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ARMA_RESID
Returns an array of cells for the standardized residuals of a given ARMA^{i} model.
Syntax
X
is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).
Order
is the time order of the data series (i.e. whether the first data point corresponds to the earliest or latest date (earliest date=1 (default), latest date=0)).
Order  Description 

1  ascending (the first data point corresponds to the earliest date) 
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^{i}).
theta
are the parameters of the MA(q) component model (starting with the lowest lag).
Remarks
 Warning: ARMA_RESID() function is deprecated as of version 1.63: use ARMA_FIT function instead.
 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:
Where:
 is the ARMA model's standardized residual at time t.
 is the ARMA model's residual at time t.
 is the value of time series at time t.

is the fitted model value (i.e. conditional mean) at time 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:
A  B  C  D  E  

1  Date  Data  
2  January 10, 2008  0.30  0.032 
ARMA 

3  January 11, 2008  1.28  0.638  Mean  0.35 
4  January 12, 2008  0.24  0.641  Sigma  1.3059 
5  January 13, 2008  1.28  0.793  Phi_1  0.4296 
6  January 14, 2008  1.20  0.925  Theta_1  0.999897 
7  January 15, 2008  1.73  1.167  
8  January 16, 2008  2.18  1.715  
9  January 17, 2008  0.23  1.058 
LLF^{i} 
stable? 
10  January 18, 2008  1.10  0.137  44  1 
11  January 19, 2008  1.09  0.212  
12  January 20, 2008  0.69  0.289  
13  January 21, 2008  1.69  0.829  
14  January 22, 2008  1.85  0.763  
15  January 23, 2008  0.98  0.230  
16  January 24, 2008  0.77  0.297  
17  January 25, 2008  0.30  0.183  
18  January 26, 2008  1.28  0.851  
19  January 27, 2008  0.24  0.951  
20  January 28, 2008  1.28  0.503  
21  January 29, 2008  1.20  1.205  
22  January 30, 2008  1.73  0.905  
23  January 31, 2008  2.18  1.570  
24  February 1, 2008  0.23  1.007  
25  February 2, 2008  1.10  0.160  
26  February 3, 2008  1.09  0.242  
27  February 4, 2008  0.69  0.262  
28  February 5, 2008  1.69  0.866  
29  February 6, 2008  1.85  0.726  
30  February 7, 2008  0.98  0.257 
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740