varwg.time_series_analysis package

Submodules

varwg.time_series_analysis.distributions module

class varwg.time_series_analysis.distributions.Beta

Bases: Dist

Beta distribution on the interval [l, u].

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 4

name = 'beta'

parameter_names = ('alpha', 'beta', 'l', 'u')

supplements_names = None

class varwg.time_series_analysis.distributions.Cauchy

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'cauchy'

parameter_names = ('x0', 'gamma')

supplements_names = None

class varwg.time_series_analysis.distributions.Censored(distribution, lc=-inf, uc=inf)

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
constraints
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

constraints(x, *args, **kwds)

n_pars = 0

name = 'censored'

parameter_names = ()

supplements_names = None

class varwg.time_series_analysis.distributions.Dist

Bases: object

Mimics part of the interface of stats.rv_continuous. Comes with a few extra goodies.

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

class Result(x, supplements, success)

Bases: tuple

Methods

count(value, /)	Return number of occurrences of value.
index(value[, start, stop])	Return first index of value.

success

Alias for field number 2

supplements

Alias for field number 1

x

Alias for field number 0

cdf(*args, **kwds)

fit(*args, **kwds)

fit_fsum(values, opt_func=<function fmin>, x0=None, *args, **kwds)

fit_ks(values, opt_func=<function fmin>, x0=None, *args, **kwds)

fit_ml(values, x0=None, *args, **kwds)

isscipy = False

mean(*args, **kwds)

Crude estimation of the expected value. Heavy tails break this!

median(*args, **kwds)

n_pars = 0

name = 'dist'

parameter_names = ()

pdf(*args, **kwds)

ppf(*args, **kwds)

sample(*args, **kwds)

property scipy_

supplements_names = None

class varwg.time_series_analysis.distributions.DistMeta(name, bases, cls_dict)

Bases: ABCMeta

Assure some class attributes are set, so that life is easier later on.

Methods

__call__(*args, **kwargs)	Call self as a function.
mro(/)	Return a type's method resolution order.
register(subclass)	Register a virtual subclass of an ABC.

class varwg.time_series_analysis.distributions.Expon

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'expon'

parameter_names = ('x0', 'lambd')

supplements_names = None

class varwg.time_series_analysis.distributions.ExponTwo

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 4

name = 'expontwo'

parameter_names = ('x0', 'q0', 'lambda1', 'lambda2')

supplements_names = None

class varwg.time_series_analysis.distributions.Frozen(dist, *params)

Bases: object

Attributes:

mean

Crude estimation of the expected value.

median

parameter_dict

Methods

plot_fit([values, n_classes])	Display a combined plot of a histogram, fitted pdf, empirical cdf and fitted cdf.
plot_qq(values, *args, **kwds)	A qq-plot.

cdf
pdf
ppf
sample

cdf(x)

property mean

Crude estimation of the expected value. Heavy tails break this!

property median

property parameter_dict

pdf(x)

plot_fit(values=None, n_classes=30)

Display a combined plot of a histogram, fitted pdf, empirical cdf and fitted cdf.

plot_qq(values, *args, **kwds)

A qq-plot. Scatters theoretic over empirical ranks.

ppf(qq)

sample(size)

class varwg.time_series_analysis.distributions.Gamma

Bases: Dist

Gamma distribution.

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'gamma'

parameter_names = ('k', 'theta')

supplements_names = None

class varwg.time_series_analysis.distributions.Gamma1

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 3

name = 'gamma1'

parameter_names = ('a', 'loc', 'scale')

supplements_names = None

class varwg.time_series_analysis.distributions.JohnsonSU

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 4

name = 'johnsonsu'

parameter_names = ('a', 'b', 'loc', 'scale')

supplements_names = None

class varwg.time_series_analysis.distributions.Kumaraswamy

Bases: Dist

Resembles the Beta distribution, but does not need a transcendental function.

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 4

name = 'kumaraswamy'

parameter_names = ('a', 'b', 'l', 'u')

supplements_names = None

class varwg.time_series_analysis.distributions.LogNormal

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'lognormal'

parameter_names = ('mu', 'sigma')

supplements_names = None

class varwg.time_series_analysis.distributions.MDFt

Bases: object

Multiple degrees of freedom t distribution.

