Calculates the out-of-sample conditional mean forecast.

## Syntax

**ARMA_FORE**(

**X**,

**Order**,

**mean**,

**sigma**,

**phi**,

**theta**,

**T**,

**Type**,

**alpha**)

**X** is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

**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) |

**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).

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

**T** is the forecast time/horizon (expressed in terms of steps beyond the end of the time series).

**Type**is an integer switch to select the forecast output type: (1=mean (default), 2=Std. Error, 3=Term Struct, 4=LL, 5=UL)

Order | Description |
---|---|

1 | Mean forecast value (default) |

2 | Forecast standard error (aka local volatility) |

3 | Volatility term structure |

4 | Lower limit of the forecast confidence interval |

5 | Upper limit of the forecast confidence interval |

**alpha** is the statistical significance level. If missing, a default of 5% is assumed.

## Remarks

- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- 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 be 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 | C | D | |
---|---|---|---|---|

1 | Date | Data | ||

2 | 1/1/2008 | -0.30 | ARMA | |

3 | 1/2/2008 | -1.28 | Mean | -0.00258 |

4 | 1/3/2008 | 0.24 | Sigma | 0.14 |

5 | 1/4/2008 | 1.28 | Phi_1 | -0.236 |

6 | 1/5/2008 | 1.20 | Theta_1 | -5.60E-05 |

7 | 1/6/2008 | 1.73 | ||

8 | 1/7/2008 | -2.18 | ||

9 | 1/8/2008 | -0.23 | ||

10 | 1/9/2008 | 1.10 | ||

11 | 1/10/2008 | -1.09 | ||

12 | 1/11/2008 | -0.69 | ||

13 | 1/12/2008 | -1.69 | ||

14 | 1/13/2008 | -1.85 | ||

15 | 1/14/2008 | -0.98 | ||

16 | 1/15/2008 | -0.77 | ||

17 | 1/16/2008 | -0.30 | ||

18 | 1/17/2008 | -1.28 | ||

19 | 1/18/2008 | 0.24 | ||

20 | 1/19/2008 | 1.28 | ||

21 | 1/20/2008 | 1.20 | ||

22 | 1/21/2008 | 1.73 | ||

23 | 1/22/2008 | -2.18 | ||

24 | 1/23/2008 | -0.23 | ||

25 | 1/24/2008 | 1.10 | ||

26 | 1/25/2008 | -1.09 | ||

27 | 1/26/2008 | -0.69 | ||

28 | 1/27/2008 | -1.69 | ||

29 | 1/28/2008 | -1.85 | ||

30 | 1/29/2008 | -0.98 |

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

=ARMA_FORE(\$B\$2:\$B\$30,1,\$D\$3,\$D\$4,\$D\$5,\$D\$6,1) | The conditional mean forecast value at T+1 (0.228) | |

=ARMA_FORE(\$B\$2:\$B\$30,1,\$D\$3,\$D\$4,\$D\$5,\$D\$6,2) | The conditional mean forecast value at T+2 (-0.057) | |

=ARMA_FORE(\$B\$2:\$B\$30,1,\$D\$3,\$D\$4,\$D\$5,\$D\$6,3) | The conditional mean forecast value at T+3 (0.010) | |

=ARMA_FORE(\$B\$2:\$B\$30,1,\$D\$3,\$D\$4,\$D\$5,\$D\$6,4) | The conditional mean forecast value at T+4 (-0.006) |

## Files Examples

## References

- D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
- James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
- Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740
- Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
- Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568

## 0 Comments