.. 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.periodogram 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) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Beginning in version 0.11, Statsmodels has introduced a new class dedicated to autoregressive models. .. 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: .. autosummary:: :toctree: generated/ arima_model.ARMA arima_model.ARMAResults arima_model.ARIMA arima_model.ARIMAResults However, beginning in version 0.11, Statsmodels has introduced a new class dedicated to ARIMA models. While this class is still in a testing phase, it should be the starting point for for most users going forwards: .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ arima.model.ARIMA arima.model.ARIMAResults The `arima.model.ARIMA` model allows estimating parameters by various methods (including conditional MLE via the Hannan-Rissanen method and full MLE via the Kalman filter). Since it is a special case of the `SARIMAX` model, it includes all features of :ref:`state space ` models (including prediction / forecasting, residual diagnostics, simulation and impulse responses, etc.). Exponential Smoothing ~~~~~~~~~~~~~~~~~~~~~ Linear and non-linear exponential smoothing models are available: .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ holtwinters.ExponentialSmoothing holtwinters.SimpleExpSmoothing holtwinters.Holt holtwinters.HoltWintersResults Linear exponential smoothing models have also been separately implemented as a special case of the state space framework. 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