Get Critical Values For Cointegration Tests

Cointegration tests identify scenarios where two or more non-stationary time series are integrated together in a way that they cannot deviate from equilibrium in the long term. The tests are used to identify the degree of sensitivity of two variables to the same average price over a specified period of time.

The Engle-Granger test statistic for cointegration reduces to an ADF unit root test of the residuals of the cointegration regression: If the residuals contain a unit root, then there is no cointegration. The null hypothesis of the ADF test is that the residuals have a unit root.

2 Pedroni's cointegration test Pedroni (1999, 2004) introduced seven test statistics that test the null hypothesis of no cointegration in nonstationary panels. The seven test statistics allow heterogeneity in the panel, both in the short-run dynamics as well as in the long-run slope and intercept coefficients.

The null hypothesis for the trace test is that the number of cointegration vectors is r = r* < k, vs. the alternative that r = k. Testing proceeds sequentially for r* = 1,2, etc. and the first non-rejection of the null is taken as an estimate of r.

Heteroscedasticity tests imply the two following hypotheses. H0 (null hypothesis): data is homoscedastic. Ha (alternative hypothesis): data is heteroscedastic.

Interpreting Our Cointegration Results The Engle-Granger test statistic for cointegration reduces to an ADF unit root test of the residuals of the cointegration regression: If the residuals contain a unit root, then there is no cointegration. The null hypothesis of the ADF test is that the residuals have a unit root.

Examples Critical values for Dickey–Fuller t-distribution. T = 100 −3.51 −2.89 T = 250 −3.46 −2.88 T = 500 −3.44 −2.87 T = ∞ −3.43 −2.865 more rows

For a product-moment correlation, the null hypothesis states that the population correlation coefficient is equal to a hypothesized value (usually 0 indicating no linear correlation), against the alternative hypothesis that it is not equal (or less than, or greater than) the hypothesized value.