# arch.unitroot.cointegration.DynamicOLS¶

class arch.unitroot.cointegration.DynamicOLS(y, x, trend='c', lags=None, leads=None, common=False, max_lag=None, max_lead=None, method='bic')[source]

Dynamic OLS (DOLS) cointegrating vector estimation

Parameters
ynumpy:array_like

The left-hand-side variable in the cointegrating regression.

xnumpy:array_like

The right-hand-side variables in the cointegrating regression.

trend{“n”,”c”,”ct”,”ctt”}, default “c”

Trend to include in the cointegrating regression. Trends are:

• “n”: No deterministic terms

• “c”: Constant

• “ct”: Constant and linear trend

• “ctt”: Constant, linear and quadratic trends

lagsint, default None

The number of lags to include in the model. If None, the optimal number of lags is chosen using method.

leadsint, default None

The number of leads to include in the model. If None, the optimal number of leads is chosen using method.

commonbool, default False

Flag indicating that lags and leads should be restricted to the same value. When common is None, lags must equal leads and max_lag must equal max_lead.

max_lagint, default None

The maximum lag to consider. See Notes for value used when None.

max_leadint, default None

The maximum lead to consider. See Notes for value used when None.

method{“aic”,”bic”,”hqic”}, default “bic”

The method used to select lag length when lags or leads is None.

• “aic” - Akaike Information Criterion

• “hqic” - Hannan-Quinn Information Criterion

• “bic” - Schwartz/Bayesian Information Criterion

Notes

The cointegrating vector is estimated from the regression

$Y_t = D_t \delta + X_t \beta + \Delta X_{t} \gamma + \sum_{i=1}^p \Delta X_{t-i} \kappa_i + \sum _{j=1}^q \Delta X_{t+j} \lambda_j + \epsilon_t$

where p is the lag length and q is the lead length. $$D_t$$ is a vector containing the deterministic terms, if any. All specifications include the contemporaneous difference $$\Delta X_{t}$$.

When lag lengths are not provided, the optimal lag length is chosen to minimize an Information Criterion of the form

$\ln\left(\hat{\sigma}^2\right) + k\frac{c}{T}$

where c is 2 for Akaike, $$2\ln\ln T$$ for Hannan-Quinn and $$\ln T$$ for Schwartz/Bayesian.

See  and  for further details.

References

1

Saikkonen, P. (1992). Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric theory, 8(1), 1-27.

2

Stock, J. H., & Watson, M. W. (1993). A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica: Journal of the Econometric Society, 783-820.

Methods

 fit([cov_type, kernel, bandwidth, …]) Estimate the Dynamic OLS regression

Methods

 fit([cov_type, kernel, bandwidth, …]) Estimate the Dynamic OLS regression