Test for no-cointegration of a univariate equation
The null hypothesis is no cointegration. Variables in y0 and y1 are
assumed to be integrated of order 1, I(1).
This uses the augmented Engle-Granger two-step cointegration test.
Constant or trend is included in 1st stage regression, i.e. in
cointegrating equation.
Parameters: | y1 : array_like, 1d
first element in cointegrating vector
y2 : array_like
remaining elements in cointegrating vector
trend : str {‘c’, ‘ct’}
trend term included in regression for cointegrating equation
* ‘c’ : constant
* ‘ct’ : constant and linear trend
* also available quadratic trend ‘ctt’, and no constant ‘nc’
method : string
currently only ‘aeg’ for augmented Engle-Granger test is available.
default might change.
maxlag : None or int
keyword for adfuller, largest or given number of lags
autolag : string
keyword for adfuller, lag selection criterion.
return_results : bool
for future compatibility, currently only tuple available.
If True, then a results instance is returned. Otherwise, a tuple
with the test outcome is returned.
Set return_results=False to avoid future changes in return.
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Returns: | coint_t : float
t-statistic of unit-root test on residuals
pvalue : float
MacKinnon’s approximate, asymptotic p-value based on MacKinnon (1994)
crit_value : dict
Critical values for the test statistic at the 1 %, 5 %, and 10 %
levels based on regression curve. This depends on the number of
observations.
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Notes
The Null hypothesis is that there is no cointegration, the alternative
hypothesis is that there is cointegrating relationship. If the pvalue is
small, below a critical size, then we can reject the hypothesis that there
is no cointegrating relationship.
P-values and critical values are obtained through regression surface
approximation from MacKinnon 1994 and 2010.
TODO: We could handle gaps in data by dropping rows with nans in the
auxiliary regressions. Not implemented yet, currently assumes no nans
and no gaps in time series.
References
- MacKinnon, J.G. 1994 “Approximate Asymptotic Distribution Functions for
- Unit-Root and Cointegration Tests.” Journal of Business & Economics
Statistics, 12.2, 167-76.
- MacKinnon, J.G. 2010. “Critical Values for Cointegration Tests.”
- Queen’s University, Dept of Economics Working Papers 1227.
http://ideas.repec.org/p/qed/wpaper/1227.html