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
y (array_like) – The left-hand-side variable in the cointegrating regression.
x (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
lags (int, default None) – The number of lags to include in the model. If None, the optimal number of lags is chosen using method.
leads (int, default None) – The number of leads to include in the model. If None, the optimal number of leads is chosen using method.
common (bool, 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_lag (int, default None) – The maximum lag to consider. See Notes for value used when None.
max_lead (int, 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 1 and 2 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