# ARMA_FORECI - Forecasting confidence interval of ARMA Model

Returns the confidence interval limits of the conditional mean forecast.

## Syntax

ARMA_FORECI(X, Order, mean, sigma, phi, theta, T, alpha, upper)

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 model 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 end of the time series).

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

upper If true, returns the upper confidence interval limit. Otherwise, returns the lower limit.

upper description
0 return lower limit
1 return upper limit

## Remarks

1. The underlying model is described here.
2. Warning: ARMA_FORECI() function is deprecated as of version 1.63: use ARMA_FORE function instead.
3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g. #N/A) at either end.
5. The number of parameters in the input argument - phi - determines the order of the AR component.
6. The number of parameters in the input argument - theta - determines the order of the MA component.

## Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A B C D
Date Data
1/1/2008 -0.30 ARMA
1/2/2008 -1.28 Mean -0.00258
1/3/2008 0.24 Sigma 0.14
1/4/2008 1.28 Phi_1 -0.236
1/5/2008 1.20 Theta_1 -5.60E-05
1/6/2008 1.73
1/7/2008 -2.18
1/8/2008 -0.23
1/9/2008 1.10
1/10/2008 -1.09
1/11/2008 -0.69
1/12/2008 -1.69
1/13/2008 -1.85
1/14/2008 -0.98
1/15/2008 -0.77
1/16/2008 -0.30
1/17/2008 -1.28
1/18/2008 0.24
1/19/2008 1.28
1/20/2008 1.20
1/21/2008 1.73
1/22/2008 -2.18
1/23/2008 -0.23
1/24/2008 1.10
1/25/2008 -1.09
1/26/2008 -0.69
1/27/2008 -1.69
1/28/2008 -1.85
1/29/2008 -0.98

Formula Description (Result)
=ARMA_FORE($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,1) The conditional mean forecast value at T+1 (0.228)
=ARMA_FORECI($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,1,5%,1) Upper confidence interval limit for the forecasted conditional mean at T+1 (0.503)
=ARMA_FORECI($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,1,5%,0) Lower confidence interval limit for the forecasted conditional mean at T+1 (-0.046)