Volume 4, Issue 1

This paper proposes a novel derivation of the Hodrick-Prescott (HP) minimization problem which leads to a generalization of the Hodrick-Prescott filter. The main result is the development of a new filter to extract a localized maximum-likelihood estimate of the cycle from a series. This new filter, the multivariate normal cyclical (MNC) filter, makes only a general assumption about the cyclical nature of the series. The output from this filtering procedure is from a nonlinear optimization routine.

The size and power of the Wald, Edgeworth expansion corrected likelihood-ratio statistic (LRE), and bootstrap tests for Granger causality in integrated-cointegrated VAR systems are considered. By using Monte Carlo methods and simple graphical techniques, the p-value plots, and power-size plots, properties of the tests in two different forms, the standard and the Dolado and L ¨ utkepohl (1996) modified form, are studied. Regarding the size of the tests, we found that the Wald performs badly in small- and medium-size samples, but the corrected tests, and especially the LRE for large samples, exhibit good performances. The bootstrap test showed the best performance in almost all situations. When considering the power results, using the size-power curves on a correct-size-adjusted basis, we found that the bootstrap tests have adequate power.

Near-neighbor regression is a popular empirical tool. In this note, we describe the general algorithm for the technique and we identify several potential problem areas that researchers should consider. Standard statistical packages are generally inflexible, and hide important modeling decisions from the researcher. We provide code for a simple but very flexible routine that readers can customize for their own use.

We provide a fast algorithm to calculate the m-dimensional distance histogram on which Brock, Dechert, and Sheinkman's (1987) BDS-type statistics are based. The algorithm generalizes a fast algorithm due to LeBaron by calculating the histogram for any finite set of distances simultaneously, and also using induction in m. By reordering the calculation appropriately, the algorithm also requires less memory and time. The two algorithms are compared using LeBaron's MS-DOS implementation in C and our Delphi (Windows Pascal) program. The generalized algorithm is faster when more than a few values of m and M (the distance parameter) are required, and is set up to calculate up to 255 values using short-integer arithmetic.