On general, the parameter estimates of the FIGARCH are found to be significant and corroborate the existence of long memory effects as in the ARFIMA model.
When the one-step ahead forecasts are considered, ARFIMA model turns out be the best performer according to MAE and RMSE criterions (see Figure 3).
We find that at earlier forecast horizons conventional autoregressive models, especially ARIMA and ARFIMA, provide better forecasting performance.
The ARFIMA (p, d, q) process can be defined as follows:
ARFIMA (p,d,q) processes are stationary and inversible when d [member]]- 1/2,1/2[ and d [not equal ] 0.
An indication of the rather unusual properties of inflation can be heuristically observed from the autocorrelations of the residuals from the previously estimated ARFIMA models.
The consistency and asymptotic normality of the QMLE has been established only for specific special cases of the ARFIMA and/or FIGARCH model.
The estimated value of the long memory parameter in the conditional mean is generally similar to that of the simpler ARFIMA with homoskedasticity model and is significantly different from zero or one.
Keywords: Informational efficiency; Exchange rates; Standard cointegration tests; Fractional integration; Long memory; Bivariate ARFIMA model; Vectoriel error correction fractional model (VECFM)
The objective of this study is to investigate the weak efficiency (Fama (1984, 1998) of the Tunisian foreign exchange market by means of fractional cointegration tests and estimation of an error correction bivariate ARFIMA model.
Fox and Taqqu (1986) propose a frequency-domain approximate maximum likelihood (ML) method to simultaneously estimate both the short- and the long-memory parameters of an ARFIMA model.
Lambda]], [Gamma]) is the spectrum of the ARFIMA model being estimated.