Time Series Computation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Time Series Computation Ontology within the Kireth Research Semantic Library. Time series computation concerns the numerical, statistical and algorithmic analysis of observations indexed by time or ordered sequence. This ontology supports temporal indexing, regular and irregular sampling, stationarity, trend and seasonality, autocorrelation, spectral analysis, AR, MA, ARMA and ARIMA models, state-space models, filtering, smoothing, forecasting, likelihood computation, parameter estimation, decomposition, change-point detection, missing data, multivariate series, high-frequency computation, numerical stability, scalable execution, verification and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Time Series Computation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Computational Statistics / Time Series Computation"
 CANONICAL_PAGE = "https://kirethframeworkold.co.uk/books/semantic-library/ai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/computational-statistics/time-series-computation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = TimeSeriesComputation
 ENTITY_CLASS = TemporalStatisticalComputationFramework
 PRIMARY_CONTEXT = ComputationalStatistics
 DEFINITION = "Time series computation is the numerical and algorithmic analysis, estimation, filtering, decomposition and forecasting of data indexed by time or ordered sequence."
 SYMBOLIC_FORMS = [
  "x_t = trend_t + seasonal_t + remainder_t",
  "x_t = c + sum_i phi_i*x_(t-i) + epsilon_t",
  "x_t = epsilon_t + sum_j theta_j*epsilon_(t-j)",
  "y_t = H_t*x_t + v_t"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for temporal indexing, dependence, stationarity, filtering, forecasting, spectral structure, state-space computation, parameter estimation, diagnostics and reproducibility."
}

