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GARCH_RESID
Returns an array of the standardized residuals for the fitted GARCH^{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 GARCH model mean (i.e. mu).
alphas
are the parameters of the ARCH(p) component model (starting with the lowest lag^{i}).
betas
are the parameters of the GARCH(q) component model (starting with the lowest lag).
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 GARCH model's standardized residuals is defined as:
Where:
 is the GARCH model's standardized residual at time t.
 is the GARCH model's residual at time t.
 is the value of the time series at time t.
 is the GARCH mean.
 is the GARCH conditional volatility at time t.
 The number of parameters in the input argument  alpha  determines the order of the ARCH component model.
 The number of parameters in the input argument  beta  determines the order of the GARCH component model.
Examples
Example 1:
A  B  C  D  E  

1  Date  Data  
2  January 10, 2008  2.827  2.669 
GARCH(1,1) 

3  January 11, 2008  0.947  0.788  Mean  0.16 
4  January 12, 2008  0.877  0.718  Alpha_0  0.608 
5  January 13, 2008  1.209  1.370  Alpha_1  0.00 
6  January 14, 2008  1.669  1.510  Beta_1  0.391 
7  January 15, 2008  0.835  0.996  
8  January 16, 2008  0.266  0.106  
9  January 17, 2008  1.361  1.522  
10  January 18, 2008  0.343  0.183  
11  January 19, 2008  0.475  0.636  
12  January 20, 2008  1.153  0.994  
13  January 21, 2008  1.144  1.305  
14  January 22, 2008  1.070  0.911  
15  January 23, 2008  1.491  1.332  
16  January 24, 2008  0.686  0.847  
17  January 25, 2008  0.975  1.136  
18  January 26, 2008  1.316  1.157  
19  January 27, 2008  0.125  0.285  
20  January 28, 2008  0.712  0.873  
21  January 29, 2008  1.530  1.371  
22  January 30, 2008  0.918  1.079  
23  January 31, 2008  0.365  0.525  
24  February 1, 2008  0.997  0.838  
25  February 2, 2008  0.360  0.200  
26  February 3, 2008  1.347  1.508  
27  February 4, 2008  1.339  1.180  
28  February 5, 2008  0.481  0.642  
29  February 6, 2008  1.270  1.111  
30  February 7, 2008  1.710  1.872  
31  February 8, 2008  0.125  0.035  
32  February 9, 2008  0.940  0.781 
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