The marginals have different degrees of freedom, therefore this is not a “true” Multivariate t distribution. See Serban et al 2007.

Methods

fit
loglikelihood
sample

static fit(data)

static loglikelihood(data, sigma, df)

static sample(size, sigma, df)

class varwg.time_series_analysis.distributions.NoncentralLaplace

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 3

name = 'noncentrallaplace'

parameter_names = ('x0', 'q0', 'lambd')

supplements_names = None

class varwg.time_series_analysis.distributions.NoncentralT

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 3

name = 'noncentralt'

parameter_names = ('df', 'nc', 'mu')

supplements_names = None

class varwg.time_series_analysis.distributions.Normal

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'normal'

parameter_names = ('mu', 'sigma')

supplements_names = None

class varwg.time_series_analysis.distributions.Rain(distribution, threshold=0.0001)

Bases: _Rain

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 1

name = 'rain'

parameter_names = ('rain_prob',)

supplements_names = None

class varwg.time_series_analysis.distributions.RainMix(distribution, threshold=0.0015, q_thresh_lower=0.6, q_thresh_upper=0.95)

Bases: _KDE, _Rain

Attributes:

scipy_

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
fit_ml(x[, x0, bounds])	This is a lie, we don't fit rainmix with ML.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_kde
fit_ks
median
pdf
ppf
sample

fit_ml(x, x0=None, bounds=None, *args, **kwds)

This is a lie, we don’t fit rainmix with ML.

mean(*args, **kwds)

Crude estimation of the expected value. Heavy tails break this!

median(*args, **kwds)

n_pars = 2

name = 'rainmix'

parameter_names = ('q_thresh', 'rain_prob', 'kernel_width', 'kernel_data', 'f_thresh', 'q_kde_eval', 'x_eval')

supplements_names = ('q_thresh', 'f_thresh', 'kernel_data', 'q_kde_eval', 'x_eval')

class varwg.time_series_analysis.distributions.StudentT

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'studentt'

parameter_names = ('mu', 'df')

supplements_names = None

class varwg.time_series_analysis.distributions.Truncated(distribution, lc=-inf, uc=inf)

Bases: Dist

Wraps around any other distribution found here to truncate its upper and/or lower tail.

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
constraints
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

constraints(x, *args, **kwds)

n_pars = 0

name = 'truncated'

parameter_names = ()

supplements_names = None

class varwg.time_series_analysis.distributions.TruncatedNormal

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 4

name = 'truncatednormal'

parameter_names = ('mu', 'sigma', 'lc', 'uc')

supplements_names = None

class varwg.time_series_analysis.distributions.Weibull

Bases: Dist

Attributes:

scipy_

supplements_names

Methods

Result(x, supplements, success)
__call__(*params)	Call self as a function.
mean(*args, **kwds)	Crude estimation of the expected value.

cdf
fit
fit_fsum
fit_ks
fit_ml
median
pdf
ppf
sample

n_pars = 2

name = 'weibull'

parameter_names = ('alpha', 'beta')

supplements_names = None

varwg.time_series_analysis.distributions.fill_lower(sequence)

varwg.time_series_analysis.distributions.max_likelihood(density_func, x0, values=None, opt_func=None, disp=False, weights=None, method='BFGS', bounds=None, *args, **kwds)

Fits parameters of a density function to data, using the log-maximum- likelihood approach.

varwg.time_series_analysis.distributions.min_fsum(cdf, x0, values, opt_func=None, disp=False, *args, **kwds)

varwg.time_series_analysis.distributions.min_ks(cdf, x0, values, opt_func=None, disp=False, *args, **kwds)

Fits parameters of a cumulative distribution function to data, minimizing the Kolmogorov-Smirnof test statistic.

varwg.time_series_analysis.models module

Various functions for time series anlysis. If not specified differently, references are given on Luetkepohl “New Introduction to Multiple Time Series Analysis”.