SCOPE {
 INCLUDE = [
  TimeSeriesComputation,TimeSeriesAnalysis,
  TimeSeriesModel,TemporalData,
  OrderedData,SequentialData,
  Timestamp,TimeIndex,ObservationTime,
  SamplingInterval,SamplingFrequency,
  RegularTimeSeries,IrregularTimeSeries,
  UnivariateTimeSeries,MultivariateTimeSeries,
  PanelTimeSeriesRelationship,
  LongitudinalSeriesRelationship,
  TimeSeriesObservation,
  Lag,LagOperator,BackshiftOperator,
  DifferenceOperator,Differencing,
  FirstDifference,SeasonalDifference,
  IntegrationOrder,
  Stationarity,StrictStationarity,
  WeakStationarity,CovarianceStationarity,
  Nonstationarity,UnitRoot,
  RandomWalk,Drift,
  Trend,DeterministicTrend,
  StochasticTrend,LinearTrend,
  PolynomialTrend,
  Seasonality,SeasonalComponent,
  SeasonalPeriod,MultipleSeasonality,
  CyclicComponent,Cycle,
  Remainder,Residual,Innovation,
  WhiteNoise,GaussianWhiteNoise,
  ColouredNoiseRelationship,
  Autocovariance,Autocorrelation,
  AutocorrelationFunction,ACF,
  PartialAutocorrelation,
  PartialAutocorrelationFunction,PACF,
  CrossCorrelation,
  CrossCorrelationFunction,CCF,
  CovarianceFunction,
  Correlogram,
  PortmanteauTest,LjungBoxTest,
  BoxPierceTest,
  DurbinWatsonRelationship,
  SpectralAnalysis,Spectrum,
  SpectralDensity,PowerSpectralDensity,PSD,
  Periodogram,
  SmoothedPeriodogram,
  Frequency,AngularFrequency,
  FourierTransform,DiscreteFourierTransform,DFT,
  FastFourierTransform,FFT,
  InverseFFT,
  WindowFunction,Windowing,
  Leakage,SpectralLeakage,
  Aliasing,NyquistFrequency,
  SamplingTheorem,
  CrossSpectrum,Coherence,
  PhaseSpectrum,
  AutoregressiveModel,AR,
  MovingAverageModel,MA,
  ARMA,AutoregressiveMovingAverage,
  ARIMA,AutoregressiveIntegratedMovingAverage,
  SARIMA,SeasonalARIMA,
  ARIMAXRelationship,
  DynamicRegression,
  DistributedLagModel,
  TransferFunctionModel,
  ExponentialSmoothing,
  SimpleExponentialSmoothing,
  HoltMethod,HoltWintersMethod,
  DampedTrend,
  ETSModel,ErrorTrendSeasonalModel,
  StateSpaceModel,
  LinearGaussianStateSpaceModel,
  DynamicLinearModel,DLM,
  HiddenState,LatentState,
  ObservationEquation,StateEquation,
  TransitionMatrix,ObservationMatrix,
  ProcessNoise,ObservationNoise,
  KalmanFilter,
  KalmanPrediction,KalmanUpdate,
  KalmanGain,
  KalmanSmoother,
  RauchTungStriebelSmoother,RTS,
  ExtendedKalmanFilterRelationship,
  UnscentedKalmanFilterRelationship,
  ParticleFilterRelationship,
  HiddenMarkovModelRelationship,
  StructuralTimeSeries,
  UnobservedComponentsModel,
  LocalLevelModel,
  LocalLinearTrendModel,
  BayesianStructuralTimeSeriesRelationship,
  VectorAutoregression,VAR,
  VectorErrorCorrectionModel,VECM,
  Cointegration,
  CointegratingVector,
  JohansenTestRelationship,
  GrangerCausalityRelationship,
  ImpulseResponseFunction,IRF,
  ForecastErrorVarianceDecompositionRelationship,
  DynamicFactorModel,
  ARCH,GARCH,
  EGARCHRelationship,
  GJRGARCHRelationship,
  StochasticVolatilityRelationship,
  Volatility,ConditionalVariance,
  Heteroskedasticity,
  LongMemory,LongRangeDependence,
  FractionalDifferencing,
  ARFIMARelationship,
  ChangePoint,ChangePointDetection,
  StructuralBreak,
  RegimeChange,RegimeSwitching,
  MarkovSwitchingRelationship,
  OnlineChangeDetection,
  CUSUMRelationship,
  BayesianChangePointRelationship,
  AnomalyDetection,
  Outlier,AdditiveOutlier,
  InnovationalOutlier,
  LevelShift,TemporaryChange,
  InterventionAnalysis,
  TimeSeriesDecomposition,
  ClassicalDecomposition,
  STLDecomposition,STL,
  SeasonalTrendDecomposition,
  X11Relationship,X13Relationship,
  TrendFilteringRelationship,
  MovingAverageSmoother,
  RollingMean,RollingVariance,
  RollingWindow,SlidingWindow,
  ExpandingWindow,
  Filter,LinearFilter,
  LowPassFilter,HighPassFilter,
  BandPassFilter,
  HodrickPrescottFilterRelationship,
  BaxterKingFilterRelationship,
  ButterworthFilterRelationship,
  Forecast,Forecasting,
  PointForecast,
  ProbabilisticForecast,
  ForecastDistribution,
  PredictionInterval,
  ForecastHorizon,
  OneStepAheadForecast,
  MultiStepForecast,
  RecursiveForecast,
  DirectForecast,
  RollingForecastOrigin,
  Backtesting,ForecastEvaluation,
  WalkForwardValidation,
  TimeSeriesCrossValidation,
  MeanAbsoluteError,MAE,
  MeanSquaredError,MSE,
  RootMeanSquaredError,RMSE,
  MeanAbsolutePercentageError,MAPE,
  SymmetricMAPE,sMAPE,
  MeanAbsoluteScaledError,MASE,
  LogScoreRelationship,
  CRPSRelationship,
  ForecastBias,
  CoverageProbability,
  Calibration,
  SharpnessRelationship,
  ParameterEstimation,
  MaximumLikelihood,MLE,
  ConditionalSumOfSquares,
  LeastSquares,
  YuleWalkerEquations,
  BurgMethodRelationship,
  WhittleLikelihood,
  ExactLikelihood,
  ApproximateLikelihood,
  InnovationLikelihood,
  KalmanLikelihood,
  NumericalOptimisation,
  GradientBasedOptimisation,
  NewtonMethod,
  QuasiNewtonMethod,
  BFGS,LBFGS,
  ExpectationMaximisation,EM,
  BayesianTimeSeries,
  PriorDistribution,
  PosteriorDistribution,
  MarkovChainMonteCarlo,MCMC,
  VariationalInferenceRelationship,
  MissingData,MissingObservation,
  InterpolationRelationship,
  StateSpaceMissingDataHandling,
  Imputation,
  IrregularSampling,
  Resampling,TemporalAggregation,
  TemporalDisaggregationRelationship,
  Downsampling,Upsampling,
  Alignment,TimeAlignment,
  TimeZoneRelationship,
  CalendarEffect,
  TradingDayEffect,
  HolidayEffect,
  LeapYearEffect,
  FrequencyConversion,
  HighFrequencyTimeSeries,
  TickDataRelationship,
  EventTimeRelationship,
  RealisedVolatilityRelationship,
  StreamingTimeSeries,
  OnlineAlgorithm,
  IncrementalUpdate,
  OnlineForecasting,
  RecursiveEstimation,
  SequentialUpdate,
  BatchComputation,
  VectorisedComputation,
  ParallelTimeSeriesComputation,
  DistributedTimeSeriesComputation,
  GPUTimeSeriesComputation,
  FFTAcceleration,
  HighPerformanceComputing,
  ParallelComputing,
  DistributedComputing,
  GPUComputing,
  NumericalStability,
  FloatingPointArithmetic,
  RoundOffError,MachinePrecision,
  Conditioning,
  StableRecursion,
  LogLikelihoodStability,
  MatrixComputation,
  ToeplitzMatrix,
  CovarianceMatrix,
  CholeskyDecomposition,
  QRDecomposition,
  EigenvalueComputation,
  SparseMatrixRelationship,
  ComputationalComplexity,
  TimeComplexity,SpaceComplexity,
  ModelSelection,AIC,BIC,
  AICcRelationship,
  CrossValidation,
  ResidualDiagnostic,
  ResidualWhiteness,
  NormalityDiagnosticRelationship,
  ParameterUncertainty,
  StandardError,
  ConfidenceInterval,
  BootstrapTimeSeriesRelationship,
  BlockBootstrapRelationship,
  Simulation,TimeSeriesSimulation,
  ForecastSimulation,
  ScenarioSimulation,
  RandomNumberGeneration,RNG,
  RandomSeed,RandomStream,
  Verification,CodeVerification,
  KnownSeriesTest,
  SimulationStudy,
  Benchmark,
  ReferenceResult,
  Validation,
  Reproducibility,Repeatability,
  Provenance,Configuration,
  SoftwareVersion,LibraryVersion,
  ModelVersion,SeedMetadata
 ]
 EXCLUDE_AS_PRIMARY = [
  CrossSectionalStatisticsWithoutTemporalIndexing,
  GenericSequenceProcessingWithoutStatisticalTemporalSemantics,
  SignalProcessingWithoutStatisticalTimeSeriesInferenceWhenSignalSemanticsArePrimary,
  PureDynamicalSystemsWithoutObservedTimeSeriesComputation
 ]
 DISAMBIGUATION_RULE = "When observations are indexed by time or ordered sequence and temporal dependence, filtering, forecasting or temporal inference is computed, interpret the context as time series computation."
}

