Page 169 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

Unit 14 : Exchange Rate : Meaning and Components

which should be white noise. Thus, any autocorrelation of the premium is not evident in the time Notes
series behavior of F – S + t 1 .
t
The autocorrelations of F – S tell a different story. The first-order autocorrelations are 0.6S or greater,
t
t
and the decay of the autocorrelations at successive lags suggests a first-order autoregressive process.
This is confirmed by the partial autocorrelations (not shown) which are large at lag 1 but close to zero
at higher-order lags. Since F – S is the premium, P , plus the expected change in the spot rate,
t
t
t
ES + − S ) t , the autocorrelations of F – S indicate that P and/or ( t1 − S ) t vary in an
ES
+
t
t
( t1
t
autocorrelated way.
F – S
ES
+
The difference between the behavior of the autocorrelations of t t and those of ( t1 − S ) t and
F – S + t 1 is easily explained. The standard deviations of t t are between 0.17 and 0.66 percent
F – S
t
per month, whereas those of either S + t1 − S or t + t 1 are typically greater than 3.0 percent per
F – S
t
ES
+
t
month. Thus, the autocorrelation of P and/or ( t1 − S ) t , which shows up in the time series
behavior of F – S , is buried in the high variability of the unexpected components of F – S + t 1 and
t
t
t
S + t1 − S .
t
Regression tests
OLS estimates
Table 2 shows the estimated regressions of F – S + t 1 and S + t1 − S on F – S . Only one set of
t
t
t
t
coefficient standard errors, residual standard errors and residual autocorrelations is shown for each
country. This reflects the complementarity of the F – S + t 1 and S + t1 − S regressions for each country.
t
t
The intercept estimates in the two regressions sum to zero, the slope coefficients sum to one, and the
sum of the two residuals is zero on a period-by-period basis.
Since the regressor F – S has low variation relative to F – S + t 1 and S + t1 − S , the coefficients of
t
t
t
t
2
2
determination ( R and R ) for the regressions are small, and they are smaller for the S + t1 − S t
1
2
regressions than for the F – S + t 1 regressions. The regression residuals, like the dependent variables,
t
show little autocorrelation.
The anomalous numbers in table 2 are the estimates of the regression slope coefficients, β and β 2
1
According to (5) and (6), the slope coefficient in the regression of F – S + t 1 on F – S contains the
t
t
t
proportion of the variance of F – S due to variation in its premium component, P , while the slope
t
t
t
coefficient in the regression of S + t1 − S on F – S contains the proportion of the variance of F – S t
t
t
t
t
ES
+
due to variation in the expected change in the spot rate, ( t1 − S ) t . The coefficients clearly cannot
be interpreted in terms of these
proportions alone, since the coefficients in the S + t1 − S regressions are always negative so that those
t
in the F – S + t 1 , regressions are greater than 1.0.
t
Inspection of (5) and (6) indicates an explanation for the strange estimates of β and β . Since
1
2
σ 2 ( (ES + t1 − S t )) in (6) must be non-negative, a negative estimate of β implies that
2
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