VAR_LS	Least-Squares parameter estimation for a vector auto-regressive model of the form Y = B*Z + U.
VAR_LS_sim	Based on a least squares estimator, simulate a time-series of the form ..math::y(t) = nu + A1*y(t-1) + .
VAREX_LS	Least-Squares parameter estimation for a vector auto-regressive model of the form
VAREX_LS_sim	Based on a least squares estimator, simulate a time-series of the form ..math::y(t) = A1*y(t-1) + .
VAR_order_selection	Order selection for VAR processes to allow parsimonious parameterization.
VAR_residuals
VAREX_residuals
VAR_LS_predict	Based on a least squares estimator, predict a time-series of the form ..math::y(t) = nu + A1*y(t-1) + .
AIC	Akaike Information Criterion for order selection of a VAR process.
FPE	Final prediction error.
HQ	Hannan-Quinn for VAR_LS order selection (p.150).
SC	Schwarz criterion for VAR_LS order selection (p.150).

varwg.time_series_analysis.models.AIC(sigma_u, p, T)

Akaike Information Criterion for order selection of a VAR process. See p.147

varwg.time_series_analysis.models.B2A(B)

varwg.time_series_analysis.models.FPE(sigma_u, p, T)

Final prediction error. See p.147

varwg.time_series_analysis.models.HQ(sigma_u, p, T)

Hannan-Quinn for VAR_LS order selection (p.150). To be minimized.

varwg.time_series_analysis.models.MGARCH_ML(residuals, q, m)

Estimating MGARCH parameters by numerically maximizing the log-likelihood.

varwg.time_series_analysis.models.MGARCH_residuals(ut, gamma0, Gammas, Gs)

varwg.time_series_analysis.models.MGARCH_sim(params, T, sigma0, epsilon=None, n_presim_steps=100)

varwg.time_series_analysis.models.SC(sigma_u, p, T)

Schwarz criterion for VAR_LS order selection (p.150). To be minimized.

varwg.time_series_analysis.models.SVAR_LS(data, doys, p=2, doy_width=60, fft_order=3, var_names=None, verbose=True)

Seasonal version of the least squares estimator.

varwg.time_series_analysis.models.SVAR_LS_fill(Bs, sigma_us, doys, Y, A=None, m=None, ia=None, m_trend=None, n_presim_steps=100, fixed_data=None, p_kwds=None)

varwg.time_series_analysis.models.SVAR_LS_sim(Bs, sigma_us, doys, m=None, ia=None, m_trend=None, u=None, n_presim_steps=100, fixed_data=None, phase_randomize=False, rphases=None, return_rphases=False, p_kwds=None, taboo_period_min=None, taboo_period_max=None, verbose=False)

varwg.time_series_analysis.models.SVAR_residuals(data, doys, B, p=2)

varwg.time_series_analysis.models.VAREX_LS(data, p, ex)

Least-Squares parameter estimation for a vector auto-regressive model of the form

..math::y_t = A_1 y_{t-1} + … + A_p y_{t-p} + C x_t + u_t

Records containing nans are excluded. Refer to the Least-Squares Estimator example 3.2.3 p.78. for method and variable names.

Parameters:

data(K, T) ndarray

K is the number of variables, T the number of timesteps

ex(T,) ndarray

An external variable

pint

Autoregressive order of the process.

Returns:

Barray

Parameters of the fitted VAR-process. B := (A_1, …, A_p, C)

sigma_u: array

Covariance matrix of the residuals of the data.

See also

VAR_order_selection

Helps to find a p for parsimonious estimation.

VAR_residuals

Returns the residuals based on given data and LS estimator

VAR_LS_sim

Simulation based on LS estimator.

VAR_LS_predict

Predict given prior data and LS estimator.

varwg.time_series_analysis.models.VAREX_LS_sim(B, sigma_u, T, ex, m=None, ia=None, m_trend=None, u=None, n_presim_steps=100, prev_data=None, ex_kwds=None)

Based on a least squares estimator, simulate a time-series of the form ..math::y(t) = A1*y(t-1) + … + Ap*y(t-p) + C*x(t-1) + ut B contains (A1, …, Ap, C). See p. 707f

Parameters:

B(K, K*p+1) ndarray

Parameters of the VAR-process as returned from VAR_LS. K is the number of variables, p the autoregressive order.

sigma_u(K, K) ndarray

Covariance matrix of the residuals as returned from VAR_LS.

ex(T,) ndarray or function

External variable. If given as a function, ex_t will be generated by calling ex(Y[:t], **ex_kwds), with Y being the simulated values.

