FARMAFIT Call

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Fractionally Integrated Time Series Analysis

FARMAFIT Call

estimate the parameters of an ARFIMA(p,d,q) model

CALL FARMAFIT( d, phi, theta, sigma, series <, p, q, opt>);

The inputs to the FARMAFIT subroutine are as follows:

series

specifies a time series (assuming mean zero).

p

specifies the set or subset of the AR order. If you do not specify p, the default is p=0.

If you specify p=3, the FARMAFIT subroutine estimates the coefficient of the lagged variable y_t-3.

If you specify p={1,2,3}, the FARMAFIT subroutine estimates the coefficients of lagged variables y_t-1, y_t-2, and y_t-3.

q

specifies the subset of the MA order. If you do not specify q, the default is q=0.

If you specify q=2, the FARMAFIT subroutine estimates the coefficient of the lagged variable ${\epsilon}_{t-2}$ .

If you specify q={1,2}, the FARMAFIT subroutine estimates the coefficients of lagged variables ${\epsilon}_{t-1}$ and ${\epsilon}_{t-2}$ .

opt

specifies the method of computing the log-likelihood function.

opt=0: requests the conditional sum of squares function. This is the default.
opt=1: requests the exact log-likelihood function. This option requires that the time series be stationary and invertible.

The FARMAFIT subroutine returns the following values:

d: is a scalar containing a fractional differencing order.
phi: is a vector containing the autoregressive coefficients.
theta: is a vector containing the moving-average coefficients.
sigma: is a scalar containing a variance of the innovation series.

To estimate parameters of an ARFIMA(1,0.3,1) model

$(1-0.5B)(1-B)^{0.3}y_t=(1+0.1B){\epsilon}_t$

where $\epsilon_t \sim NID(0, 1)$ , you can specify

 
   d    = 0.3;  
   phi  = 0.5;
   theta= -0.1;
   call farmasim(yt, d, phi, theta);
   call farmafit(d, ar, ma, sigma, yt) p=1 q=1;
   print d ar ma sigma;

The FARMAFIT subroutine estimates parameters d, $\phi(B)$ , $\theta(B)$ , and $\sigma_{\epsilon}^2$ of an ARFIMA(p,d,q) model. The log-likelihood function needs to be solved by iterative numerical procedures such as the quasi-Newton optimization. The starting value d is obtained by the approach of Geweke and Poter-Hudak (1983); the starting value of the AR and MA parameters are obtained from the least squares estimates.

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