Multifractality of US Dollar/Deutsche Mark Exchange Rates - Studies2

7.2 Consistency in Subsamples
We split the twenty-four year sample span of FED1 into two separate twelve year samples, 1973 −
1985, and 1985 − 1997. Figure 22 shows partition functions and Figure 23 shows estimated multi-
fractal spectra. The results are very similar to full sample results, suggesting near stationarity in
the model. This is an important result, and probably the most substantial test of robustness in
DM/USD scaling.
Also of interest is the small, but noticeable, difference between the two subsamples. The break
point occurs in 1985, a major turning point in international monetary policy. In February of 1985,
a concerted intervention by major central banks reversed appreciation of the dollar, and marked a
shift from “near complete flexibility to a managed float” (Catte, et al., 1994). 40 Consistent with
this institutional shift, we notice a longer tail in the spectrum of the earlier, less managed, period.
7.3 Seasonal Adjustment Filters
This section tests robustness of scaling in the high frequency data to different deseasonalizing
methods. We use four additional seasonal adjustment filters. Briefly, SEAS1 adjusts by number
of quotes received per fifteen minutes. Like the previously used SEAS2, this method is market-
activity based. The other three methods simply remove slow (on average) trading times from the
data, expanding remaining time so as to keep total time constant. These are crude deseasonalizing
methods. Details of construction are in Appendix 9.2.
Figure 20 shows graphs of the partition function around q = 2 for each new seasonal filter.
Figure 21 shows partition functions for higher moments. For comparison with Figures 6 and 7, the
format and aspect ratio are identical, and the high frequency plots are shown next to the same
daily data as previously.
All methods, except to some degree SEAS4, result in strongly linear partition functions.
Crossover occurs at roughly the same point, again with the possible exception of SEAS4, which
appears to have a later crossover. The slopes of all partition functions appear slightly lower than
in Figure 7. The lower slope is pronounced for SEAS4. Lower slopes result in wider estimated
upon lower variability in the ask series than in the bid-ask midpoint. It would be interesting to see whether the same
effect is present in other currencies.
40
This shift is clearest when viewed from the perspective of international agreements. Individual countries varied
with respect to their exchange rate policies from 1973-1985.
29