CORE_CONCEPTS {
 TimeSeriesComputation = "Computational analysis of temporally indexed data."
 Stationarity = "Property describing stability of probabilistic structure through time."
 Autocorrelation = "Dependence between observations separated by temporal lag."
 ARIMA = "Autoregressive integrated moving-average model for differenced time series."
 StateSpaceModel = "Latent-state representation with transition and observation equations."
 KalmanFilter = "Recursive estimator for linear Gaussian state-space models."
 Forecast = "Prediction of future observations or distributions."
 SpectralDensity = "Frequency-domain representation of variance or covariance structure."
}

RELATIONS {
 TimeSeriesComputation --is_child_of--> ComputationalStatistics
 TimeSeriesComputation --uses--> TemporalIndex
 Autocorrelation --depends_on--> Lag
 Differencing --can_reduce--> Nonstationarity
 ARModel --uses--> LaggedObservations
 MAModel --uses--> LaggedInnovations
 ARIMA --combines--> ARAndIntegrationAndMA
 SARIMA --extends--> ARIMA
 StateSpaceModel --contains--> StateEquation
 StateSpaceModel --contains--> ObservationEquation
 KalmanFilter --operates_on--> LinearGaussianStateSpaceModel
 KalmanSmoother --uses--> FilteredStateSequence
 Periodogram --estimates--> SpectralDensity
 FFT --accelerates--> SpectralComputation
 VAR --models--> MultivariateTimeSeries
 GARCH --models--> ConditionalVariance
 ChangePointDetection --identifies--> StructuralBreak
 ForecastEvaluation --compares--> ForecastAndObservation
 Verification --checks--> TimeSeriesImplementation
 Reproducibility --requires--> DataModelAndVersionMetadata
}