Tint

Number of timesteps to simulate.

m(K,) ndarray, optional

Process means (will be scaled according to B).

ia(K, T) ndarray, optional

Interannual variability. Additional time-varying disturbance to the process means (will be scaled according to B).

m_trend(K,) ndarray, optional

Change in means, that will be applied linearly so that this change is reached after the T timesteps.

u(K, T) ndarray, optional

Residuals to be used instead of multivariate gaussian serially independent random numbers.

n_presim_stepsint, optional

Number of presimulation timesteps that will be thrown away.

ex_kwdsdict, optional

Keyword arguments to be passed to ex.

Returns:

Y(K, T) ndarray

Simulated values.

ex_out(T,) ndarray

External variable.

See also

VAR_LS

Least-squares estimator (to get B and sigma_u).

VAR_order_selection

Helps to find a p for parsimonious estimation.

VAR_residuals

Returns the residuals based on given data and LS estimator

VAR_LS_predict

Predict given prior data and LS estimator.

varwg.time_series_analysis.models.VAREX_residuals(data, ex, B, p=2, ex_kwds=None)

varwg.time_series_analysis.models.VARMA_LS(data, p, q, rel_change=0.001)

Implementation of the scoring algorithm to fit a VARMA model. p.470ff

varwg.time_series_analysis.models.VARMA_LS_prelim(data, p, q)

Preliminary version of the general simple least-squares vector autoregressive estimator for a vector autoregressive moving-average process. See p.474ff

varwg.time_series_analysis.models.VARMA_LS_sim(AM, p, q, sigma_u, means, T, S=None, m=None, ia=None, m_trend=None, n_sim_multiple=2, fixed_data=None)

Generates a time series based on the VARMA-parameters AM. S and m should be sequences of length K. S is a variable-discerning multiplier and m a adder, respectively.

Parameters:

AM(K,K*(p+q)) array

The parameters of the VARMA-process. The first p columns are interpreted as the Ai-matrices of the auto regressive part. The last q columns as the Mi-matrices of the moving average part. K is the number of variables simulated.

pinteger

Order of the auto regressive process.

qinteger

Order of the moving average process.

sigma_u(K,K) array

Covariance matrix of the residuals.

means(K,) array

Process means. Used as starting values.

Tinteger

Desired length of the output time series.

S(K,K) array, optional

Used as multiplicative change of the disturbance vector to increase the variance of the output.

m(K,T) array_like, optional

Used as additive change during simulation to increase mean of the output.

n_sim_multipleinteger

Generate n_sim_multiple * T timesteps. Only the last T timesteps will be returned.

ia(K,T) array_like, optional

Interannual variability. Used as an additive change during simulation to get time-dependent disturbances.

m_trend(K,) array_like, optional

Used as additive change gradient during simulation to increase mean of the output gradually.

fixed_data(K,T) array_like, optional

Keeps the provided time-series fixed. Use np.nans to signify values that are not fixed. Can be used to simulate hierarchically.

Returns:

out(K, T) ndarray

K-dimensional simulated time series.

varwg.time_series_analysis.models.VARMA_order_selection(data, p_max=5, q_max=5, criterion=<function SC>, plot_table=False, *args, **kwds)

Returns p and q, the orders of a VARMA process that allows for parsimonious parameterization. Naive extension of VAR_order_selection without a theoretical basis!

varwg.time_series_analysis.models.VARMA_residuals(data, AM, p, q)

varwg.time_series_analysis.models.VAR_LS(data, p=2, biased=True)

Least-Squares parameter estimation for a vector auto-regressive model of the form Y = B*Z + U. Records containing nans are excluded. Refer to the Least-Squares Estimator example 3.2.3 p.78. for method and variable names.

Parameters:

data(K, T) ndarray

K is the number of variables, T the number of timesteps

pint

Autoregressive order of the process.

Returns:

Barray

Parameters of the fitted VAR-process.

sigma_uarray

Covariance matrix of the residuals.

biasedbool, optional

If true, use the number of non-nan observations (n_obs) to ‘unbias’ sigma_u. Otherwise, use n_obs - K * p - 1.

See also

VAR_order_selection

Helps to find a p for parsimonious estimation.

VAR_residuals

Returns the residuals based on given data and LS estimator

VAR_LS_sim

Simulation based on LS estimator.

