Stata 15 help for mf_arfimaacf

Title

[M-5] arfimaacf() -- Autocovariance functions

Syntax

real colvector arfimaacf(real scalar n, real colvector phi, real colvector theta, real scalar d, real scalar v)

Description

arfimaacf(n, phi, theta, d, v) computes the autocovariance function (ACF) of an autoregressive fractionally integrated moving-average (ARFIMA) process defined by the autoregressive parameters, phi, the moving-average parameters, theta, the fractional integration parameter, d, and the idiosyncratic error variance, v.

Remarks

arfimaacf() returns a vector of length n+1, where the first element is the variance of the ARFIMA or ARMA process and elements k = 2, ..., n+1 are the autocovariances of the time-series process k-1 time units apart. The ACF of an ARMA process is obtained when d = 0.

Conformability

arfimaacf(n, phi, theta, d, v): n: 1 x 1 phi: p x 1 theta: q x 1 d: 1 x 1 v: 1 x 1 result: n+1 x 1

Diagnostics

The AR(p) and MA(q) polynomials defined by phi and theta must have roots outside the unit circle, and the two polynomials may not have common roots. The fractional integration parameter must be in (-1,1/2). The variance parameter, v, must be greater than zero.

Source code

arfimaacf.mata


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