Maximum likelihood estimation of structural VARFIMA models

This paper considers the maximum likelihood estimation of a class of structural vector autoregressive fractionally integrated moving-average (VARFIMA) models. The structural VARFIMA model includes the fractional cointegration model as one of its special cases. We show that the conditional likelihood Durbin–Levinson (CLDL) algorithm of Tsay (2010a) is a fast and reliable approach to estimate the long-run effects as well as the short- and long-term dynamics of a structural VARFIMA process simultaneously. In particular, the computational cost of the CLDL algorithm is much lower than that proposed in Sowell (1989) and Dueker and Startz (1998). We apply the CLDL method to the Congressional approval data of Durr et al. (1997) and find that the long-run effect of economic expectations on Congressional approval is at least 0.5718, which is over twice the estimate of 0.24 found in Table 2 of Box-Steffensmeier and Tomlinson (2000). This paper also tests the divided party government hypothesis with the CLDL algorithm.