ARMA_FORE - Forecasting for ARMA Model

Calculates the out-of-sample conditional mean forecast.

Syntax

ARMA_FORE(X, Order, mean, sigma, phi, theta, T, Type, alpha)
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 long-run 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).
T
is the forecast time/horizon (expressed in 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

  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 long-run mean can take any value or be omitted, in which case a zero value is assumed.
  5. The residuals/innovations standard deviation (sigma) must be greater than zero.
  6. For the input argument - phi:
    • The input argument is optional and can be omitted, so 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 last value solely determines the order of the AR component model in the array with a numeric value (vs. missing or error).
  7. For the input argument - theta:
    • The input argument is optional and can be omitted, so 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 last value solely determines the order of the MA component model in the array with a numeric value (vs. missing or error).

Examples

Example 1:

 
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A B C D
Date Data    
1/1/2008 -0.30 ARMA  
1/2/2008 -1.28 Mean -0.00258
1/3/2008 0.24 Sigma 0.14
1/4/2008 1.28 Phi_1 -0.236
1/5/2008 1.20 Theta_1 -5.60E-05
1/6/2008 1.73    
1/7/2008 -2.18    
1/8/2008 -0.23    
1/9/2008 1.10    
1/10/2008 -1.09    
1/11/2008 -0.69    
1/12/2008 -1.69    
1/13/2008 -1.85    
1/14/2008 -0.98    
1/15/2008 -0.77    
1/16/2008 -0.30    
1/17/2008 -1.28    
1/18/2008 0.24    
1/19/2008 1.28    
1/20/2008 1.20    
1/21/2008 1.73    
1/22/2008 -2.18    
1/23/2008 -0.23    
1/24/2008 1.10    
1/25/2008 -1.09    
1/26/2008 -0.69    
1/27/2008 -1.69    
1/28/2008 -1.85    
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)

 

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