Three Equivalent Methods for Filtering Finite Nonstationary Time Series

Gómez, Víctor

doi:10.1080/07350015.1999.10524800

Cited by 27 publications

(30 citation statements)

References 10 publications

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“…Different approaches can be used for the computational implementation of the HP filter (see, e.g., Gomez, 1999). From the (quadratic) optimization problems in (1) and (5) one can derive the FOCs relative to {x t } T t=1 and {x t } T +H t=1 , respectively, which would compose a system of linear equations in these unknown terms and could then be solved by standard matrix algebra for a given λ and a sample of observations (see Danthine and Girardin, 1989, pp.…”

Section: Implementation and Calibrationmentioning

confidence: 99%

Improving the Reliability of Real-Time Hodrick-Prescott Filtering Using Survey Forecasts

Galimberti

Moura

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Insper -Institute of Education and Research AbstractMeasuring economic activity in real-time is a crucial issue in applied research and in the decision-making process of policy makers; however, it also poses intricate challenges to statistical filtering methods that are built to operate optimally under the auspices of an infinite number of observations. In this paper, we propose and evaluate the use of survey forecasts to augment one of those methods, namely the largely used Hodrick-Prescott filter so as to attenuate the end-of-sample uncertainty observed in the resulting gap estimates. We find that this approach achieves powerful improvements to the real-time reliability of these economic activity measures, and we argue that the use of surveys is preferable relative to model-based forecasts due to both an usually superior accuracy in predicting current and future states of the economy and its parsimony.

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Section: Implementation and Calibrationmentioning

confidence: 99%

Improving the Reliability of Real-Time Hodrick-Prescott Filtering Using Survey Forecasts

Galimberti

Moura

2014

SSRN Journal

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“…If the basic theory is given in a few papers (Gómez andMaravall 1994, 2001a, b, andothers), and can be checked empirically, some of the more sophisticated features like the selection of the canonical decomposition, the derivation of the Wiener-Kolmogorov filters, revisions, and the various diagnostics are more difficult to grasp. We will therefore describe It is based on the file CH13EX06.xls on the CD-Rom of Mélard (2007) except that there a model with a constant was used, see footnote 1 .…”

Section: Verification Of the Results In The Examplementioning

confidence: 99%

“…These simple approaches do not appear often in the literature (e.g. Gómez 1999) although Burman (1980) already mentions developments by Tunnicliffe Wilson (1979).…”

Section: Principles Behind Seatsmentioning

confidence: 99%

“…There were some difficulties to use them outside the context of stationary processes but these were solved (Bell 1984). Moreover, Gómez (1999) has shown the equivalence of the three approaches of Wiener-Kolmogorov filter, Kalman filtering, penalized least-squares. See also Pollock (2002).…”

Section: Principles Behind Seatsmentioning

confidence: 99%

“…Census X-12-ARIMA (Findley et al 1998) has improved on this by including a better outlier detection procedure and trading day corrections by regression with ARIMA errors, within a regARIMA module, while leaving nearly unchanged the old extraction of components by moving averages. Bank of Spain TRAMO-SEATS (Gómez andMaravall 1994, 2001a, b) has used a more powerful automatic model selection (AMS) procedure called TRAMO (Time series Regression with ARIMA noise, Missing values and Outliers), see below, before a very different signal extraction-based procedure called SEATS (Signal Extraction in ARIMA Time Series). While keeping regARIMA and the available model selection procedures, versions of X-12-ARIMA after version 0.3 have added the automdl spec based on TRAMO.…”

Section: Introductionmentioning

confidence: 99%

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On some remarks about SEATS signal extraction

Mélard

2015

SERIEs

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In seasonal adjustment a time series is considered as a juxtaposition of several components, the trend-cycle, and the seasonal and irregular components. The Bureau of the Census X-11 method, based on moving averages, correction of large errors and trading day adjustments, has long dominated. With the success of ARIMA modelling at the end of the 20th century, methods with better outlier detection and trading day corrections by regression with ARIMA errors have appeared, with the regARIMA module of Census X-12-ARIMA or Bank of Spain TRAMO-SEATS. SEATS consists of extracting the components by an ARIMA-model-based unobserved components approach. This means that models are used for each component such that the sum of the components is compatible with the ARIMA model for the corrected time series. The underlying theory of the SEATS program is studied in many papers but there is no complete and systematic description of its output. Our purpose is to examine SEATS text output and to explain the results in simple words and formulas. This is done on a simple example, a time series with a non-seasonal model so that the computations can be verified step by step. The principles behind SEATS are first described, including the admissible decompositions and the canonical decomposition, and the derivation of the Wiener-Kolmogorov filter. Then the example is introduced: the interest rates of US certificates of deposits. The text output from SEATS is presented in edited form in several tables. Finally, the main results are checked on the example by means of a Microsoft Excel workbook and direct computations. In particular, the forecasts and backcasts are obtained; the admissible and canonical decompositions with two components are discussed; the filters are first derived using autocorrelations of two auxiliary ARMA processes, then applied on the prolonged time series; and the characteristics of the estimates, the revisions and the growth rates are analyzed.

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Seasonal Adjustment and Signal Extraction Time Series

Gómez¹,

Maravall²

2000

Wiley Series in Probability and Statistics

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Three Equivalent Methods for Filtering Finite Nonstationary Time Series

Cited by 27 publications

References 10 publications

Improving the Reliability of Real-Time Hodrick-Prescott Filtering Using Survey Forecasts

Improving the Reliability of Real-Time Hodrick-Prescott Filtering Using Survey Forecasts

On some remarks about SEATS signal extraction

Seasonal Adjustment and Signal Extraction Time Series

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