VAR_LS_predict

Predict given prior data and LS estimator.

varwg.time_series_analysis.models.VAR_LS_asy(data, skewed_i, p=None)

Skewness of the differences of the residuals.

varwg.time_series_analysis.models.VAR_LS_extro(data, data_trans, transforms, backtransforms, p=2)

varwg.time_series_analysis.models.VAR_LS_predict(data_past, B, sigma_u, T=1, n_realizations=1)

Based on a least squares estimator, predict a time-series of the form ..math::y(t) = nu + A1*y(t-1) + … + Ap*y(t-p) + ut B contains (nu, A1, …, Ap).

Parameters:

data_past(K, p) ndarray

B(K, p * K + 1) ndarray

Parameters of the VAR-process of order p.

sigma_u(K, K) ndarray

Covariance matrix of the residuals of the VAR-process.

Tint

Number of timesteps to predict.

n_realizationsint

Number of realizations. If > 1, gaussian disturbances are added. So if n_realizations=1, the prediction is a best guess.

Returns:

Y(K, T) or (K, T, n_realizations) ndarray

References

See p. 707f

varwg.time_series_analysis.models.VAR_LS_sim(B, sigma_u, T, m=None, ia=None, m_trend=None, u=None, n_presim_steps=100, fixed_data=None, prev_data=None, transform=None, phase_randomize=False, rphases=None, return_rphases=False, p_kwds=None, taboo_period_min=None, taboo_period_max=None)

Based on a least squares estimator, simulate a time-series of the form ..math::y(t) = nu + A1*y(t-1) + … + Ap*y(t-p) + ut B contains (nu, A1, …, Ap). See p. 707f

Parameters:

B(K, K*p+1) ndarray

Parameters of the VAR-process as returned from VAR_LS. K is the number of variables, p the autoregressive order.

sigma_u(K, K) ndarray

Covariance matrix of the residuals as returned from VAR_LS.

Tint

Number of timesteps to simulate.

m(K,) ndarray, optional

Process means (will be scaled according to B).

ia(K, T) ndarray, optional

Interannual variability. Additional time-varying disturbance to the process means (will be scaled according to B).

m_trend(K,) ndarray, optional

Change in means, that will be applied linearly so that this change is reached after the T timesteps.

u(K, T) ndarray, optional

Residuals to be used instead of multivariate gaussian serially independent random numbers.

n_presim_stepsint, optional

Number of presimulation timesteps that will be thrown away.

fixed_data(K, T) ndarray, optional

Data that will be fixed, i.e. at each timestep, these will be put in instead of the actual simulated values. Where fixed_data is nan, the simulated values will not be overwritten.

transformcallable, optional

On-the-fly transformation that accepts a sequence of length K (values of all variables at one time step) and the time index t.

Returns:

Y(K, T) ndarray

Simulated values.

See also

VAR_LS

Least-squares estimator (to get B and sigma_u).

VAR_order_selection

Helps to find a p for parsimonious estimation.

VAR_residuals

Returns the residuals based on given data and LS estimator

VAR_LS_predict

Predict given prior data and LS estimator.

varwg.time_series_analysis.models.VAR_LS_sim_asy(B, sigma_u, T, data, p, skewed_i, n_presim_steps=100, verbose=False, var_names=None, *args, **kwds)

varwg.time_series_analysis.models.VAR_YW(data, p=2)

Yule-Walker parameter estimation for a vector auto-regressive model of the form Y^0 = A*X + U Refer to p. 83ff. Here we assume that the data is already mean-adjusted!

varwg.time_series_analysis.models.VAR_YW_sim(A, sigma_u, T)

Based on a Yule-Walker estimator, simulate a time-series of the form ..math:: y(t) = A_1*y(t-1) + … + A_p*y(t-p) + u(t) A contains (A1, …, Ap). See p. 707f

varwg.time_series_analysis.models.VAR_mean(B)

varwg.time_series_analysis.models.VAR_onestep_predictions(data, B, p=2)

varwg.time_series_analysis.models.VAR_order_selection(data, p_max=10, criterion=<function SC>, estimator=<function VAR_LS>, est_kwds=None)

Order selection for VAR processes to allow parsimonious parameterization.

