# ARMA_FORESD - Forecasting Error of ARMA Model

Calculates the estimated error/standard deviation of the conditional mean forecast.

## Syntax

ARMA_FORESD(X, Order, mean, sigma, phi, theta, T)
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 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).

## Remarks

1. The underlying model is described here.
2. Warning: ARMA_FORESD() function is deprecated as of version 1.63: use the 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:

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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_FORESD(\$B\$2:\$B\$30,1,\$D\$3,\$D\$4,\$D\$5,\$D\$6,1) The conditional mean forecast error at T+1 (0.140)