Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models

Bell, William R.; Martin, Donald E. K.

doi:10.1111/j.1467-9892.2004.01920.x

Cited by 28 publications

(24 citation statements)

References 28 publications

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“…While fixed filters such as X11 cannot exhibit this property, it should characterize a model-based approach, where the adjustment depends on the dynamic structure of the series (see Gómez and Maravall (2001b), and Bell and Martin (2004)). To check whether the default automatic procedure of TRAMO-SEATS satisfies the idempotency property, the procedure was applied to the set of 15,624 series; seasonal adjustment was performed for the 13,138 of them for which seasonality had been detected.…”

Section: Idempotencymentioning

confidence: 99%

Reg-ARIMA model identification: empirical evidence

Maravall¹,

Pavón²,

Cañete³

2017

STAT SINICA

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Abstract:The results of applying the default Automatic Model Identification of program TRAMO to a set of 15,642 socio-economic monthly series are analyzed. The series cover a wide variety of activities and indicators for a large number of countries, and the number of observations ranges between 60 and 600. The model considered by the automatic procedure is an ARIMA model with -when detectedoutliers and calendar effects. For series with no more than 360 observations the results are found satisfactory for slightly more than 90% of the series, excellent indeed as far as whitening of the series and the capture of seasonality are concerned. For longer series the normality assumption is the weak point. Still, in so far as kurtosis is the main cause, non-normality does not seem to be a dramatic feature. The relevance of including possible outliers and calendar effects is discussed in an Appendix.

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Section: Idempotencymentioning

confidence: 99%

Reg-ARIMA model identification: empirical evidence

Maravall¹,

Pavón²,

Cañete³

2017

STAT SINICA

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“…These techniques are by no means exhaustive of those available that have this property. For example, Bell and Martin (2004) provide a method for estimating the trend when the underlying unobserved components follow ARIMA processes, while Gray and Thomson (2002) and Quenneville et al (2003) extend the Henderson-Musgrave-type trend filters used in seasonal adjustment procedures such as X-12-ARIMA (Findlay et al, 1998) to enable them to be used right up to the end of the sample.…”

Section: Discussion and Summarymentioning

confidence: 99%

Modelling current trends in Northern Hemisphere temperatures

Mills

2006

Intl Journal of Climatology

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Fitting a trend is of interest in many disciplines, but it is of particular importance in climatology, where estimating the current and recent trend in temperature is thought to provide a major indication of the presence of global warming. A range of ad hoc methods of trend fitting have been proposed, with little consensus as to the most appropriate techniques to use. The aim of this paper is to consider a range of trend extraction techniques, none of which require 'padding' out the series beyond the end of the available observations, and to use these to estimate the trend of annual mean Northern Hemisphere (NH) temperatures. A comparison of the trends estimated by these methods thus provides a robust indication of the likely range of current trend temperature increases and hence inform, in a timely quantitative fashion, arguments based on global temperature data concerning the nature and extent of global warming and climate change. For the complete sample 1856-2003, the trend is characterised as having long waves about an underlying increasing level. Since around 1970, all techniques display a pronounced warming trend. However, they also provide a range of trend functions so that extrapolation far into the future would be a hazardous exercise.

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“…This problem is the subject of several papers (Maravall 1986;Gómez and Maravall 2001b;Bell and Martin 2002). There is no impact on the derivation of the estimates of the component, but on the interpretation side.…”

Section: Revisionsmentioning

confidence: 99%

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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Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models

Cited by 28 publications

References 28 publications

Reg-ARIMA model identification: empirical evidence

Reg-ARIMA model identification: empirical evidence

Modelling current trends in Northern Hemisphere temperatures

On some remarks about SEATS signal extraction

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