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ARMA_FORE (Pro.)
Calculates the out-of-sample conditional mean forecast.
Syntax
ARMAi_FORE(X, Order, mean, sigma, phi, theta, T)
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 ARMA model 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 terms of steps beyond end of the time series).
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 number of parameters in the input argument - phi - determines the order of the AR component.
- The number of parameters in the input argument - theta - determines the order of the MA component.
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 | -5.60E-05 |
| 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) |
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
