Forum Replies Created

  • terryyao

    Member
    January 13, 2022 at 12:00 am in reply to: Several question of KDB+ and Q

    thanks Laura :

    for cointegration

    this is python example code?
    def coint(
        y0,
        y1,
        trend="c",
        method="aeg",
        maxlag=None,
        autolag="aic",
        return_results=None,
        """
        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.
    
        **Warning:** The autolag default has changed compared to statsmodels 0.8.
        In 0.8 autolag was always None, no the keyword is used and defaults to
        "aic". Use `autolag=None` to avoid the lag search.
    
        Parameters
        ----------
        y0 : array_like
            The first element in cointegrated system. Must be 1-d.
        y1 : array_like
            The remaining elements in cointegrated system.
        trend : str {"c", "ct"}
            The 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 : {"aeg"}
            Only "aeg" (augmented Engle-Granger) is available.
        maxlag : None or int
            Argument for `adfuller`, largest or given number of lags.
        autolag : str
            Argument for `adfuller`, lag selection criterion.
    
            * If None, then maxlag lags are used without lag search.
            * If "AIC" (default) or "BIC", then the number of lags is chosen
              to minimize the corresponding information criterion.
            * "t-stat" based choice of maxlag.  Starts with maxlag and drops a
              lag until the t-statistic on the last lag length is significant
              using a 5%-sized test.
        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.
    
        Returns
        -------
        coint_t : float
            The 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.
    
        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.
    
        If the two series are almost perfectly collinear, then computing the
        test is numerically unstable. However, the two series will be cointegrated
        under the maintained assumption that they are integrated. In this case
        the t-statistic will be set to -inf and the pvalue to zero.
    
        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
        ----------
        .. [1] MacKinnon, J.G. 1994  "Approximate Asymptotic Distribution Functions
           for Unit-Root and Cointegration Tests." Journal of Business & Economics
           Statistics, 12.2, 167-76.
        .. [2] 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
        """
        y0 = array_like(y0, "y0")
        y1 = array_like(y1, "y1", ndim=2)
        trend = string_like(trend, "trend", options=("c", "nc", "ct", "ctt"))
        method = string_like(method, "method", options=("aeg",))
        maxlag = int_like(maxlag, "maxlag", optional=True)
        autolag = string_like(
            autolag, "autolag", optional=True, options=("aic", "bic", "t-stat")
        )
        return_results = bool_like(return_results, "return_results", optional=True)

    nobs, k_vars = y1.shape
    k_vars += 1 # add 1 for y0

    if trend == “nc”:
    xx = y1
    else:
    xx = add_trend(y1, trend=trend, prepend=False)

    res_co = OLS(y0, xx).fit()

    if res_co.rsquared < 1 – 100 * SQRTEPS:
    res_adf = adfuller(
    res_co.resid, maxlag=maxlag, autolag=autolag, regression=”nc”
    )
    else:
    warnings.warn(
    “y0 and y1 are (almost) perfectly colinear.”
    “Cointegration test is not reliable in this case.”,
    CollinearityWarning,
    )
    # Edge case where series are too similar
    res_adf = (-np.inf,)

    # no constant or trend, see egranger in Stata and MacKinnon
    if trend == “nc”:
    crit = [np.nan] * 3 # 2010 critical values not available
    else:
    crit = mackinnoncrit(N=k_vars, regression=trend, nobs=nobs – 1)
    # nobs – 1, the -1 is to match egranger in Stata, I do not know why.
    # TODO: check nobs or df = nobs – k

    pval_asy = mackinnonp(res_adf[0], regression=trend, N=k_vars)
    return res_adf[0], pval_asy, crit