.. currentmodule:: statsmodels.tsa


.. _tsa:


Time Series analysis :mod:`tsa`
===============================

:mod:`statsmodels.tsa` contains model classes and functions that are useful
for time series analysis. This currently includes univariate autoregressive models (AR),
vector autoregressive models (VAR) and univariate autoregressive moving average models
(ARMA). It also includes descriptive statistics for time series, for example autocorrelation, partial
autocorrelation function and periodogram, as well as the corresponding theoretical properties
of ARMA or related processes. It also includes methods to work with autoregressive and
moving average lag-polynomials.
Additionally, related statistical tests and some useful helper functions are available.

Estimation is either done by exact or conditional Maximum Likelihood or conditional
least-squares, either using Kalman Filter or direct filters.

Currently, functions and classes have to be imported from the corresponding module, but
the main classes will be made available in the statsmodels.tsa namespace. The module
structure is within statsmodels.tsa is

 - stattools : empirical properties and tests, acf, pacf, granger-causality,
   adf unit root test, ljung-box test and others.
 - ar_model : univariate autoregressive process, estimation with conditional
   and exact maximum likelihood and conditional least-squares
 - arima_model : univariate ARMA process, estimation with conditional
   and exact maximum likelihood and conditional least-squares
 - vector_ar, var : vector autoregressive process (VAR) estimation models,
   impulse response analysis, forecast error variance decompositions, and data
   visualization tools
 - kalmanf : estimation classes for ARMA and other models with exact MLE using
   Kalman Filter
 - arma_process : properties of arma processes with given parameters, this
   includes tools to convert between ARMA, MA and AR representation as well as
   acf, pacf, spectral density, impulse response function and similar
 - sandbox.tsa.fftarma : similar to arma_process but working in frequency domain
 - tsatools : additional helper functions, to create arrays of lagged variables,
   construct regressors for trend, detrend and similar.
 - filters : helper function for filtering time series



Some additional functions that are also useful for time series analysis are in
other parts of statsmodels, for example additional statistical tests.

Some related functions are also available in matplotlib, nitime, and
scikits.talkbox. Those functions are designed more for the use in signal
processing where longer time series are available and work more often in the
frequency domain.


.. currentmodule:: statsmodels.tsa


Descriptive Statistics and Tests
""""""""""""""""""""""""""""""""

.. autosummary::
   :toctree: generated/

   stattools.acovf
   stattools.acf
   stattools.pacf
   stattools.pacf_yw
   stattools.pacf_ols
   stattools.ccovf
   stattools.ccf
   stattools.periodogram
   stattools.adfuller
   stattools.q_stat
   stattools.grangercausalitytests
   stattools.levinson_durbin
   stattools.arma_order_select_ic
   x13.x13_arima_select_order
   x13.x13_arima_analysis

Estimation
""""""""""

The following are the main estimation classes, which can be accessed through
statsmodels.tsa.api and their result classes

Univariate Autogressive Processes (AR)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. currentmodule:: statsmodels.tsa

.. autosummary::
   :toctree: generated/

   ar_model.AR
   ar_model.ARResults


Autogressive Moving-Average Processes (ARMA) and Kalman Filter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. currentmodule:: statsmodels.tsa

.. autosummary::
   :toctree: generated/

   arima_model.ARMA
   arima_model.ARMAResults
   arima_model.ARIMA
   arima_model.ARIMAResults
   kalmanf.kalmanfilter.KalmanFilter

Vector Autogressive Processes (VAR)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. autosummary::
   :toctree: generated/

   vector_ar.var_model.VAR
   vector_ar.var_model.VARResults
   vector_ar.dynamic.DynamicVAR

.. seealso:: tutorial :ref:`VAR documentation <var>`

.. currentmodule:: statsmodels.tsa

Vector Autogressive Processes (VAR)
"""""""""""""""""""""""""""""""""""

Besides estimation, several process properties and additional results after
estimation are available for vector autoregressive processes.

.. autosummary::
   :toctree: generated/

   vector_ar.var_model.VAR
   vector_ar.var_model.VARProcess
   vector_ar.var_model.VARResults
   vector_ar.irf.IRAnalysis
   vector_ar.var_model.FEVD
   vector_ar.dynamic.DynamicVAR

.. seealso:: tutorial :ref:`VAR documentation <var>`

ARMA Process
""""""""""""

The following are tools to work with the theoretical properties of an ARMA
process for given lag-polynomials.

.. autosummary::
   :toctree: generated/

   arima_process.ArmaProcess
   arima_process.ar2arma
   arima_process.arma2ar
   arima_process.arma2ma
   arima_process.arma_acf
   arima_process.arma_acovf
   arima_process.arma_generate_sample
   arima_process.arma_impulse_response
   arima_process.arma_pacf
   arima_process.arma_periodogram
   arima_process.deconvolve
   arima_process.index2lpol
   arima_process.lpol2index
   arima_process.lpol_fiar
   arima_process.lpol_fima
   arima_process.lpol_sdiff

.. currentmodule:: statsmodels

.. autosummary::
   :toctree: generated/

   sandbox.tsa.fftarma.ArmaFft

.. currentmodule:: statsmodels.tsa

Time Series Filters
"""""""""""""""""""

.. autosummary::
   :toctree: generated/

   filters.bk_filter.bkfilter
   filters.hp_filter.hpfilter
   filters.cf_filter.cffilter
   filters.filtertools.convolution_filter
   filters.filtertools.recursive_filter
   filters.filtertools.miso_lfilter
   filters.filtertools.fftconvolve3
   filters.filtertools.fftconvolveinv


TSA Tools
"""""""""

.. autosummary::
   :toctree: generated/

   tsatools.add_constant
   tsatools.add_trend
   tsatools.detrend
   tsatools.lagmat
   tsatools.lagmat2ds

VARMA Process
"""""""""""""

.. autosummary::
   :toctree: generated/

   varma_process.VarmaPoly

Interpolation
"""""""""""""

.. autosummary::
   :toctree: generated/

   interp.denton.dentonm
