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
- 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 long-run 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, 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).
- 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:
|
|
| 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
Related Links
References
- D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
- James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
- Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740
- Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
- Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568
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