HMath.TimeSeries.Diagnostics¶

Description

Explicit-lag stationarity statistics, bounded change-point/warping reference algorithms, and forecast diagnostics. Statistical critical values are model-dependent approximations, not guarantees of stationarity.

On this page¶

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.

Documentation

Deterministic

data Deterministic Source #

Stationarity-test deterministic terms: level-only or linear-trend specification.

Constructors

Level
LinearTrend

Instances

Instances details

Show Deterministic Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods showsPrec :: Int -> Deterministic -> ShowS # show :: Deterministic -> String # showList :: [Deterministic] -> ShowS #
Eq Deterministic Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods (==) :: Deterministic -> Deterministic -> Bool # (/=) :: Deterministic -> Deterministic -> Bool #

Stationarity

data Stationarity Source #

Significance level paired with critical value. ADF rejects for smaller statistics, KPSS for larger ones. No interpolated p value is fabricated.

Constructors

Stationarity

Fields

stationarityStatistic :: Double
Computed ADF/KPSS stationarity test statistic.
stationarityCriticalValues :: [(Double, Double)]
Significance-level and critical-value pairs for the selected test/deterministic specification.
stationarityObservations :: Int
Number of effective observations used by the test.
stationarityNull :: String
Human-readable null hypothesis, which differs between ADF and KPSS.

Instances

Instances details

Show Stationarity Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods showsPrec :: Int -> Stationarity -> ShowS # show :: Stationarity -> String # showList :: [Stationarity] -> ShowS #
Eq Stationarity Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods (==) :: Stationarity -> Stationarity -> Bool # (/=) :: Stationarity -> Stationarity -> Bool #

augmentedDickeyFuller

augmentedDickeyFuller :: Deterministic -> Int -> [Double] -> Either MathError Stationarity Source #

OLS of delta x_t on x_(t-1), an intercept, optional trend, and explicitly supplied lagged differences. Returns the lagged-level t statistic. Critical values use MacKinnon (2010) finite-sample polynomials for one series: https:/www.statsmodels.orgstablegeneratedstatsmodels.tsa.stattools.adfuller.html . There is no automatic lag selection or normal/Student-t p-value shortcut.

kpss

kpss :: Deterministic -> Int -> [Double] -> Either MathError Stationarity Source #

KPSS leveltrend stationarity with an explicit BartlettNewey--West lag bandwidth. Critical values are Table 1 of Kwiatkowski et al. (1992), as documented at https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.kpss.html .

changePoints

changePoints :: Double -> Int -> [Double] -> Either MathError [Int] Source #

Exact quadratic dynamic programming for piecewise-constant least squares, minimizing total within-segment SSE plus penalty per change. Break indices are zero-based starts of new segments. No pruning/approximation is used.

cusum

cusum :: Double -> Double -> Double -> Double -> [Double] -> Either MathError [Int] Source #

Two-sided Page CUSUM with supplied baseline mean/SD. A threshold crossing emits its index and resets both cumulative scores. drift and threshold are in standardized observation units.

anomalies

anomalies :: Double -> [Double] -> Either MathError [Int] Source #

Median/MAD outliers, using the normal-consistency factor 1.4826022185. If MAD is zero, every value different from the median is an anomaly.

DTWResult

data DTWResult Source #

Dynamic-time-warping accumulated distance and original-series zero-based alignment path.

Constructors

DTWResult
Fields dtwDistance :: Double Accumulated dynamic-time-warping path cost. dtwPath :: [(Int, Int)] Optimal alignment as zero-based index pairs from the two input series.

Instances

Instances details

Show DTWResult Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods showsPrec :: Int -> DTWResult -> ShowS # show :: DTWResult -> String # showList :: [DTWResult] -> ShowS #
Eq DTWResult Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods (==) :: DTWResult -> DTWResult -> Bool # (/=) :: DTWResult -> DTWResult -> Bool #

dynamicTimeWarping

dynamicTimeWarping :: Int -> [Double] -> [Double] -> Either MathError DTWResult Source #

Absolute local cost; Sakoe--Chiba radius must include both endpoints. Returns the unnormalized path cost, with diagonalupleft tie priority.

spectrum

spectrum :: Double -> [Double] -> Either MathError [(Double, Double)] Source #

One-sided unwindowed periodogram density. Non-DC/Nyquist bins are doubled; integral of density over frequency equals the sample mean square.

ForecastMetric

data ForecastMetric Source #

Prediction-error metric selector; scale/zero-denominator preconditions are checked by the metric function.

Constructors

MAE
MSE
RMSE
MAPE
SMAPE
MASE Int [Double]

Instances

Instances details

Show ForecastMetric Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods showsPrec :: Int -> ForecastMetric -> ShowS # show :: ForecastMetric -> String # showList :: [ForecastMetric] -> ShowS #
Eq ForecastMetric Source #
Instance details Defined in HMath.TimeSeries.Diagnostics Methods (==) :: ForecastMetric -> ForecastMetric -> Bool # (/=) :: ForecastMetric -> ForecastMetric -> Bool #

forecastError

forecastError :: ForecastMetric -> [Double] -> [Double] -> Either MathError Double Source #

MAPE and sMAPE are percentages; zero/zero sMAPE contributes zero. MASE supplies its separate training set and seasonal lag to avoid test leakage.