ARIMA models

Example

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
import numpy as np
import pandas as pd
from pandas.io.data import DataReader
from datetime import datetime
import pyflux as pf

ibm = DataReader('IBM',  'yahoo', datetime(2000,1,1), datetime(2016,3,10))
ibm['Logged Open'] = np.log(ibm['Open'].values)

model = pf.ARIMA(data=ibm,ar=1,ma=1,integ=1,target='Logged Open')

Class Arguments

The ARIMA() model class has the following arguments:

  • data : requires a pd.DataFrame object or an np.array
  • ar : the number of autoregressive lags
  • ma : the number of moving average lags
  • integ : (default : 0) order of integration (0 : no difference, 1 : first difference, ...)
  • target : (default: None) specify the pandas column name or numpy index if the input is a matrix. If None, the first column will be chosen as the data.

Class Attributes

An ARIMA() object holds the following attributes:

Model Attributes:

  • ar : the number of autoregressive lags
  • ma : the number of moving average lags
  • integ : order of integration (0 : no difference, 1 : first difference, ...)
  • index : the timescale of the time-series
  • data : the dependent variable held as a np.array
  • data_name : string variable containing name of the time series
  • data_type : whether original datatype is numpy or pandas

Parameter Attributes:

The attribute param.desc is a dictionary holding information about individual parameters:

  • name : name of the parameter
  • index : index of the parameter (begins with 0)
  • prior : the prior specification for the parameter
  • q : the variational distribution approximation

Inference Attributes:

  • params : holds any estimated parameters
  • ses : holds any estimated standard errors for parameters (MLE/MAP)
  • ihessian : holds any estimated inverse Hessian (MLE/MAP)
  • chains : holds trace information for MCMC runs
  • supported_methods : which inference methods are supported
  • default_method : default inference method

Class Methods

adjust_prior(index,prior)

Adjusts a prior with the given parameter index. Arguments are:

  • index : taking a value in range(0,no of parameters)
  • prior : one of the prior objects listed in the Bayesian Inference section
1
2
model.list_priors()
model.adjust_prior(2,ifr.Normal(0,1))

fit(method)

Fits parameters for the model. Arguments are:

  • method : one of [‘BBVI’,MLE’,’MAP’,’M-H’,’Laplace’]
  • printed : (default: True) whether to print output
  • nsims : (default: 100000) how many simulations if M-H is chosen
  • cov_matrix (default: None) covariance matrix for M-H
  • iterations : (default: 30000) how many iterations if BBVI is chosen
  • step : (default: 0.001) step size for BBVI
1
model.fit("M-H",nsims=20000)

list_priors()

Lists the current prior specification.

plot_fit()

Graphs the fit of the model.

predict(h)

Predicts h timesteps ahead. Arguments are:

  • h : (default: 5) how many timesteps to predict ahead
  • past_values : (default: 20) how many past observations to plot
  • intervals : (default: True) whether to plot 95/90 prediction intervals
1
model.predict(h=12,past_values=36)