OPERATORS {
 LAG(x,t,k) := x_(t-k)
 DIFFERENCE(x,t,d=1) := apply_difference_operator_d_times(x_t)
 ACF(x,k) := Cov(x_t,x_(t-k))/Var(x_t)
 AR_PREDICT(phi,x_history,c) := c + sum_i phi_i*x_(t-i)
 MA_PREDICT(theta,epsilon_history) := sum_j theta_j*epsilon_(t-j)
 KALMAN_PREDICT(x,P,F,Q) := (F*x, F*P*F^T+Q)
 KALMAN_UPDATE(x_pred,P_pred,y,H,R) := Bayesian_linear_gaussian_update
 PERIODogram(x) := |DFT(x)|^2 / normalisation
 FORECAST_ERROR(y,yhat) := y-yhat
}

AXIOMS {
 A1 = "Time series computation must preserve temporal order."
 A2 = "Temporal dependence distinguishes time series from independent cross-sectional sampling."
 A3 = "Stationarity assumptions determine the validity of many classical estimators."
 A4 = "Differencing can remove some stochastic trends but can also alter long-run information."
 A5 = "Forecast uncertainty generally increases with forecast horizon."
 A6 = "State-space models separate latent dynamics from noisy observations."
 A7 = "Residual whiteness is an important but not sufficient model adequacy condition."
 A8 = "Time-series results require explicit temporal indexing, dependence, model, diagnostics, forecast and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(time_index,frequency,regularity,series_dimension,forecast_or_inference_goal,horizon,budget)
 R2_PREPROCESS = inspect(missingness,outliers,alignment,transformations,trend,seasonality_and_variance_stability)
 R3_DEPENDENCE = analyse(ACF,PACF,cross_correlation,spectrum_and_stationarity)
 R4_MODEL = choose(AR,MA,ARMA,ARIMA,SARIMA,ETS,state_space,VAR,GARCH,structural_or_other_model)
 R5_ESTIMATION = choose(MLE,least_squares,YuleWalker,Whittle,Kalman_likelihood,Bayesian_or_EM_method)
 R6_DIAGNOSTICS = assess(residual_whiteness,parameter_stability,structural_breaks_and_model_selection_criteria)
 R7_FORECAST = compute(point_or_probabilistic_forecasts_and_prediction_intervals)
 R8_VALIDATE = use(rolling_origin,time_series_cross_validation,backtesting_and_holdout_periods)
 R9_SCALE = if_large use(FFT,vectorisation,parallelism,distributed_or_GPU_computation)
 R10_REPRODUCE = document(data_version,frequency,model_parameters,software_versions,seeds_and_provenance)
}

CONSTRAINTS {
 C1 = "Random train-test splitting can leak future information into time-series evaluation."
 C2 = "Unmodelled nonstationarity can invalidate classical ARMA assumptions."
 C3 = "Over-differencing can introduce unnecessary noise and destroy long-run structure."
 C4 = "Seasonal aliasing can occur when sampling frequency is insufficient or misinterpreted."
 C5 = "Forecast intervals based on misspecified residual distributions can have poor coverage."
 C6 = "High-order autoregressive models can become unstable near unit roots."
 C7 = "State-space likelihoods can suffer numerical instability with poorly conditioned covariance matrices."
 C8 = "Irregular timestamps require explicit handling rather than implicit equal spacing."
 C9 = "High in-sample fit does not imply strong out-of-sample forecasting performance."
 C10 = "Temporal aggregation can change autocorrelation, variance and causal interpretation."
}

