7.8. Time Series analysis tsa¶

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.