time_series.piecewise

Fits a synthetic signal to data over a time period by ordinary or weighted least-squares for breakpoint analysis

Calling Sequence

import gravity_toolkit.time_series
tsbeta = gravity_toolkit.time_series.piecewise(t_in, d_in, BREAKPOINT=len(t_in)//2, CYCLES=[0.5,1.0])

Source code

gravity_toolkit.time_series.piecewise(t_in, d_in, BREAK_TIME=None, BREAKPOINT=None, CYCLES=[0.5, 1.0], TERMS=[], DATA_ERR=0, WEIGHT=False, STDEV=0, CONF=0, AICc=False)[source]

Fits a synthetic signal to data over a time period by ordinary or weighted least-squares for breakpoint analysis [68]

Parameters:

t_in: float

input time array

d_in: float

input data array

BREAK_TIME: float or NoneType, default None

breakpoint time for piecewise regression

BREAKPOINT: int or NoneType, default None

breakpoint indice of piecewise regression

CYCLES: list, default [0.5, 1.0]

list of cyclical terms in fractions of year

TERMS: list, default []

list of extra fit terms

DATA_ERR: float or list

data precision

single value if equal

array if unequal for weighted least squares

WEIGHT: bool, default False

Use weighted least squares with measurement errors

STDEV: float, default 0

Standard deviation of output error

CONF: float, default 0

Confidence interval of output error

AICc: bool, default False

Use second order AIC for small sample sizes [6]

Returns:

beta: float

regressed coefficients array

error: float

regression fit error for each coefficient for an input deviation

STDEV: standard deviation of output error

CONF: confidence interval of output error

std_err: float

standard error for each coefficient

R2: float

coefficient of determination (r²)

R2Adj: float

r² adjusted for the number of terms in the model

MSE: float

mean square error

WSSE: float

Weighted sum of squares error

NRMSE: float

normalized root mean square error

AIC: float

Akaike information criterion

BIC: float

Bayesian information criterion (Schwarz criterion)

model: float

modeled timeseries

simple: float

modeled timeseries without oscillating components

residual: float

model residual

DOF: int

degrees of freedom

N: int

number of terms used in fit

cov_mat: float

covariance matrix