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Abstract:
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The growth rate of a time-series component gives the percentage change from one time to another. Growth rates, calculated from seasonally adjusted macroeconomic indicators and trends, are among the most widely used statistics in discussions of the state of the economy. Model-based methods of calculating mean square optimal estimates of seasonal adjustments, trends, and other data components can be extended to produce optimal estimates of their growth rates, as well as associated standard error measures of their uncertainty. This is useful information that non-model--based approaches cannot provide readily. In a model-based context, we present formulas for growth rates, which are minimum mean square error estimates given a finite sample of log-normal data. We also derive formulas for the standard errors and extend to the non-Gaussian case through the use of approximate formulas.
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