Returns the Johansen (cointegration) test statistics for two or more time series.
X is a two dimensional array of cells where each column represent a separate time series.
Order is the time order in the data series (i.e. the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
|1||ascending (the first data point corresponds to the earliest date) (default)|
|0||descending (the first data point corresponds to the latest date)|
Mask is the boolean array to choose the explanatory variables in the model. If missing, all variables in X are included.
k is the number of lagged difference terms used when computing the estimator.
p is the order of the time polynomial in the null hypothesis: (-1 = no deterministic term, 0 = constant-only (default), 1 = constant and trend).
|-1||no deterministic part|
|0||deterministic constant only|
|1||deterministic constant and trend|
Test is a flag to select test: 0 = trace (default), 1 = maximal eigenvalue test.
r is the number of cointegrating relationships between the variables (if missing, r = 1).
Alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, a 5% alpha is assumed.
Return_type is a switch to select the return output (1 = test statistics (default), 2 = critical value).
|1||Test Statistics (e.g. Z-score)|
- Each column in the input matrix corresponds to a separate time series variable.
- The input matrix can have no more than twelve (12) columns (or variables).
- Each row in the input matrix corresponds to an observation.
- The number of cointegrating relationships should be no greater than the number of input variables.
- The time series data are homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- There are two types of Johansen tests: one with trace and one with eigenvalue. Each test will produce slightly different inferences.
- The null hypothesis for the trace test is the number of cointegration vectors r ≤ ?
- The null hypothesis for the eigenvalue test is r = ?
- The function was added in version 1.62 DEWDROP.
- Johansen, Søren (1991). "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models". Econometrica 59 (6): 1551–1580.
- Johansen (1988), 'Statistical Analysis of Co-integration vectors', Journal of Economic Dynamics and Control, 12, pp. 231-254.
- MacKinnon, Haug, Michelis (1996) 'Numerical distribution functions of likelihood ratio tests for cointegration', Queen's University Institute for Economic Research Discussion paper.