Behind the Numbers U.S. Trade in the World Economy (1992) / Chapter Skim
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Appendix D: Variability in Month-to-Month Changes in the Seasonally Adjusted Merchandise Trade Balance
Appendix D: Variability in Month-to-Month Changes in the Seasonally Adjusted Merchandise Trade Balance
Pages 225-236
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From page 225... ...
But this phenomenon raises the key question: How should the variability in the data be measured? This appendix explores the issue of variability in the month-to-month changes in the seasonally adjusted trade balance, develops a measure of this variability that takes account of the autocorrelation that is present in the data series, and uses this measure to determine a band for the monthly changes from February 1987 through February 1991, thus providing a simple characterization of the variability in the data.
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From page 226... ...
These carryovers mean that a plot of the time series of monthly changes in the trade balance could have a large spike for a given month when a substantial portion of the figure did not represent a large change taking place in the month but rather transactions attributable to underreporting in one or more previous months. They also mean that not only is the observation for the given month incorrectly reported, but also that those for one or more prior periods were understated and thus inaccurate.: Figure D-3 shows the first differences of the seasonally adjusted trade balance data for the period January 1977 through March 1990, unadjusted for carryovers.
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.o -10 ._ m -11 -12 -13 -14 -15 ... 1987 1988 1989 1990 1991 Year 5r Or 1 FIGURE D-1 Seasonally adjusted merchandise trade balance: lanuary 1987-February 1991.
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From page 228... ...
Unfortunately, it is not possible for the Census Bureau to make adjustments for carryover errors in the data prior to January 1987. The data in Figures D-1 and D-2 and in Table D-1, however, have been adjusted by Census Bureau personnel for carryover problems.
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From page 229... ...
Largely because of this small number we have used autoregressive, integrated, moving-average models, often referred to as ARIMA models, to model the autocorrelation in the DATB time series and to measure data variability. We also experimented with mod
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From page 230... ...
trade deficits appearing in the business media strongly suggests that data users appear to be much more interested in the month-tomonth changes than in the levels of the trade deficit.) iA similar situation exists with other major economic variables.
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A similar result can occur when an MAW process can be expressed as an infinite-order AR process. Moreover, in applied ARIMA modeling it is not unusual to encounter a time series that can be reasonably interpreted as being generated by either and ARjl)
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The negative autocorrelation estimate, hi= -0.56076, suggests that the process generating the time series tends to produce observations that alternate in sign. positive observation in a given period to be followed period by an observation having a negative value.
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. Thus, the standard error of the month-to-month changes in the seasonally adjusted trade balance is approximately six times larger than the mean.
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model by OLS produces biased parameter estimates in finite samples. (The statistical properties of ARIMA model estimates under various nonlinear estimation procedures are examined extensively in Box and Jenkins t19764~.
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Model = $249 million Mean of First Diff. Upper Control Limit - - Lower Control Limit FIGURE D-7 Control chart for data on monthly changes, seasonally adjusted merchandise trade balance.
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From page 236... ...
Stated another way, none of the monthly changes over this period would have been regarded as sufficiently unusual to lead one to believe that the process generating the data had shifted its mean or changed in any other important way. To sum up: the key issue here, as noted at the beginning of this appendix, is the large variability in the month-to-month changes in merchandise trade balance data.
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