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 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)).

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 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.

## Files Examples

## 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.

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