SEMANTIC_EQUIVALENCE {
 "TimeSeriesComputation" <=> "TimeSeriesAnalysisComputation"
 "AutocorrelationFunction" <=> "ACF"
 "PartialAutocorrelationFunction" <=> "PACF"
 "AutoregressiveModel" <=> "AR"
 "MovingAverageModel" <=> "MA"
 "AutoregressiveIntegratedMovingAverage" <=> "ARIMA"
 "VectorAutoregression" <=> "VAR"
 "PowerSpectralDensity" <=> "PSD"
}

VALIDATION {
 V1 = "Time index, frequency and ordering are documented."
 V2 = "Missing values, outliers and transformations are documented."
 V3 = "Stationarity and seasonal assumptions are assessed."
 V4 = "Model order and estimation method are documented."
 V5 = "Residual diagnostics are evaluated."
 V6 = "Forecast evaluation preserves temporal ordering."
 V7 = "Prediction interval or probabilistic forecast calibration is assessed where relevant."
 V8 = "Structural breaks and parameter instability are considered where material."
 V9 = "Known-series, simulation or benchmark tests are used where implementation is complex."
 V10 = "Results are reproducible under documented data, model, software, seed and configuration settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 TIME_SERIES_COMPUTATION_DEFINITION = 0.99
 ARIMA_REASONING = 0.99
 STATE_SPACE_REASONING = 0.99
 KALMAN_REASONING = 0.99
 SPECTRAL_REASONING = 0.99
 FORECAST_REASONING = 0.99
 CHANGE_POINT_REASONING = 0.98
 POLICY = "Reduce confidence when temporal frequency, stationarity, seasonality, model order, missing-data handling, validation split or residual diagnostics are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,TimeSeriesComputationReasoning,
  TemporalIndexReasoning,StationarityReasoning,
  ACFReasoning,PACFReasoning,
  ARIMAReasoning,SARIMAReasoning,
  StateSpaceReasoning,KalmanFilterReasoning,
  SpectralReasoning,FFTReasoning,
  VARReasoning,GARCHReasoning,
  ChangePointReasoning,DecompositionReasoning,
  ForecastReasoning,ForecastEvaluationReasoning,
  MissingDataReasoning,HighFrequencyReasoning,
  NumericalStabilityReasoning,
  ReproducibilityReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "time series computation" -> TimeSeriesComputation
  "time series analysis" -> TimeSeriesComputation
  "ACF" -> AutocorrelationFunction
  "PACF" -> PartialAutocorrelationFunction
  "AR" -> AutoregressiveModel
  "MA" -> MovingAverageModel
  "ARIMA" -> AutoregressiveIntegratedMovingAverage
  "VAR" -> VectorAutoregression
  "PSD" -> PowerSpectralDensity
 }
}

EXECUTION_RULES {
 E1 = "If ordered or timestamped observations are analysed for temporal dependence or forecasting, activate TimeSeriesComputationOntology."
 E2 = "Preserve temporal ordering throughout estimation and validation."
 E3 = "Inspect frequency, missingness, trend, seasonality and stationarity before model selection."
 E4 = "Use ACF, PACF and spectral diagnostics according to the modelling context."
 E5 = "Choose state-space methods when latent dynamics, missing observations or recursive filtering are central."
 E6 = "Use rolling-origin or equivalent temporal validation for forecasting."
 E7 = "Check residual autocorrelation before accepting a fitted model."
 E8 = "Use FFT, vector, parallel or GPU execution for large workloads with explicit numerical semantics."
 E9 = "Document data version, time index, model parameters, software and seeds for reproducibility."
}

