HMath.TimeSeries¶

Description

Timestamped observations, bounded CPU forecasting, decomposition and diagnostics. See the individual modules for missing-data, fit and error contracts.

On this page¶

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.

Documentation

difference

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

Apply (1-B^lag)^order. Zero order preserves data; at least one output is required.

autocorrelation

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

Biased covariance divided by lag-zero covariance, global sample mean.

resample

resample :: Resampling -> Double -> Double -> Int -> Series -> Either MathError Series Source #

Linear samples require brackets (or an exact timestamp). Bins are [start+i*step,start+(i+1)*step); the final right endpoint is excluded.

crossCorrelation

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

Corr(x_t,y_(t+lag)), global means and full lag-zero energy normalization.

Series

data Series Source #

Opaque, validated timestamps paired with optional observations.

Instances

Instances details

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

series

series :: [(Double, Maybe Double)] -> Either MathError Series Source #

Preserve order and missing values; reject duplicate or nonfinite times.

regularSeries

regularSeries :: Double -> Double -> [Maybe Double] -> Either MathError Series Source #

Sample times start+i*step. Rounded duplicate times are rejected as well.

observations

observations :: Series -> [(Double, Maybe Double)] Source #

Extract time-ordered (timestamp,Maybe value) observations from a validated Series. Missing values remain Nothing.

seriesValues

seriesValues :: Series -> Either MathError [Double] Source #

Complete-data conversion never silently drops a missing observation.

isRegular

isRegular :: Double -> Series -> Either MathError Bool Source #

Relative spacing tolerance; fewer than three observations are regular.

Alignment

data Alignment Source #

Time-series timestamp join policy: Inner intersection or Outer union,with missing values explicit.

Constructors

Inner
Outer
LeftAligned

Instances

Instances details

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

align

align :: Alignment -> Series -> Series -> Either MathError (Series, Series) Source #

Exact timestamp equality. Missing alignment positions are explicit Nothing.

Fill

data Fill Source #

Missing-value strategy selecting forward fill,backward fill,or linear interpolation under the checked boundary rules.

Constructors

ForwardFill
BackwardFill
LinearFill

Instances

Instances details

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

fillMissing

fillMissing :: Fill -> Series -> Either MathError Series Source #

Directional filling leaves the unavailable leading/trailing end missing. Linear filling interpolates between finite anchors and never extrapolates.

Resampling

data Resampling Source #

Series resampling policy selecting bin means,last-bin values,or linear point samples.

Constructors

LinearSamples
BinMean
BinLast

Instances

Instances details

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

Rolling

data Rolling Source #

Rolling-window statistic selector for mean,variance,standard deviation,minimum,or maximum.

Constructors

MovingMean
MovingVariance
MovingSD
MovingMinimum
MovingMaximum

Instances

Instances details

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

rolling

rolling :: Rolling -> Int -> [Double] -> Either MathError [Double] Source #

Full trailing windows only; variance is population variance (ddof=0).

exponentialAverage

exponentialAverage :: Double -> [Double] -> Either MathError [Double] Source #

Recursive EMA, initialized at the first observation; 0<alpha<=1.

weightedAverage

weightedAverage :: [Double] -> [Double] -> Either MathError [Double] Source #

Nonnegative chronological weights: first weight multiplies oldest sample.

cumulativeReturns

cumulativeReturns :: [Double] -> Either MathError [Double] Source #

Cumulative simple return relative to the first strictly positive price.

logarithmicReturns

logarithmicReturns :: [Double] -> Either MathError [Double] Source #

Consecutive log returns, using log prices to avoid ratio overflow.

durbinLevinson

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

Levinson recursion for a positive definite Toeplitz covariance. Returns AR coefficients, innovation variance, and PACF (without the lag-zero one).

yuleWalker

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

Biased sample autocovariances with centered data; returns mean separately.

partialAutocorrelation

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

Given maximum lag then samples, compute ACF and Durbin-Levinson partial correlations, returning lag zero (1) followed by requested PACF lags. Invalid lag/data or singular covariance recurrence returns Left MathError.

module HMath.TimeSeries.Models

module HMath.TimeSeries.Diagnostics