# ARMA_MEAN - ARMA fitted values of conditional mean

Returns an array of cells for the fitted values of the conditional mean.

## Syntax

ARMA_MEAN(X, Order, mean, sigma, phi, theta)
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).

## Remarks

1. The underlying model is described here.
2. Warning: ARMA_MEAN() function is deprecated as of version 1.63: use ARMA_FIT 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 ARMA model fitted values are defined as:

$$\hat x_t = \mu + \sum_{i=1}^p \phi_i x_{t-i} + \sum_{j=1}^q \theta_j a_{t-j}$$

Where:
• $\hat x_t$ is the fitted model value (i.e. conditional mean) at time t.

$1\leq t \leq T$
• $T$ is the number of non-missing values in the data sample.
6. The number of parameters in the input argument - phi - determines the order of the AR component.
7. 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 E
Date Data ARMA_MEAN
January 10, 2008 -0.30 -0.342 ARMA
January 11, 2008 -1.28 -0.447 Mean -0.35
January 12, 2008 0.24 -0.597 Sigma 1.3059
January 13, 2008 1.28 0.244 Phi_1 -0.4296
January 14, 2008 1.20 -0.008 Theta_1 0.999897
January 15, 2008 1.73 0.207
January 16, 2008 -2.18 0.060
January 17, 2008 -0.23 -1.611
January 18, 2008 1.10 0.921
January 19, 2008 -1.09 -0.813
January 20, 2008 -0.69 -0.312
January 21, 2008 -1.69 -0.607
January 22, 2008 -1.85 -0.853
January 23, 2008 -0.98 -0.679
January 24, 2008 -0.77 -0.382
January 25, 2008 -0.30 -0.539
January 26, 2008 -1.28 -0.168
January 27, 2008 0.24 -1.002
January 28, 2008 1.28 0.623
January 29, 2008 1.20 -0.373
January 30, 2008 1.73 0.545
January 31, 2008 -2.18 -0.130
February 1, 2008 -0.23 -1.545
February 2, 2008 1.10 0.892
February 3, 2008 -1.09 -0.774
February 4, 2008 -0.69 -0.348
February 5, 2008 -1.69 -0.559
February 6, 2008 -1.85 -0.901
February 7, 2008 -0.98 -0.644