ARMA_VOL - ARMA fitted values of conditional volatility

Returns an array of cells for the fitted (in-sample) conditional volatility/standard deviation.

Syntax

ARMA_VOL(X, Order, mean, sigma, phi, theta)

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 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).

Remarks

1. The underlying model is described here.
2. Warning: ARMA_VOL() function is deprecated as of version 1.63: use ARMA_FIT function instead.
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 ARMA model has independent and normally distributed residuals with constant variance.

$\sigma_t = \sigma$

Where:
• $\sigma_t$ is the conditional volatility at time t.
• $\sigma$ is the standard deviation of the ARMA residuals/innovations.
6. The number of parameters in the input argument - phi - determines the order of the AR component.
7. The number of parameters in the input argument - theta - determines the order of the MA component.

Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A B C D E
Date Data
January 10, 2008 -0.30 0.14 ARMA
January 11, 2008 -1.28 0.14 Mean -0.00258
January 12, 2008 0.24 0.14 Sigma 0.14
January 13, 2008 1.28 0.14 Phi_1 -0.236
January 14, 2008 1.20 0.14 Theta_1 -5.60E-05
January 15, 2008 1.73 0.14
January 16, 2008 -2.18 0.14
January 17, 2008 -0.23 0.14
January 18, 2008 1.10 0.14
January 19, 2008 -1.09 0.14
January 20, 2008 -0.69 0.14
January 21, 2008 -1.69 0.14
January 22, 2008 -1.85 0.14
January 23, 2008 -0.98 0.14
January 24, 2008 -0.77 0.14
January 25, 2008 -0.30 0.14
January 26, 2008 -1.28 0.14
January 27, 2008 0.24 0.14
January 28, 2008 1.28 0.14
January 29, 2008 1.20 0.14
January 30, 2008 1.73 0.14
January 31, 2008 -2.18 0.14
February 1, 2008 -0.23 0.14
February 2, 2008 1.10 0.14
February 3, 2008 -1.09 0.14
February 4, 2008 -0.69 0.14
February 5, 2008 -1.69 0.14
February 6, 2008 -1.85 0.14
February 7, 2008 -0.98 0.14