J. Carlos Escanciano and Ignacio N. Lobato 975Sweeney (1986) all find evidence against the MDH for nominal or real exchange
rates at different frequencies, whereas Diebold and Nason (1990), Fong, Koh and
Ouliaris (1997), Hsieh (1988, 1989, 1993), McCurdy and Morgan (1987) and Meese
and Rogoff (1983a, 1983b) find little evidence against the MDH. Here we consider
data that consists of four daily and weekly exchange rate returns against the US
dollar: the euro (Euro), the Canadian dollar (Can), the pound sterling (Pound) and
the Japanese yen (Yen). The daily data is taken from January 1, 2004, to August
17, 2007, with a total of 908 observations. For the weekly data, we consider the
returns on Wednesdays from January 14, 2000, to August 17, 2007, with a total
of 382 observations. The daily noon buying rates in New York City certified by
the Federal Reserve Bank of New York for customs and cable transfers purposes
are obtained from http://www.federalreserve.gov/Releases/h10/hist. In Figures 20.1
and 20.2 we have plotted the evolution of these four daily and weekly exchange
rates, respectively, and, similar to previous analyzes, the two main features of these
plots are their unpredictability and their volatility. Table 20.1 provides summary
statistics for the most relevant aspects of the marginal distribution of the data.
Similar to most financial series, the main feature from Table 20.1 is kurtosis that,
in line with previous studies, is larger for daily than for weekly data. Note that
skewness is moderate and slightly negative for daily data. As has been observed
repeatedly before, the marginal distribution of weekly data is closer to the normal
distribution than that of daily data.
20.3 Tests based on linear measures of dependence
Recall the m.d.s. definition in equation (20.2) that should hold for any function
w(·). The simplest approach is to consider linear functions, such asw(It− 1 )=Yt−j,
04-Jan-2004 20-Mar-2005 04-Jun-2006 19-Aug-2007
–3–2–10123(^) 04-Jan-2004–3 20-Mar-2005 04-Jun-2006 19-Aug-2007
–2
–1
0
1
2
3
Euro Pound
04-Jan-2004 20-Mar-2005 04-Jun-2006 19-Aug-2007
–2
–1
0
1
2
Can^
04-Jan-2004 20-Mar-2005 04-Jun-2006 19-Aug-2007
–3
–2
–1
0
1
2
3
Yen
Figure 20.1 Daily returns of the euro, Canadian dollar (Can), pound sterling (Pound) and
the Japanese yen (Yen) against the US dollar
Data from January 4, 2004, to August 17, 2007.