ARMA_FORECI - Forecasting Confidence Interval of ARMA Model

Mohamad

December 09, 2016 15:50

Returns the confidence interval limits of the conditional mean forecast.

Syntax

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

[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).

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

Optional. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series).

α

Optional. Is the statistical significance of the test (i.e., alpha). If missing or omitted, an alpha value of 5% is assumed.

Return

Optional. if true, returns the upper confidence interval limit. Otherwise, returns the lower limit.

Value	Return
0	Returns the lower limit. (default)
1	Returns the upper limit.

Warning

ARMA_FORECI(.) function is deprecated as of version 1.63: use the ARMA_FORE(.) function instead.

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 - ([φ]) - determines the order of the AR component.
The number of parameters in the input argument - ([θ]) - determines the order of the MA component.

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 Reinsel; 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.