.. module:: statsmodels.tsa
:synopsis: Time-series analysis
.. currentmodule:: statsmodels.tsa
.. _tsa:
Time Series analysis :mod:`tsa`
===============================
:mod:`statsmodels.tsa` contains model classes and functions that are useful
for time series analysis. Basic models include univariate autoregressive models (AR),
vector autoregressive models (VAR) and univariate autoregressive moving average models
(ARMA). Non-linear models include Markov switching dynamic regression and
autoregression. 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, kpss test, bds 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
- statespace : Comprehensive statespace model specification and estimation. See
the :ref:`statespace documentation `.
- vector_ar, var : vector autoregressive process (VAR) and vector error correction
models, estimation, impulse response analysis, forecast error variance decompositions,
and data visualization tools. See the :ref:`vector_ar documentation ``.
- 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
- regime_switching : Markov switching dynamic regression and autoregression models
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.pacf_burg
stattools.ccovf
stattools.ccf
stattools.adfuller
stattools.kpss
stattools.zivot_andrews
stattools.coint
stattools.bds
stattools.q_stat
stattools.grangercausalitytests
stattools.levinson_durbin
stattools.innovations_algo
stattools.innovations_filter
stattools.levinson_durbin_pacf
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 Autoregressive Processes (AR)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The basic autoregressive model in Statsmodels is:
.. currentmodule:: statsmodels.tsa
.. autosummary::
:toctree: generated/
ar_model.AutoReg
ar_model.AutoRegResults
ar_model.ar_select_order
The `ar_model.AutoReg` model estimates parameters using conditional MLE (OLS),
and supports exogenous regressors (an AR-X model) and seasonal effects.
AR-X and related models can also be fitted with the `arima.ARIMA` class and the
`SARIMAX` class (using full MLE via the Kalman Filter).
Finally, the old class, `ar_model.AR`, is still available but it has been
deprecated.
.. autosummary::
:toctree: generated/
ar_model.AR
ar_model.ARResults
Autoregressive Moving-Average Processes (ARMA) and Kalman Filter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Basic ARIMA model and results classes are as follows:
.. currentmodule:: statsmodels.tsa
.. autosummary::
:toctree: generated/
arima.model.ARIMA
arima.model.ARIMAResults
This model allows estimating parameters by various methods (including
conditional MLE via the Hannan-Rissanen method and full MLE via the Kalman
filter). It is a special case of the `SARIMAX` model, and it includes a large
number of inherited features from the :ref:`state space ` models
(including prediction / forecasting, residual diagnostics, simulation and
impulse responses, etc.).
Prior to version 0.11, the basic ARIMA model and results classes were the
following:
.. autosummary::
:toctree: generated/
arima_model.ARMA
arima_model.ARMAResults
arima_model.ARIMA
arima_model.ARIMAResults
These classes are still available, but they are no longer recommended.
Exponential Smoothing
~~~~~~~~~~~~~~~~~~~~~
Linear and non-linear exponential smoothing models are available:
.. currentmodule:: statsmodels.tsa.holtwinters
.. autosummary::
:toctree: generated/
ExponentialSmoothing
SimpleExpSmoothing
Holt
HoltWintersResults
Separately, linear and non-linear exponential smoothing models have also been
implemented based on the "innovations" state space approach. In addition to the
usual support for parameter fitting, in-sample prediction, and out-of-sample
forecasting, these models also support prediction intervals, simulation, and
more.
.. currentmodule:: statsmodels.tsa
.. autosummary::
:toctree: generated/
exponential_smoothing.ets.ETSModel
exponential_smoothing.ets.ETSResults
Finally, linear exponential smoothing models have also been separately
implemented as a special case of the general state space framework (this is
separate from the "innovations" state space approach described above). Although
this approach does not allow for the non-linear (multiplicative) exponential
smoothing models, it includes all features of :ref:`state space `
models (including prediction / forecasting, residual diagnostics, simulation
and impulse responses, etc.).
.. currentmodule:: statsmodels.tsa
.. autosummary::
:toctree: generated/
statespace.exponential_smoothing.ExponentialSmoothing
statespace.exponential_smoothing.ExponentialSmoothingResults
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.sandbox.tsa.fftarma
.. autosummary::
:toctree: generated/
ArmaFft
.. currentmodule:: statsmodels.tsa
Statespace Models
"""""""""""""""""
See the :ref:`statespace documentation `.
