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# ARMA_CHECK

Examines the model's parameters for stability constraints (e.g. stationary, invertibility, causality, etc.).

## Syntax

**ARMA**(

^{i}_CHECK**mean**,

**sigma**,

**phi**,

**theta**)

**mean**

is the ARMA model long-run mean (i.e. mu).

**sigma**

is the standard deviation of the model's residuals/innovations.

**phi**

are the parameters of the AR(p) component model (starting with the lowest lag^{i}).

**theta**

are the parameters of the MA(q) component model (starting with the lowest lag).

## Remarks

- The underlying model is described here.
- ARMA_CHECK checks the process for stability: stationarity, invertability, and causality.
- Using the Solver add-in in Excel, you can specify the return value of ARMA_CHECK as a constraint to ensure a stationary ARMA model.
- The long-run mean can take any value or be omitted, in which case a zero value is assumed.
- The residuals/innovations standard deviation (sigma) must greater than zero.
- For the input argument - phi:
- The input argument is optional and can be omitted, in which case no AR component is included.
- The order of the parameters starts with the lowest lag.
- One or more parameters may have missing values or an error code (i.e. #NUM!, #VALUE!, etc.).
- The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

- For the input argument - theta:
- The input argument is optional and can be omitted, in which case no MA component is included.
- The order of the parameters starts with the lowest lag.
- One or more values in the input argument can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
- The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

## Examples

**Example 1: **

A | B | |
---|---|---|

1 | ARMA | |

2 | Mean | -0.35 |

3 | Sigma | 1.3059 |

4 | Phi_1 | -0.4296 |

5 | Theta | 0.999897 |

Formula | Description (Result) | |
---|---|---|

=ARMA_CHECK($B$2,$B$3,$B$4,$B$5) | Is the model stable? (1) |

## Files Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740