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A Comparison Between Direct and Indirect Seasonal Adjustment of the Chilean GDP 1986–2009 with X-12-ARIMA

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Abstract

It is well known among practitioners that the seasonal adjustment applied to economic time series involves several decisions to be made by the econometrician. As such, it would always be desirable to have an informed opinion on the risks taken by each of those decisions. In this paper, I assess which disaggregation strategy delivers the best results for the case of the Chilean 1986–2009 GDP quarterly dataset (base year: 2003). This is done by performing an aggregate-by-disaggregate analysis under different schemes, as the fixed base year dataset allows this fair comparison. The analysis is based on seasonal adjustment diagnostics contained in the X-12-ARIMA program plus some statistical tests for robustness. This exercise is relevant for conjunctural economic assessment, as it concerns signal extraction from seasonal, noisy series, direction of change detection, and econometric applications based on reliable and accurate unobserved variables. The results show that it is preferable, in terms of stability, to use the first block of supply-side disaggregation, while demand-side disaggregation tends to be less reliable. This result carries important implications for policymakers aiming to evaluate its short-term effectiveness in both households and firms.

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Fig. 1

Source: Author’s elaboration based on Central Bank of Chile’s database

Fig. 2

Source: Author’s elaboration

Fig. 3

Source: Author’s elaboration

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Notes

  1. See Findley et al. (1998) and Gómez and Maravall (1997) for details.

  2. Astolfi et al. (2001).

  3. See Findley et al. (1998) and US Census Bureau (2011) for a full description and analysis of the X-12-ARIMA statistical capabilities.

  4. Notice that this article already offers an analysis with linked-chain dataset for robustness purposes.

  5. See Findley et al. (1990) for more details on sliding spans diagnostics.

  6. This assumption also refers to comparisons with same data vintages without revisions.

  7. See, in the empirical application section, the cases of the supply sectors Capture fishery and Electricity, gas and water, to name a few, with respect to the case of GDP itself.

  8. “Appendix C” displays the share of every sector of real GDP at 2003 prices, while “Appendix D” displays some typical statistics of sectors with the full sample for the transformations used in the analysis. “Appendix E” depicts all aggregation components in log levels to provide a general overview of their shape in the time domain.

  9. There are several (pay licensed) software alternatives to estimate the spectrum. For instance, using the command pergram in Stata, or the command periodogram in Matlab.

  10. Note that this component, despite its name, does not necessarily match the concept of trend in the traditional economics usage.

  11. Whether the indirect adjustment performs better than the direct method is a matter treated in Sect. 2.1. In particular, for this case, some arguments are the use of different filters across the disaggregations and ad-hoc forecasting models with better out-of-sample performance.

References

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Author information

Authors and Affiliations

  1. Central Bank of Chile, Santiago, Chile

    Carlos A. Medel

Authors
  1. Carlos A. Medel
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Correspondence to Carlos A. Medel.

Additional information

I thank Rodrigo Alfaro, Carlos Alvarado, Mario Giarda, Pablo Medel, Michael Pedersen, Pablo Pincheira, Damián Romero, and two anonymous referees for comments and suggestions. I also thank Applied Econometrics II (second semester 2012) students at the University of Chile for comments. Finally, I thank Consuelo Edwards for editing services. X-12-ARIMA is a product of the US Census Bureau. This article constitutes an independent analysis on the use of a seasonal adjust procedure applied to a vintage of the Quarterly National Accounts of Chile. It does not reflect the official manner in which the Central Bank of Chile conducts the official data issuance nor a recommendation on how it should be performed. The views and ideas expressed in this paper do not necessarily represent those of the Central Bank of Chile or its authorities. Any errors or omissions are the author’s exclusive responsibility.

Appendices

Chilean GDP by Demand Side

See Table 8.

Table 8 Chilean GDP in levels by demand side.
Full size table

Chilean GDP by Supply Side

See Table 9.

Table 9 Chilean GDP in levels by supply side.
Full size table

Shares of Sectorial Components on Real GDP

See Table 10.

Table 10 Shares of sectorial components on real GDP of 2003 (average of the base year).
Full size table

Typical Statistics of Time Series

See Tables 11 and 12.

Table 11 Typical statistics of demand side series, full sample.
Full size table
Table 12 Typical statistics of supply side series, full sample.
Full size table

GDP Components: Original Series in Levels

See Fig. 4.

Fig. 4
figure 4

Source: Author’s elaboration based on Central Bank of Chile’s database

Chilean GDP—Original series in logarithmic levels.

Full size image

Diagnostic Result 1

1.1 Spectral Plots of Final Seasonally Adjusted and Irregular Series

See Figs. 5 and 6.

Fig. 5
figure 5

Source: Author’s elaboration

Spectral plots of final seasonally adjusted series. 10 \({\times }\) (log-diff.). Bartlett window length = 30.

Full size image
Fig. 6
figure 6

Source: Author’s elaboration

Spectral plots of irregular series. Bartlett window length = 30.

Full size image

Diagnostic Result 3

1.1 Revision History of Trend-Cycle and Final Seasonally Adjusted Series

See Figs. 7 and 8.

Fig. 7
figure 7

Source: Author’s elaboration

Revision history of trend-cycle series (log-differenced). \({\blacktriangledown }\) = Most recent.

Full size image
Fig. 8
figure 8

Source: Author’s elaboration

Revision history of seasonally adjusted series (log-differenced). Aggregation 3 contains an outlier at 2008.III: from − 106.9 (concurrent) to − 0.4 (most recent) \({\blacktriangledown }\) = Most recent.

Full size image

Diagnostic Result 1: Linked-Chain Dataset

1.1 Spectral Plots of Final Seasonally Adjusted and Irregular Series

See Fig. 9 and 10.

Fig. 9
figure 9

Source: Author’s elaboration

Spectral plots of final seasonally adjusted series. 10 \({\times }\) (log-diff.). Bartlett window length = 30.

Full size image
Fig. 10
figure 10

Source: Author’s elaboration

Spectral plots of irregular series. Bartlett window length = 30.

Full size image

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Medel, C.A. A Comparison Between Direct and Indirect Seasonal Adjustment of the Chilean GDP 1986–2009 with X-12-ARIMA. J Bus Cycle Res 14, 47–87 (2018). https://doi.org/10.1007/s41549-018-0023-3

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