Timeseries

AR1(k, tau_e, *args, **kwargs) Autoregressive process with 1 lag.
AR(rho[, sigma, tau, constant, init, sd]) Autoregressive process with p lags.
GaussianRandomWalk([tau, init, sigma, mu, sd]) Random Walk with Normal innovations
GARCH11(omega, alpha_1, beta_1, initial_vol, …) GARCH(1,1) with Normal innovations.
EulerMaruyama(dt, sde_fn, sde_pars, *args, …) Stochastic differential equation discretized with the Euler-Maruyama method.
MvGaussianRandomWalk([mu, cov, tau, chol, …]) Multivariate Random Walk with Normal innovations
MvStudentTRandomWalk(nu, *args, **kwargs) Multivariate Random Walk with StudentT innovations
class pymc3.distributions.timeseries.AR1(k, tau_e, *args, **kwargs)

Autoregressive process with 1 lag.

Parameters:

k : tensor

effect of lagged value on current value

tau_e : tensor

precision for innovations

class pymc3.distributions.timeseries.AR(rho, sigma=None, tau=None, constant=False, init=<pymc3.distributions.continuous.Flat object>, sd=None, *args, **kwargs)

Autoregressive process with p lags.

\[x_t = \rho_0 + \rho_1 x_{t-1} + \ldots + \rho_p x_{t-p} + \epsilon_t, \epsilon_t \sim N(0,\sigma^2)\]

The innovation can be parameterized either in terms of precision or standard deviation. The link between the two parametrizations is given by

\[\tau = \dfrac{1}{\sigma^2}\]
Parameters:

rho : tensor

Tensor of autoregressive coefficients. The first dimension is the p lag.

sigma : float

Standard deviation of innovation (sigma > 0). (only required if tau is not specified)

tau : float

Precision of innovation (tau > 0). (only required if sigma is not specified)

constant: bool (optional, default = False)

Whether to include a constant.

init : distribution

distribution for initial values (Defaults to Flat())

class pymc3.distributions.timeseries.GaussianRandomWalk(tau=None, init=<pymc3.distributions.continuous.Flat object>, sigma=None, mu=0.0, sd=None, *args, **kwargs)

Random Walk with Normal innovations

Parameters:

mu: tensor

innovation drift, defaults to 0.0

sigma : tensor

sigma > 0, innovation standard deviation (only required if tau is not specified)

tau : tensor

tau > 0, innovation precision (only required if sigma is not specified)

init : distribution

distribution for initial value (Defaults to Flat())

class pymc3.distributions.timeseries.GARCH11(omega, alpha_1, beta_1, initial_vol, *args, **kwargs)

GARCH(1,1) with Normal innovations. The model is specified by

\[y_t = \sigma_t * z_t\]
\[\sigma_t^2 = \omega + \alpha_1 * y_{t-1}^2 + \beta_1 * \sigma_{t-1}^2\]

with z_t iid and Normal with mean zero and unit standard deviation.

Parameters:

omega : tensor

omega > 0, mean variance

alpha_1 : tensor

alpha_1 >= 0, autoregressive term coefficient

beta_1 : tensor

beta_1 >= 0, alpha_1 + beta_1 < 1, moving average term coefficient

initial_vol : tensor

initial_vol >= 0, initial volatility, sigma_0

class pymc3.distributions.timeseries.EulerMaruyama(dt, sde_fn, sde_pars, *args, **kwds)

Stochastic differential equation discretized with the Euler-Maruyama method.

Parameters:

dt : float

time step of discretization

sde_fn : callable

function returning the drift and diffusion coefficients of SDE

sde_pars : tuple

parameters of the SDE, passed as *args to sde_fn

class pymc3.distributions.timeseries.MvGaussianRandomWalk(mu=0.0, cov=None, tau=None, chol=None, lower=True, init=<pymc3.distributions.continuous.Flat object>, *args, **kwargs)

Multivariate Random Walk with Normal innovations

Parameters:

mu : tensor

innovation drift, defaults to 0.0

cov : tensor

pos def matrix, innovation covariance matrix

tau : tensor

pos def matrix, inverse covariance matrix

chol : tensor

Cholesky decomposition of covariance matrix

init : distribution

distribution for initial value (Defaults to Flat())

Notes

Only one of cov, tau or chol is required.

class pymc3.distributions.timeseries.MvStudentTRandomWalk(nu, *args, **kwargs)

Multivariate Random Walk with StudentT innovations

Parameters:

nu : degrees of freedom

mu : tensor

innovation drift, defaults to 0.0

cov : tensor

pos def matrix, innovation covariance matrix

tau : tensor

pos def matrix, inverse covariance matrix

chol : tensor

Cholesky decomposition of covariance matrix

init : distribution

distribution for initial value (Defaults to Flat())