ARMA_FORECI - Forecasting confidence interval of ARMA Model

Returns the confidence interval limits of the conditional mean forecast.

Syntax

ARMA_FORECI(X, Order, Mean, sigma, phi, theta, T, alpha, Upper)

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)).

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).

Mean

is the 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 the end of the time series).

alpha

is the statistical significance level. If missing, a default of 5% is assumed.

Upper

If true, returns the upper confidence interval limit. Otherwise, it returns the lower limit.

Value	Upper
0	Returns the lower limit.
1	Returns the upper limit.

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. The number of parameters in the input argument - phi - determines the order of the AR component.
5. The number of parameters in the input argument - theta - determines the order of the MA component.

Files Examples

Related Links

• Wikipedia - Autoregressive moving average model.
• Wikipedia - Confidence Interval.

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.