Returns the Johansen (cointegration) test statistics for two or more time series.

## Syntax

**JohansenTest**(

**X**,

**Order**,

**Mask**,

**k**,

**p**,

**Test**,

**r**,

**Alpha**,

**Return_type**)

- X
- is a two-dimensional array of cells where each column represents 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)).
Order Description 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).
Method Description -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).
Method Description 1 Test Statistics (e.g., Z-score) 2 Critical Value

## Remarks

- Each column in the input matrix corresponds to a separate time series variable.
- The input matrix can have up to 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.

## Files Examples

## Related Links

## References

- 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.

## Comments

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