Returns an array of cells for the standardized residuals of a given ARMA model.
Syntax
ARMA_RESID(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 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).
Warning
ARMA_RESID() function is deprecated as of version 1.63: use ARMA_FIT function instead.
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 standardized residuals have a mean of zero and a variance of one (1).
 The ARMA model's standardized residuals is defined as:
$$\epsilon_t = \frac{a_t}{\sigma_t} $$
$$a_t = x_t  \hat x_t $$
$$\hat x_t = \mu + \sum_{i=1}^p \phi_i x_{ti} + \sum_{j=1}^q \theta_j a_{tj} $$
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 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 nonmissing values in the data sample.
 The number of parameters in the input argument  phi  determines the order of the AR component.
 The number of parameters in the input argument  theta  determines the order of the MA component.
Examples
Example 1:


Files Examples
Related Links
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: 0471690740
 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
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