# ARMA_RESID - ARMA Fitted Values of Standardized Residuals.

Returns an array of cells for the standardized residuals of a given ARMA model.

## Syntax

ARMA_RESID ([x], order, µ, σ, [φ], [θ])

[X]
Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
Order
Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Value Order
1 Ascending (the first data point corresponds to the earliest date) (default).
0 Descending (the first data point corresponds to the latest date).
µ
Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
σ
Required. Is the standard deviation value of the model's residuals/innovations.
[φ]
Optional. Are the parameters of the AR(p) component model: [φ1, φ2 … φp] (starting with the lowest lag).
[θ]
Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (starting with the lowest lag).

Warning

ARMA_RESID(.) function is deprecated as of version 1.63: use the ARMA_FIT(.) function instead.

## Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. The standardized residuals have a mean of zero and a variance of one (1).
5. The ARMA model's standardized residuals are defined as:$$\epsilon_t = \frac{a_t}{\sigma_t}$$ $$a_t = x_t - \hat x_t$$ $$\hat x_t = \mu + \sum_{i=1}^p \phi_i x_{t-i} + \sum_{j=1}^q \theta_j a_{t-j}$$

Where:

• $\epsilon$ is the ARMA model's standardized residual at time $t$.
• $a_t$ is the ARMA model's residual at time $t$.
• $x_t$ is the value of the time series at time $t$.
• $\hat x_t$ 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 - ([φ]) - determines the order of the AR component.
7. The number of parameters in the input argument - ([θ]) - determines the order of the MA component.