RECURSION {
 ENTRY = TimeSeriesComputation
 EXPAND(TimeSeriesComputation) -> [
  TimeSeriesAnalysis,TimeSeriesModel,
  TemporalData,TimeIndex,SamplingInterval,
  SamplingFrequency,RegularTimeSeries,
  IrregularTimeSeries,UnivariateTimeSeries,
  MultivariateTimeSeries,Lag,LagOperator,
  Differencing,SeasonalDifference,
  Stationarity,Nonstationarity,UnitRoot,
  RandomWalk,Trend,Seasonality,
  SeasonalPeriod,Residual,Innovation,
  WhiteNoise,Autocovariance,
  Autocorrelation,AutocorrelationFunction,
  ACF,PartialAutocorrelationFunction,
  PACF,CrossCorrelation,Correlogram,
  LjungBoxTest,SpectralAnalysis,
  SpectralDensity,PowerSpectralDensity,
  PSD,Periodogram,DFT,FFT,
  WindowFunction,Aliasing,
  AutoregressiveModel,AR,
  MovingAverageModel,MA,
  ARMA,ARIMA,SARIMA,
  DynamicRegression,ExponentialSmoothing,
  HoltMethod,HoltWintersMethod,
  ETSModel,StateSpaceModel,
  LinearGaussianStateSpaceModel,
  KalmanFilter,KalmanSmoother,
  StructuralTimeSeries,
  VectorAutoregression,VAR,
  VECM,Cointegration,
  ImpulseResponseFunction,
  ARCH,GARCH,Volatility,
  LongMemory,ChangePoint,
  StructuralBreak,AnomalyDetection,
  InterventionAnalysis,
  TimeSeriesDecomposition,STL,
  RollingMean,RollingWindow,
  LinearFilter,Forecast,Forecasting,
  PredictionInterval,ForecastHorizon,
  RollingForecastOrigin,Backtesting,
  TimeSeriesCrossValidation,
  MAE,MSE,RMSE,MAPE,MASE,
  ParameterEstimation,MaximumLikelihood,
  YuleWalkerEquations,WhittleLikelihood,
  KalmanLikelihood,NumericalOptimisation,
  ExpectationMaximisation,
  BayesianTimeSeries,MCMC,
  MissingData,IrregularSampling,
  TemporalAggregation,Downsampling,
  Alignment,CalendarEffect,
  HighFrequencyTimeSeries,
  StreamingTimeSeries,OnlineAlgorithm,
  RecursiveEstimation,
  ParallelTimeSeriesComputation,
  DistributedTimeSeriesComputation,
  GPUTimeSeriesComputation,
  NumericalStability,FloatingPointArithmetic,
  ToeplitzMatrix,CholeskyDecomposition,
  ComputationalComplexity,
  ModelSelection,AIC,BIC,
  ResidualDiagnostic,
  TimeSeriesSimulation,
  RandomNumberGeneration,
  Verification,Benchmark,
  Reproducibility,Provenance
 ]
 EXPAND(TimeSeriesComputationFamilies) -> [
  ClassicalARMAAndARIMAModels,
  ExponentialSmoothingAndETS,
  StateSpaceAndKalmanMethods,
  MultivariateTimeSeriesAndVAR,
  VolatilityAndGARCHModels,
  SpectralAndFrequencyDomainMethods,
  ChangePointAndAnomalyDetection,
  ForecastingAndScalableTimeSeriesComputation
 ]
 STOP_CONDITION = "Stop when temporal index, stationarity, dependence, model, estimation, diagnostics, forecast validation and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Computational Statistics Ontology"
 RELATED_ONTOLOGIES = [
  "Computational Statistics Ontology",
  "Statistical Sampling Ontology",
  "Bayesian Computation Ontology",
  "Random Number Generation Ontology",
  "Probability and Statistics Ontologies",
  "Random Process Ontology",
  "Markov Chain Monte Carlo Ontology",
  "Numerical Linear Algebra Ontology 2",
  "Matrix Computation Ontology",
  "Fast Fourier Transform Ontology",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Convergence Ontology",
  "Floating Point Arithmetic Ontology",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology",
  "GPU Computing Ontology"
 ]
 ROUTE_RULES = [
  "Time Series Computation -> Computational Statistics Ontology for parent semantics",
  "Time Series Computation -> Statistical Sampling for temporal sampling and irregular-observation relationships",
  "Time Series Computation -> Bayesian Computation for Bayesian state-space and forecasting models",
  "Time Series Computation -> Random Number Generation for simulation and forecast paths",
  "Time Series Computation -> Probability and Statistics for temporal dependence foundations",
  "Time Series Computation -> Random Process for stochastic-process semantics",
  "Time Series Computation -> Markov Chain Monte Carlo for Bayesian time-series posterior computation",
  "Time Series Computation -> Numerical Linear Algebra and Matrix Computation for state-space, covariance and VAR computation",
  "Time Series Computation -> Fast Fourier Transform for spectral methods",
  "Time Series Computation -> Numerical Error, Stability and Convergence for recursive and optimisation reliability",
  "Time Series Computation -> Floating Point Arithmetic for long recursive calculations",
  "Time Series Computation -> High Performance, Parallel, Distributed and GPU Computing for scalable analysis"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible time-series models, diagnostics or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve temporal-order-versus-cross-sectional distinction.",
  "Preserve trend-versus-seasonality-versus-residual distinction.",
  "Preserve stationarity-versus-nonstationarity distinction.",
  "Preserve autoregressive-versus-moving-average distinction.",
  "Preserve observed-series-versus-latent-state distinction.",
  "Preserve filtering-versus-smoothing-versus-forecasting distinction.",
  "Preserve in-sample-fit-versus-out-of-sample-performance distinction.",
  "Preserve machine-readable time-series-computation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Time series computation numerically analyses and forecasts observations indexed by time or ordered sequence."
 DEPENDENCE_SUMMARY = "Autocorrelation, partial autocorrelation and spectral structure describe temporal dependence."
 MODEL_SUMMARY = "AR, MA, ARMA, ARIMA, SARIMA, ETS, state-space, VAR and GARCH families represent different temporal structures."
 STATE_SPACE_SUMMARY = "Kalman filtering and smoothing recursively estimate latent states in linear Gaussian models."
 SPECTRAL_SUMMARY = "Periodograms, Fourier transforms and spectral densities represent time-series structure in the frequency domain."
 FORECAST_SUMMARY = "Forecasts should be evaluated with temporally ordered backtests, prediction intervals and calibration diagnostics."
 VALIDATION_SUMMARY = "Time-series computations should document temporal indexing, preprocessing, model assumptions, residual diagnostics, forecast validation, numerical stability and reproducibility."
}