Parameters:

data(K, T) ndarray

Input data with K variables and T timesteps.

p_maxint, optional

Maximum number of autoregressive order to evaluate.

criterionfunction, optional

Information criterion that accepts sigma_u, p, and T and returns something that gives small values for a parsimonious set of these parameters.

Returns:

pint

Suggested autoregressive order.

See also

AIC

Akaike Information criterion

FPE

Final Prediction Error

HQ

Hannan-Quinn information criterion

SC

Schwartz Criterion

VAR_LS

Least-squares estimator.

VAR_residuals

Returns the residuals based on given data and LS estimator

VAR_LS_sim

Simulation based on LS estimator.

VAR_LS_predict

Predict given prior data and LS estimator.

varwg.time_series_analysis.models.VAR_residuals(data, B, p=2)

varwg.time_series_analysis.models.matrix_exp_sym(A)

varwg.time_series_analysis.models.matrix_log_spd(A, eps=1e-10)

class varwg.time_series_analysis.models.mgarch_param_factory(gamma0, Gammas, Gs, cov_residuals)

Bases: tuple

Methods

count(value, /)	Return number of occurrences of value.
index(value[, start, stop])	Return first index of value.

Gammas

Alias for field number 1

Gs

Alias for field number 2

cov_residuals

Alias for field number 3

gamma0

Alias for field number 0

varwg.time_series_analysis.models.scale_z(z, i, x_i, A)

varwg.time_series_analysis.models.sqrtm(A)

Square root of a positive-definite Matrix.

>>> A = np.array([[4., 0, 0], [0, 9., 0], [0, 0, 16.]])
>>> sqrtm(A)
array([[2., 0., 0.],
       [0., 3., 0.],
       [0., 0., 4.]])

Notes

See Appendix 9.4.

varwg.time_series_analysis.models.symmetrize(A)

varwg.time_series_analysis.models.unvec(sequence, K)

The inverse of vec.

>>> a = list(range(6))
>>> a
[0, 1, 2, 3, 4, 5]
>>> unvec(a, K=2)
array([[0, 2, 4],
       [1, 3, 5]])
>>> A = np.array([[0, 3, 1, 4, 2, 5]]).T
>>> unvec(A, K=2)
array([[0, 1, 2],
       [3, 4, 5]])

varwg.time_series_analysis.models.unvech(sequence, K)

The inverse of vech.

>>> a = np.array([0, 2, 3])
>>> unvech(a, K=2)
array([[0., 2.],
       [2., 3.]])

varwg.time_series_analysis.models.vec(A)

The vec operator stacks 2dim matrices into 1dim vectors column-wise. See p.661f.

>>> A = np.arange(6).reshape(2, 3)
>>> A
array([[0, 1, 2],
       [3, 4, 5]])
>>> vec(A)
array([[0],
       [3],
       [1],
       [4],
       [2],
       [5]])

varwg.time_series_analysis.models.vech(A)

The vech operator removes the upper triangular part of a matrix and returns the rest in a column-stacked form. See p.661f.

>>> A = np.arange(4).reshape(2, 2)
>>> A
array([[0, 1],
       [2, 3]])
>>> vech(A)
array([[0],
       [2],
       [3]])

varwg.time_series_analysis.optimize module

varwg.time_series_analysis.optimize.simulated_annealing(func, x0, args=(), k=0.99, M=None, step_length=None, T0=None, step_length0=5, feps=1e-05, constraints=None, callback=None)

Simulated Annealing algorithm with support for constraints, estimation for acceptance rate based initial temperature and gradient based calculation of the step lengths.

varwg.time_series_analysis.phase_randomization module

varwg.time_series_analysis.phase_randomization.randomize2d(data, T=None, taboo_period_min=None, taboo_period_max=None, return_rphases=False, rphases=None, qq=True)

assumes daily discretization and does not touch yearly cycles.

varwg.time_series_analysis.phase_randomization.randomize2d_old(data, T=None, taboo_period_min=None, taboo_period_max=None, return_rphases=False)

assumes daily discretization and does not touch yearly cycles.

varwg.time_series_analysis.seasonal module

This provides common ground for seasonal_distributions and seasonal_kde.

class varwg.time_series_analysis.seasonal.Seasonal(data, datetimes, kill_leap=False)

