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GARCH_FORECI (Pro.)
Returns the confidence interval limits of the conditional mean forecast.
Syntax
GARCHi_FORECI(X, Order, mean, 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)).
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).
betas
are the parameters of the GARCH(q) component model (starting with the lowest lag).
innovation
is the probability distribution function of the innovations/residuals (1=Gaussian, 2=t-Distribution, 3=GEDi). If missing, a gaussian distribution is assumed.
| 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).
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
- 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 significance level (i.e.
) must be greater than zero and less than one. Otherwise, a #VALUE! is returned - The number of steps must be greater than zero. Otherwise, a #VALUE! is returned
Examples
Example 1:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Date | Data | ||
| 2 | January 10, 2008 | -2.827 |
GARCH(1,1) |
|
| 3 | January 11, 2008 | -0.947 | Mean | -0.160 |
| 4 | January 12, 2008 | -0.877 | Alpha_0 | 0.608 |
| 5 | January 14, 2008 | 1.209 | Alpha_1 | 0.00 |
| 6 | January 13, 2008 | -1.669 | Beta_1 | 0.391 |
| 7 | January 15, 2008 | 0.835 | ||
| 8 | January 16, 2008 | -0.266 | ||
| 9 | January 17, 2008 | 1.361 | ||
| 10 | January 18, 2008 | -0.343 | ||
| 11 | January 19, 2008 | 0.475 | ||
| 12 | January 20, 2008 | -1.153 | ||
| 13 | January 21, 2008 | 1.144 | ||
| 14 | January 22, 2008 | -1.070 | ||
| 15 | January 23, 2008 | -1.491 | ||
| 16 | January 24, 2008 | 0.686 | ||
| 17 | January 25, 2008 | 0.975 | ||
| 18 | January 26, 2008 | -1.316 | ||
| 19 | January 27, 2008 | 0.125 | ||
| 20 | January 28, 2008 | 0.712 | ||
| 21 | January 29, 2008 | -1.530 | ||
| 22 | January 30, 2008 | 0.918 | ||
| 23 | January 31, 2008 | 0.365 | ||
| 24 | February 1, 2008 | -0.997 | ||
| 25 | February 2, 2008 | -0.360 | ||
| 26 | February 3, 2008 | 1.347 | ||
| 27 | February 4, 2008 | -1.339 | ||
| 28 | February 5, 2008 | 0.481 | ||
| 29 | February 6, 2008 | -1.270 | ||
| 30 | February 7, 2008 | 1.710 | ||
| 31 | February 8, 2008 | -0.125 | ||
| 32 | February 9, 2008 | -0.940 |
| Formula | Description (Result) | |
|---|---|---|
| =GARCH_FORE($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,1) | Forecasted conditional mean at T+1 (-0.160) | |
| =GARCH_FORECI($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,,,1,5%,1) | Upper confidence interval for forecasted value at T+1 (1.798) | |
| =GARCH_FORECI($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,,,1,5%,0) | Lower confidence interval for forecasted value at T+1 (-2.118) |
References
- Hamilton, J .D.; Time Series Analysis
, Princeton University Press (1994), ISBN 0-691-04289-6 - Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