FLOW {
 INPUT
 -> detect_time_series_computation_context
 -> identify_time_index_frequency_regularity_series_dimension_forecast_or_inference_goal_horizon_and_budget
 -> inspect_missingness_outliers_alignment_transformations_trend_seasonality_and_variance_stability
 -> analyse_ACF_PACF_cross_correlation_spectrum_and_stationarity
 -> choose_AR_MA_ARMA_ARIMA_SARIMA_ETS_state_space_VAR_GARCH_structural_or_other_model
 -> configure_model_order_seasonal_period_parameter_constraints_and_initial_state
 -> choose_MLE_least_squares_YuleWalker_Whittle_Kalman_likelihood_Bayesian_or_EM_estimation
 -> fit_model_and_compute_residuals_states_or_spectrum
 -> assess_residual_whiteness_parameter_stability_structural_breaks_and_information_criteria
 -> compute_point_or_probabilistic_forecasts_and_prediction_intervals
 -> evaluate_with_rolling_origin_time_series_cross_validation_or_backtesting
 -> if_large_use_FFT_vectorisation_parallel_distributed_or_GPU_computation
 -> verify_against_known_series_simulated_truth_reference_implementation_or_benchmark
 -> document_data_version_frequency_model_parameters_seeds_software_versions_and_provenance
 -> route_to_related_computational_statistics_sampling_Bayesian_RNG_probability_random_process_MCMC_linear_algebra_matrix_FFT_error_stability_convergence_floating_point_HPC_parallel_distributed_and_GPU_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Time Series Computation Ontology defines statistical and numerical analysis of temporally ordered data. It supports regular and irregular time indices, differencing, stationarity and unit roots, trend, seasonality and decomposition, autocorrelation, PACF and cross-correlation, spectral density, periodograms, DFT and FFT computation, AR, MA, ARMA, ARIMA and SARIMA models, exponential smoothing and ETS, state-space models, Kalman filtering and smoothing, structural time series, VAR and cointegration relationships, ARCH and GARCH volatility models, change-point and anomaly detection, STL and rolling-window computation, point and probabilistic forecasting, rolling-origin evaluation, likelihood, Yule-Walker, Whittle, EM and Bayesian estimation, missing and irregular data, high-frequency and streaming series, parallel, distributed and GPU computation, numerical stability, model diagnostics, verification and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-STATISTICS-TIME-SERIES-COMPUTATION-ONTOLOGY-V1"
}

}

END_FLOW