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ARMA_FORE
Calculates the outofsample conditional mean forecast.
Syntax
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 longrun 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).
T
is the forecast time/horizon (expressed in terms of steps beyond the end of the time series).
Type
is an integer switch to select the forecast output type: (1=mean (default), 2=Std. Error, 3=Term Struct, 4=LL, 5=UL)
Order  Description 

1  Mean forecast value (default) 
2  Forecast standard error (aka local volatility) 
3  Volatility term structure 
4  Lower limit of the forecast confidence interval 
5  Upper limit of the forecast confidence interval 
alpha
is the statistical significance level. If missing, a default of 5% is assumed.
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 longrun mean can take any value or be omitted, in which case a zero value is assumed.
 The residuals/innovations standard deviation (sigma) must be greater than zero.
 For the input argument  phi:
 The input argument is optional and can be omitted, in which case no AR component is included.
 The order of the parameters starts with the lowest lag.
 One or more parameters may have missing values or an error code (i.e. #NUM!, #VALUE!, etc.).
 The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
 For the input argument  theta:
 The input argument is optional and can be omitted, in which case no MA component is included.
 The order of the parameters starts with the lowest lag.
 One or more values in the input argument can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
 The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
Examples
Example 1:
A  B  C  D  

1  Date  Data  
2  1/1/2008  0.30 
ARMA 

3  1/2/2008  1.28  Mean  0.00258 
4  1/3/2008  0.24  Sigma  0.14 
5  1/4/2008  1.28  Phi_1  0.236 
6  1/5/2008  1.20  Theta_1  5.60E05 
7  1/6/2008  1.73  
8  1/7/2008  2.18  
9  1/8/2008  0.23  
10  1/9/2008  1.10  
11  1/10/2008  1.09  
12  1/11/2008  0.69  
13  1/12/2008  1.69  
14  1/13/2008  1.85  
15  1/14/2008  0.98  
16  1/15/2008  0.77  
17  1/16/2008  0.30  
18  1/17/2008  1.28  
19  1/18/2008  0.24  
20  1/19/2008  1.28  
21  1/20/2008  1.20  
22  1/21/2008  1.73  
23  1/22/2008  2.18  
24  1/23/2008  0.23  
25  1/24/2008  1.10  
26  1/25/2008  1.09  
27  1/26/2008  0.69  
28  1/27/2008  1.69  
29  1/28/2008  1.85  
30  1/29/2008  0.98 
Formula  Description (Result)  

=ARMA_FORE($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,1)  The conditional mean forecast value at T+1 (0.228)  
=ARMA_FORE($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,2)  The conditional mean forecast value at T+2 (0.057)  
=ARMA_FORE($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,3)  The conditional mean forecast value at T+3 (0.010)  
=ARMA_FORE($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6,4)  The conditional mean forecast value at T+4 (0.006) 
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