Note that the sum of the two component series differs from the original series by 0.000004 on average, see cell BG116, showing only 5 correct significant digits.
Typically, these component series' will be built as moving weighted averages of the observations of the corrected series duly extended in both directions by forecasts and backcasts.
Assuming we have obtained the models for the components, there remains to implement the decomposition, i.e. to construct the component series.
When the multivariate time series is converted to a single-component series, an excellent agreement is obtained between the actual and forecasted values.
It consists of making use of statistical relationships between a component series estimate and the residual errors of the water mass balance series.
The second, 'residual-redistribution', consists of redistributing each residual error over initial water balance component estimates, in accord with an error minimization criterion for each component series.
In this paper, we study the problem of allocating two exponentially distributed active [standby] redundancies in a two-component series system using the tools of stochastic ordering.
The component series are fit with specific auto-regressive models to obtain forecasts which are later combined to obtain the actual predictions.
Component series: Production: future tendency manufacturing, % balance; Order books/demand: future tendency in manufacturing, % balance; Finished goods stocks: level manufacturing, % balance, inverted; Source: Ministerio de Industria, Comercio y Turismo.
Component series: beginning 1982, real GDP (PIB, Source: Contabilidad Nacional Trimestral de España. Instituto Nacional de Estadística: www.ine.es ), electricity consumption (Source: Red Eléctrica de España), social security afiliations (Source: Ministerio de Trabajo).
