ARMA_VOL - ARMA fitted values of conditional volatility

Jacquie Nesbitt

October 25, 2016 17:47

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)).

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 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).

Warning

ARMA_VOL() function is deprecated as of version 1.63: use the ARMA_FIT 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 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.
The number of parameters in the input argument - phi - determines the order of the AR component.
The number of parameters in the input argument - theta - 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 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.