class statsmodels.tsa.vector_ar.var_model.VARResults(endog, endog_lagged, params, sigma_u, lag_order, model=None, trend='c', names=None, dates=None, exog=None) [source]

Estimate VAR(p) process with fixed number of lags

  • endog (array) –
  • endog_lagged (array) –
  • params (array) –
  • sigma_u (array) –
  • lag_order (int) –
  • model (VAR model instance) –
  • trend (str {'nc', 'c', 'ct'}) –
  • names (array-like) – List of names of the endogenous variables in order of appearance in endog.
  • dates
  • exog (array) –
  • **Attributes**
  • aic
  • bic
  • bse
  • coefs (ndarray (p x K x K)) – Estimated A_i matrices, A_i = coefs[i-1]
  • cov_params
  • dates
  • detomega
  • df_model (int)
  • df_resid (int)
  • endog
  • endog_lagged
  • fittedvalues
  • fpe
  • intercept
  • info_criteria
  • k_ar (int)
  • k_trend (int)
  • llf
  • model
  • names
  • neqs (int) – Number of variables (equations)
  • nobs (int)
  • n_totobs (int)
  • params
  • k_ar (int) – Order of VAR process
  • params (ndarray (Kp + 1) x K) – A_i matrices and intercept in stacked form [int A_1 … A_p]
  • pvalues
  • names (list) – variables names
  • resid
  • roots (array) – The roots of the VAR process are the solution to (I - coefs[0]*z - coefs[1]*z**2 … - coefs[p-1]*z**k_ar) = 0. Note that the inverse roots are returned, and stability requires that the roots lie outside the unit circle.
  • sigma_u (ndarray (K x K)) – Estimate of white noise process variance Var[u_t]
  • sigma_u_mle
  • stderr
  • trenorder
  • tvalues
  • y
  • ys_lagged


acf([nlags]) Compute theoretical autocovariance function
acorr([nlags]) Compute theoretical autocorrelation function
bse() Standard errors of coefficients, reshaped to match in size
cov_params() Estimated variance-covariance of model coefficients
cov_ybar() Asymptotically consistent estimate of covariance of the sample mean
detomega() Return determinant of white noise covariance with degrees of freedom correction:
fevd([periods, var_decomp]) Compute forecast error variance decomposition (“fevd”)
fittedvalues() The predicted insample values of the response variables of the model.
forecast(y, steps[, exog_future]) Produce linear minimum MSE forecasts for desired number of steps ahead, using prior values y
forecast_cov([steps, method]) Compute forecast covariance matrices for desired number of steps
forecast_interval(y, steps[, alpha, exog_future]) Construct forecast interval estimates assuming the y are Gaussian
get_eq_index(name) Return integer position of requested equation name
info_criteria() information criteria for lagorder selection
intercept_longrun() Long run intercept of stable VAR process
irf([periods, var_decomp, var_order]) Analyze impulse responses to shocks in system
irf_errband_mc([orth, repl, T, signif, …]) Compute Monte Carlo integrated error bands assuming normally distributed for impulse response functions
irf_resim([orth, repl, T, seed, burn, cum]) Simulates impulse response function, returning an array of simulations.
is_stable([verbose]) Determine stability based on model coefficients
llf() Compute VAR(p) loglikelihood
long_run_effects() Compute long-run effect of unit impulse
ma_rep([maxn]) Compute MA(\(\infty\)) coefficient matrices
mean() Long run intercept of stable VAR process
mse(steps) Compute theoretical forecast error variance matrices
orth_ma_rep([maxn, P]) Compute orthogonalized MA coefficient matrices using P matrix such that \(\Sigma_u = PP^\prime\).
plot() Plot input time series
plot_acorr([nlags, resid, linewidth]) Plot autocorrelation of sample (endog) or residuals
plot_forecast(steps[, alpha, plot_stderr]) Plot forecast
plot_sample_acorr([nlags, linewidth]) Plot theoretical autocorrelation function
plotsim([steps, offset, seed]) Plot a simulation from the VAR(p) process for the desired number of steps
pvalues() Two-sided p-values for model coefficients from Student t-distribution
reorder(order) Reorder variables for structural specification
resid() Residuals of response variable resulting from estimated coefficients
resid_acorr([nlags]) Compute sample autocorrelation (including lag 0)
resid_acov([nlags]) Compute centered sample autocovariance (including lag 0)
resid_corr() Centered residual correlation matrix
sigma_u_mle() (Biased) maximum likelihood estimate of noise process covariance
simulate_var([steps, offset, seed]) simulate the VAR(p) process for the desired number of steps
stderr() Standard errors of coefficients, reshaped to match in size
summary() Compute console output summary of estimates
test_causality(caused[, causing, kind, signif]) Test Granger causality
test_inst_causality(causing[, signif]) Test for instantaneous causality
test_normality([signif]) Test assumption of normal-distributed errors using Jarque-Bera-style omnibus Chi^2 test.
test_whiteness([nlags, signif, adjusted]) Residual whiteness tests using Portmanteau test
tvalues() Compute t-statistics.


aic Akaike information criterion
bic Bayesian a.k.a.
df_model Number of estimated parameters, including the intercept / trends
df_resid Number of observations minus number of estimated parameters
fpe Final Prediction Error (FPE)
hqic Hannan-Quinn criterion

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.