Bases: object

Attributes:

hours

hours_per_day

n_years

Methods

doys2doys_ii(doys)	Doys indices from doy values.
duplicate_feb28(doys)	Put doys in the range [1, 365] by duplicating February 28th and decrementing all following doys of the year.
qq_shift(theta_incr, trig_pars[, x, doys])	Empirical estimation of shift in std-normal for given theta_incr.

rain_probs

doys2doys_ii(doys)

Doys indices from doy values.

duplicate_feb28(doys)

Put doys in the range [1, 365] by duplicating February 28th and decrementing all following doys of the year.

property hours

property hours_per_day

property n_years

qq_shift(theta_incr, trig_pars, x=None, doys=None, **kwds)

Empirical estimation of shift in std-normal for given theta_incr.

rain_probs(threshold, doys=None)

class varwg.time_series_analysis.seasonal.Torus(hour_neighbors)

Bases: Seasonal

Attributes:

doy_hour_weights

To be used as a kernel to weight distances in the doy-hour domain.

hours

hours_per_day

n_years

torus

Methods

doys2doys_ii(doys)	Doys indices from doy values.
duplicate_feb28(doys)	Put doys in the range [1, 365] by duplicating February 28th and decrementing all following doys of the year.
qq_shift(theta_incr, trig_pars[, x, doys])	Empirical estimation of shift in std-normal for given theta_incr.

rain_probs
smooth_torus
torus_fft

property doy_hour_weights

To be used as a kernel to weight distances in the doy-hour domain.

smooth_torus(values, fft_order=5, padded=False)

property torus

torus_fft(values, hours=None, doys=None, years=None, fft_order=5, padded=False)

varwg.time_series_analysis.seasonal.build_doy_mask(doys, doy_width, doys_unique=None)

Mask to access doy neighborhood in data.

varwg.time_series_analysis.seasonal_kde module

class varwg.time_series_analysis.seasonal_kde.SeasonalHourlyKDE(data, dtimes, solution=None, doy_width=5, hour_neighbors=4, *args, **kwds)

Bases: SeasonalKDE, Torus

Estimates kernel densities for time series exhibiting seasonalities in daily cycles.

Attributes:

cdf_interp_per_day

data_bounds

Here for optimization: We do not let lower and upper bound make a long loop over the data for min and max resp.

density_grid

doy_hour_weights

To be used as a kernel to weight distances in the doy-hour domain.

doy_mask

Returns a (n_unique_doys, len(data)) ndarray

doy_mask_dict

hours

hours_per_day

kernel_widths

n_years

ppf_interp_per_day

quantile_grid

solution

torus

x_grid

Methods

chi2_test([k])	Chi-square goodness-of-fit test. H0: The given data x follows distribution with parameters aquired by func::SeasonalDist.fit To side-step complications arising from having a different distribution for every doy, we test whether the quantiles (which are deseasonalized) are uniformly distributed.
doys2doys_ii(doys)	Doys indices from doy values.
duplicate_feb28(doys)	Put doys in the range [1, 365] by duplicating February 28th and decrementing all following doys of the year.
fit([silverman, order])
qq_shift(theta_incr, trig_pars[, x, doys])	Empirical estimation of shift in std-normal for given theta_incr.
scotts_rule([n_data, n_dim])	Scott's rule of thumb for kernel bandwidth.
sum_log_density(kernel_width, data)	objective function to optimize kernel width with MLM leave one out

cdf
density_per_doy
lower_bound
median
pdf
ppf
rain_probs
scatter_cdf
scatter_pdf
smooth_torus
torus_fft
upper_bound

property data_bounds

Here for optimization: We do not let lower and upper bound make a long loop over the data for min and max resp. We do it here once and cache it.

property density_grid

density_per_doy(kernel_width, data, hour_width, eval_data=None, leave_one_out=False)

fit(silverman=False, order=4)

Parameters:

silvermanboolean or callable, optional

Use rule of silverman instead of leave-one-out maximum likelihood estimation. Callable is executed with (n_data, n_dim).

lower_bound(doy)

pdf(solution, x, doys)

scotts_rule(n_data=None, n_dim=3)

Scott’s rule of thumb for kernel bandwidth.

