GARCHM_FORECI - Forecasting confidence interval of GARCH-M Model

(deprecated) Returns the confidence interval limits of the conditional mean forecast.

Syntax

GARCHM_FORECI(X, Sigmas, Order, mean, lambda, alphas, betas, innovation, v, T, alpha-level, upper)

X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

Sigmas is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)) of the last q realized volatilities.

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 GARCH-M model mean (i.e. mu).

lambda is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.

alphas are the parameters of the ARCH(p) component model (starting with the lowest lag).

betas are the parameters of the GARCH(q) component model (starting with the lowest lag).

innovation is the probability distribution model for the innovations/residuals (1=Gaussian (default), 2=t-Distribution, 3=GED).

value Description
1 Gaussian or Normal Distribution (default)
2 Student's t-Distribution
3 Generalized Error Distribution (GED)

v is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function.

T is the forecast time/horizon (expressed in terms of steps beyond end of the time series X).

alpha-level is the statistical significance level. If missing, a default of 5% is assumed.

upper If true, returns the upper confidence interval limit. Otherwise, returns lower limit.

upper description
0 return lower limit
1 return upper limit

Remarks

  1. The underlying model is described here.
  2. Warning: GARCHM_FORECI() function is deprecated as of version 1.63: use GARCHM_FORE function instead.
  3. The time series is homogeneous or equally spaced.
  4. The time series may include missing values (e.g. #N/A) at either end.
  5. The significance level (i.e. $\alpha$) must be greater than zero and less than one. Otherwise, the function returns #VALUE!
  6. The number of steps must be greater than zero. Otherwise, the function returns #VALUE!
  7. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
  8. The number of parameters in the input argument - beta - determines the order of the GARCH component model.

Examples

Example 1:

 
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A B C D
Date Data    
January 10, 2008 -2.827 GARCH-M(1,1)  
January 11, 2008 -0.947 Mean -0.076
January 12, 2008 -0.877 Lambda 0.145
January 14, 2008 1.209 Alpha_0 0.593
January 13, 2008 -1.669 Alpha_1 0.000
January 15, 2008 0.835 Beta_1 0.403
January 16, 2008 -0.266    
January 17, 2008 1.361    
January 18, 2008 -0.343    
January 19, 2008 0.475    
January 20, 2008 -1.153    
January 21, 2008 1.144    
January 22, 2008 -1.070    
January 23, 2008 -1.491    
January 24, 2008 0.686    
January 25, 2008 0.975    
January 26, 2008 -1.316    
January 27, 2008 0.125    
January 28, 2008 0.712    
January 29, 2008 -1.530    
January 30, 2008 0.918    
January 31, 2008 0.365    
February 1, 2008 -0.997    
February 2, 2008 -0.360    
February 3, 2008 1.347    
February 4, 2008 -1.339    
February 5, 2008 0.481    
February 6, 2008 -1.270    
February 7, 2008 1.710    
February 8, 2008 -0.125    
February 9, 2008 -0.940    


  Formula Description (Result)
  =GARCHM_FORECI($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,1,0.05,1) Upper confidence interval limit (2.0219)
  =GARCHM_FORECI($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,1,0.05,0) Lower confidence interval limit (-1.885)

Files Examples

References

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