Non-Gaussian State Space models

Example

import numpy as np
import pyflux as pf
import pandas as pd

leicester = pd.read_csv('http://www.pyflux.com/notebooks/leicester_goals_scored.csv')
leicester.columns= ["Time","Leicester Goals Scored"]

model = pf.NLLEV.Poisson(data=leicester,target='Leicester Goals Scored')

fb = DataReader('FB',  'yahoo', datetime(2015,5,1), datetime(2016,5,10))
returns = pd.DataFrame(np.diff(np.log(fb['Open'].values)))
returns.index = fb.index.values[1:fb.index.values.shape[0]]
returns.columns = ['Facebook Returns']

model2 = pf.NLLEV.t(data=returns,target='Close')

Class Arguments

The non-linear local level model (NLLEV) model has the options: NLLEV.Exponential, NLLEV.Laplace, NLLEV.Poisson, NLLEV.t,

class NLLEV(data, integ, target)

data

pd.DataFrame or array-like : the time-series data

integ

int : how many times to difference the time series (default: 0)

target

string (data is DataFrame) or int (data is np.array) : which column to use as the time series. If None, the first column will be chosen as the data.

The non-linear local linear trend model (NLLT) model has the options: NLLT.Exponential, NLLT.Laplace, NLLT.Poisson, NLLT.t,

class NLLT(data, integ, target)

data

pd.DataFrame or array-like : the time-series data

integ

int : how many times to difference the time series (default: 0)

target

string (data is DataFrame) or int (data is np.array) : which column to use as the time series. If None, the first column will be chosen as the data.

The non-linear dynamic regression model (NDynLin) model has the options: NDynLin.Exponential, NDynLin.Laplace, NDynLin.Poisson, NDynLin.t,

class NDynLin(formula, data)

formula

patsy notation string describing the regression

data

pd.DataFrame or array-like : the time-series data

Class Methods

adjust_prior(index, prior)

Adjusts the priors of the model. index can be an int or a list. prior is a prior object, such as Normal(0,3).

Here is example usage for adjust_prior():

import pyflux as pf

# model = ... (specify a model)
model.list_priors()
model.adjust_prior(2,pf.Normal(0,1))

fit(method, iterations, step, **kwargs)

Estimates parameters for the model using BBVI. Returns a Results object. iterations is the number of iterations for BBVI, and step is the step size for RMSProp (default : 0.001).

Optional arguments include animate for the local level and local linear trend models: outputs an animation of stochastic optimization.

Here is example usage for fit():

import pyflux as pf

# model = ... (specify a model)
model.fit("M-H",nsims=20000)

plot_fit(intervals, **kwargs)

Graphs the fit of the model. intervals is a boolean; if true shows 95% C.I. intervals for the states.

Optional arguments include figsize - the dimensions of the figure to plot - and series_type which has two options: Filtered or Smoothed.

plot_parameters(indices, figsize)

Returns a plot of the parameters and their associated uncertainty. indices is a list referring to the parameter indices that you want ot plot. Figsize specifies how big the plot will be.

plot_predict(h, past_values, intervals, **kwargs)

Plots predictions of the model. h is an int of how many steps ahead to predict. past_values is an int of how many past values of the series to plot. intervals is a bool on whether to include confidence/credibility intervals or not.

Optional arguments include figsize - the dimensions of the figure to plot.

plot_predict_is(h, past_values, intervals, **kwargs)

Plots in-sample rolling predictions for the model. h is an int of how many previous steps to simulate performance on. past_values is an int of how many past values of the series to plot. intervals is a bool on whether to include confidence/credibility intervals or not.

Optional arguments include figsize - the dimensions of the figure to plot.

predict(h)

Returns DataFrame of model predictions. h is an int of how many steps ahead to predict.

predict_is(h)

Returns DataFrame of in-sample rolling predictions for the model. h is an int of how many previous steps to simulate performance on.

simulation_smoother(data, beta, H, mu)

Outputs a simulated state trajectory from a simulation smoother. Arguments are data : the data to simulate from - use self.data usually - and beta : the parameters to use, H is the measurement covariance matrix from an approximate Gaussian model, and mu is a measurement density constant from an approximate Gaussian model.