time_series.regress

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

Calling Sequence

import gravity_toolkit.time_series
tsbeta = gravity_toolkit.time_series.regress(t_in, d_in, ORDER=1, CYCLES=[0.5,1.0], CONF=0.95)

Source code

gravity_toolkit.time_series.regress(t_in, d_in, ORDER=1, CYCLES=[0.5, 1.0], TERMS=[], DATA_ERR=0, WEIGHT=False, RELATIVE=Ellipsis, STDEV=0, CONF=0, AICc=True)[source]

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

Parameters:
t_in: float

input time array

d_in: float

input data array

ORDER: int, default 1

maximum polynomial order in fit

  • 0: constant

  • 1: linear

  • 2: quadratic

CYCLES: list, default [0.5, 1.0]

list of cyclical terms

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

RELATIVE: float or List, default Ellipsis

Epoch for calculating relative dates

  • float: use exact value as epoch

  • list: use mean from indices of available times

  • Ellipsis: use mean of all available times

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