IRIS Toolbox Reference Manual

## arf

Run autoregressive function on a tseries object

#### Syntax

    X = arf(X,A,Z,RANGE,...)

#### Input arguments

- `X` [ tseries ] - Input data from which initial condition will be taken.

- `A` [ numeric ] - Vector of coefficients of the autoregressive polynomial.

- `Z` [ numeric | tseries ] - Exogenous input or constantn in the autoregressive process.

- `RANGE` [ numeric | Inf ] - Date range on which the new time series observations will be computed; `RANGE` does not include pre-sample initial condition. `Inf` means the entire possible range will be used (taking into account the length of pre-sample initial condition needed).

#### Output arguments

- `X` [ tseries ] - 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 `A` vector,

    A = [a1,a2,...,an].

#### Example

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 = tseries(1:20,@randn);
    X = arf(X,[1,-rho],X,2:20);

IRIS Toolbox. Copyright © 2007—2013 Jaromir Benes.