Vector ARs and Vector Error Correction Models
"""""""""""""""""""""""""""""""""""""""""""""
See the :ref:`vector_ar documentation. ```
Regime switching models
"""""""""""""""""""""""
.. currentmodule:: statsmodels.tsa.regime_switching.markov_regression
.. autosummary::
:toctree: generated/
MarkovRegression
.. currentmodule:: statsmodels.tsa.regime_switching.markov_autoregression
.. autosummary::
:toctree: generated/
MarkovAutoregression
Time Series Filters
"""""""""""""""""""
.. currentmodule:: statsmodels.tsa.filters.bk_filter
.. autosummary::
:toctree: generated/
bkfilter
.. currentmodule:: statsmodels.tsa.filters.hp_filter
.. autosummary::
:toctree: generated/
hpfilter
.. currentmodule:: statsmodels.tsa.filters.cf_filter
.. autosummary::
:toctree: generated/
cffilter
.. currentmodule:: statsmodels.tsa.filters.filtertools
.. autosummary::
:toctree: generated/
convolution_filter
recursive_filter
miso_lfilter
fftconvolve3
fftconvolveinv
.. currentmodule:: statsmodels.tsa.seasonal
.. autosummary::
:toctree: generated/
seasonal_decompose
STL
DecomposeResult
TSA Tools
"""""""""
.. currentmodule:: statsmodels.tsa.tsatools
.. autosummary::
:toctree: generated/
add_lag
add_trend
detrend
lagmat
lagmat2ds
VARMA Process
"""""""""""""
.. currentmodule:: statsmodels.tsa.varma_process
.. autosummary::
:toctree: generated/
VarmaPoly
Interpolation
"""""""""""""
.. currentmodule:: statsmodels.tsa.interp.denton
.. autosummary::
:toctree: generated/
dentonm
Deterministic Processes
"""""""""""""""""""""""
Deterministic processes simplify creating deterministic sequences with time
trend or seasonal patterns. They also provide methods to simplify generating
deterministic terms for out-of-sample forecasting. A
:class:`~statsmodels.tsa.deterministic.DeterministicProcess` can be directly
used with :class:`~statsmodels.tsa.ar_model.AutoReg` to construct complex
deterministic dynamics and to forecast without constructing exogenous trends.
.. currentmodule:: statsmodels.tsa.deterministic
.. autosummary::
:toctree: generated/
DeterministicProcess
TimeTrend
Seasonality
Fourier
CalendarTimeTrend
CalendarSeasonality
CalendarFourier
DeterministicTerm
CalendarDeterministicTerm
FourierDeterministicTerm
TimeTrendDeterministicTerm
Users who wish to write custom deterministic terms must subclass
:class:`~statsmodels.tsa.deterministic.DeterministicTerm`.
.. currentmodule:: statsmodels.tsa.deterministic
.. autosummary::
:toctree: generated/
DeterministicTerm
Forecasting Models
""""""""""""""""""
.. module:: statsmodels.tsa.forecasting
:synopsis: Models designed for forecasting
.. currentmodule:: statsmodels.tsa.forecasting
The Theta Model
~~~~~~~~~~~~~~~
The Theta model is a simple forecasting method that combines a linear time
trend with a Simple Exponential Smoother (Assimakopoulos & Nikolopoulos).
An estimator for the parameters of the Theta model and methods to forecast
are available in:
.. module:: statsmodels.tsa.forecasting.theta
:synopsis: Models designed for forecasting
.. currentmodule:: statsmodels.tsa.forecasting.theta
.. autosummary::
:toctree: generated/
ThetaModel
ThetaModelResults
Forecasting after STL Decomposition
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
:class:`statsmodels.tsa.seasonal.STL` is commonly used to remove seasonal
components from a time series. The deseasonalized time series can then
be modeled using a any non-seasonal model, and forecasts are constructed
by adding the forecast from the non-seasonal model to the estimates of
the seasonal component from the final full-cycle which are forecast using
a random-walk model.
.. module:: statsmodels.tsa.forecasting.stl
:synopsis: Models designed for forecasting
.. currentmodule:: statsmodels.tsa.forecasting.stl
.. autosummary::
:toctree: generated/
STLForecast
STLForecastResults
Prediction Results
""""""""""""""""""
Most forecasting methods support a ``get_prediction`` method that return
a ``PredictionResults`` object that contains both the prediction, its
variance and can construct a prediction interval.
Results Class
~~~~~~~~~~~~~
.. module:: statsmodels.tsa.base.prediction
:synopsis: Shared objects for predictive methods
.. currentmodule:: statsmodels.tsa.base.prediction
.. autosummary::
:toctree: generated/
PredictionResults
`