`arf` (Series)

Create autoregressive time series from input data

Syntax

x = arf(x, A, Z, range, ...)

Input arguments

x [ Series ] -

Input data from which initial condition will be taken.

A [ numeric ] -

Vector of coefficients of the autoregressive polynomial.

Z [ numeric | Series ] -

Exogenous input series or constant in the autoregressive process.

range [ Dater | @all ] -

Date range on which the new time series observations will be computed; range does not include pre-sample initial condition. @all means the entire possible range will be used (taking into account the length of pre-sample initial condition needed).

Output Arguments

x [ Series ]

Output data with new observations created by running an autoregressive process described by A and Z.

Description

The autoregressive process has one of the following forms:

A1*x + A2*x(-1) + ... + An*x(-n) = z,

or

A1*x + A2*x(+1) + ... + An*x(+n) = z,

depending on whether the range is increasing (running forward in time), or decreasing (running backward in time). The coefficients A1, ...An are gathered in the input vector A,

A = [A1, A2, ..., An].

Examples

The following two lines create an autoregressive process constructed from normally distributed residuals

\[ x_t = \rho x_{t-1} + \epsilon_t \]

rho = 0.8;
x = Series(1:20, @randn);
x = arf(x, [1, -rho], x, 2:20);

arf (Series)