property solution

sum_log_density(kernel_width, data)

objective function to optimize kernel width with MLM leave one out

upper_bound(doy)

class varwg.time_series_analysis.seasonal_kde.SeasonalKDE(data, datetimes, solution=None, doy_width=15, nx=1000.0, fixed_pars=None, verbose=True, freibord=0, smooth_len=None, kill_leap=False)

Bases: Seasonal

Attributes:

cdf_interp_per_day

data_bounds

Here for optimization: We do not let lower and upper bound make a long loop over the data for min and max resp.

density_grid

doy_mask

Returns a (n_unique_doys, len(data)) ndarray

doy_mask_dict

hours

hours_per_day

kernel_widths

n_years

ppf_interp_per_day

quantile_grid

solution

x_grid

Methods

chi2_test([k])	Chi-square goodness-of-fit test. H0: The given data x follows distribution with parameters aquired by func::SeasonalDist.fit To side-step complications arising from having a different distribution for every doy, we test whether the quantiles (which are deseasonalized) are uniformly distributed.
doys2doys_ii(doys)	Doys indices from doy values.
duplicate_feb28(doys)	Put doys in the range [1, 365] by duplicating February 28th and decrementing all following doys of the year.
fit([silverman])	This estimates the kernel widths per doy AND returns the interpolating functions for cdf and ppf.
qq_shift(theta_incr, trig_pars[, x, doys])	Empirical estimation of shift in std-normal for given theta_incr.
sum_log_density(kernel_width, data, doys, ...)	objective function to optimize kernel width with MLM leave one out

cdf
density_per_doy
lower_bound
median
pdf
ppf
rain_probs
scatter_cdf
scatter_pdf
upper_bound

cdf(solution=None, x=None, doys=None, **kwds)

property cdf_interp_per_day

chi2_test(k=5)

Chi-square goodness-of-fit test. H0: The given data x follows distribution with parameters

aquired by func::SeasonalDist.fit

To side-step complications arising from having a different distribution for every doy, we test whether the quantiles (which are deseasonalized) are uniformly distributed.

Parameters:

kint

Number of classes (bins)

Returns:

p_valuefloat

property data_bounds

Here for optimization: We do not let lower and upper bound make a long loop over the data for min and max resp. We do it here once and cache it.

property density_grid

density_per_doy(kernel_width, data, doys, doy_middle, eval_data=None, leave_one_out=False)

property doy_mask

Returns a (n_unique_doys, len(data)) ndarray

property doy_mask_dict

fit(silverman=False)

This estimates the kernel widths per doy AND returns the interpolating functions for cdf and ppf.

property kernel_widths

lower_bound(doy)

median(solution, doys, **kwds)

pdf(solution, data, doys, **kwds)

ppf(solution, quantiles, doys=None, mean_shift=None, **kwds)

property ppf_interp_per_day

property quantile_grid

scatter_cdf(solution, n_sumup=1, figsize=None, title=None)

scatter_pdf(solution, n_sumup=24, figsize=None, title=None, opacity=0.25, plot_kernel_width=False, s_kwds=None)

property solution

sum_log_density(kernel_width, data, doys, doy_middle)

objective function to optimize kernel width with MLM leave one out

upper_bound(doy)

property x_grid

varwg.time_series_analysis.seasonal_kde.array_gen(scalar)

varwg.time_series_analysis.seasonal_kde.doy_hour_fft(data, dtimes, order=4)

Remove yearly and daily cycle.

Parameters:

data1d array

dtimes1d array of datetime objects

orderint, optional

number of frequencies to use

Returns:

xx1d array

fft_pars24d array

fast fourier parameters for each hour.

varwg.time_series_analysis.seasonal_kde.fft2par(fft_pars, doys, ifft_func=None, period_length=None, lower_bound=None)

Converts from the frequency into the time domain. The output is repeated for as many periods underlying the doys (think of years).

Parameters:

fft_parsndarray

As returned from numpy.fft.fft (or its siblings).

doysfloat 1d array

Doys associated with the output.

ifft_funccallable or None, optional

Function to use for frequency-time-domain transformation. If None, np.fft.irfft will be used.

period_lengthint or None, optional

Length of period.

lower_boundfloat or None, optional

Smallest desired value of trans.

Returns:

trans1d array with len = len(doys)

Module contents