPoints._window
      • TurningPointsResult
        • TurningPointsResult._summary_table
    • cultivars.spectral.density
      • SpectralDensity
        • SpectralDensity._n_frequencies
        • SpectralDensity._result
      • SpectralDensityResult
        • SpectralDensityResult._index
        • SpectralDensityResult._summary_table
    • cultivars.spectral.filters
      • BeveridgeNelsonDecomposition
        • BeveridgeNelsonDecomposition._result
      • ButterworthFilter
        • ButterworthFilter._order
        • ButterworthFilter._period
      • DecompositionFilterResult
        • DecompositionFilterResult._method_notes
        • DecompositionFilterResult._penalized_result
        • DecompositionFilterResult._summary_table
      • HamiltonFilter
        • HamiltonFilter._horizon
        • HamiltonFilter._lags
      • HodrickPrescottFilter
        • HodrickPrescottFilter._penalty
    • cultivars.spectral.periodogram
      • DaniellSpectrum
        • DaniellSpectrum._detrend
        • DaniellSpectrum._names
        • DaniellSpectrum._panel
        • DaniellSpectrum._span
      • MultitaperSpectrum
        • MultitaperSpectrum._bandwidth
        • MultitaperSpectrum._detrend
        • MultitaperSpectrum._names
        • MultitaperSpectrum._panel
        • MultitaperSpectrum._tapers
      • SpectrumEstimate
        • SpectrumEstimate._index
        • SpectrumEstimate._summary_table
      • WelchSpectrum
        • WelchSpectrum._detrend
        • WelchSpectrum._names
        • WelchSpectrum._panel
        • WelchSpectrum._segment
    • cultivars.spectral.wavelets
      • MODWT
        • MODWT._levels
        • MODWT._wavelet
      • MODWTResult
        • MODWTResult._summary_table
      • WaveletCoherence
        • WaveletCoherence._alpha
        • WaveletCoherence._omega0
        • WaveletCoherence._per_octave
        • WaveletCoherence._seed
        • WaveletCoherence._smallest
        • WaveletCoherence._surrogates
      • WaveletCoherenceResult
        • WaveletCoherenceResult._summary_table
  • Engine reference
  • cultivars.multivariate
  • cultivars.multivariate.structural
  • cultivars.multivariate.structural.sign_restrictions
  • NarrativeSignRestrictedSVAR
  • NarrativeSignRestrictedSVAR._seed

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API reference

Every public model, test and result, with the mathematics it implements and a runnable example.

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Examples

Research workflows on live FRED data, from identification to forecast evaluation, as scripts and notebooks.

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Engine

The numerical core and internal layers the public surface is built on, for contributors and the curious.

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© 2026, Nikhil Sunder. Released under the MIT License. cultivars is an independent open-source project and is not affiliated with the Federal Reserve Bank of St. Louis; FRED® is a registered trademark of the Federal Reserve Bank of St. Louis.

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