arch.unitroot.cointegration.DynamicOLS.fit¶
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DynamicOLS.fit(cov_type='unadjusted', kernel='bartlett', bandwidth=None, force_int=False, df_adjust=False)[source]¶ Estimate the Dynamic OLS regression
- Parameters
cov_type (str, default "unadjusted") -- Either "unadjusted" (or is equivalent "homoskedastic") or "robust" (or its equivalent "kernel").
kernel (str, default "bartlett") -- The string name of any of any known kernel-based long-run covariance estimators. Common choices are "bartlett" for the Bartlett kernel (Newey-West), "parzen" for the Parzen kernel and "quadratic-spectral" for the Quadratic Spectral kernel.
bandwidth (int, default None) -- The bandwidth to use. If not provided, the optimal bandwidth is estimated from the data. Setting the bandwidth to 0 and using "unadjusted" produces the classic OLS covariance estimator. Setting the bandwidth to 0 and using "robust" produces White's covariance estimator.
force_int (bool, default False) -- Whether the force the estimated optimal bandwidth to be an integer.
df_adjust (bool, default False) -- Whether the adjust the parameter covariance to account for the number of parameters estimated in the regression. If true, the parameter covariance estimator is multiplied by T/(T-k) where k is the number of regressors in the model.
- Returns
The estimation results.
- Return type
See also
arch.unitroot.cointegration.engle_granger()Cointegration testing using the Engle-Granger methodology
statsmodels.regression.linear_model.OLS()Ordinal Least Squares regression.
Notes
When using the unadjusted covariance, the parameter covariance is estimated as
\[T^{-1} \hat{\sigma}^2_{HAC} \hat{\Sigma}_{ZZ}^{-1}\]where \(\hat{\sigma}^2_{HAC}\) is an estimator of the long-run variance of the regression error and \(\hat{\Sigma}_{ZZ}=T^{-1}Z'Z\). \(Z_t\) is a vector the includes all terms in the regression (i.e., deterministics, cross-sectional, leads and lags) When using the robust covariance, the parameter covariance is estimated as
\[T^{-1} \hat{\Sigma}_{ZZ}^{-1} \hat{S}_{HAC} \hat{\Sigma}_{ZZ}^{-1}\]where \(\hat{S}_{HAC}\) is a Heteroskedasticity-Autocorrelation Consistent estimator of the covariance of the regression scores \(Z_t\epsilon_t\).