ARIMA_FORE - Forecasting for ARIMA Model

Calculates the out-of-sample conditional forecast (i.e., mean, error, and confidence interval).

Syntax

ARIMA_FORE ([x], order, d, µ, σ, [φ], [θ], t, return, α)

[X]
Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
Order
Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Value Order
1 Ascending (the first data point corresponds to the earliest date) (default).
0 Descending (the first data point corresponds to the latest date).
d
Required. Is the integration order.
µ
Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
σ
Required. Is the standard deviation value of the model's residuals/innovations.
[φ]
Optional. Are the parameters of the AR(p) component model: [φ1, φ2 … φp] (starting with the lowest lag).
[θ]
Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (starting with the lowest lag).
t
Required. Is the forecast time/horizon (expressed in steps beyond the end of the time series).
Return
Optional. Is an integer switch to select the forecast output type: (1 = mean (default), 2 = Std. Error, 3 = Term Struct, 4 = LL, 5 = UL).
Value Return
1 Mean forecast value (default).
2 Forecast standard error (aka local volatility).
3 Volatility term structure.
4 The lower limit of the forecast confidence interval.
5 The upper limit of the forecast confidence interval.
α
Optional. Is the statistical significance level (i.e., alpha). If missing or omitted, an alpha value of 5% is assumed.

Remarks

  1. The underlying model is described here.
  2. The Log-Likelihood Function (LLF) is described here.
  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 integration order argument (d) must be a positive integer.
  6. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
  7. The residuals/innovations standard deviation (σ) must be greater than zero.
  8. For the input argument ([φ]):
    • The input argument is optional and can be omitted, in which case no AR component is included.
    • The order of the parameters starts with the lowest lag.
    • One or more parameters can be missing or an error code (i.e., #NUM!, #VALUE!, etc.).
    • The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
  9. For the input argument ([θ]):
    • The input argument is optional and can be omitted, in which case 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 MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
  10. The function was added in version 1.63 SHAMROCK.

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