Estimation error and the specification of unobserved component models

Maravall, Agustín; Planas, Christophe

doi:10.1016/s0304-4076(98)00094-3

Cited by 11 publications

(9 citation statements)

References 27 publications

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“…We identify a decomposition using the canonical assumption, i.e. by considering the non-invertible ARMA(1,1) representation of σ 2 t (see Maravall and Planas, 1999). This yields the smoothest estimate of the actual variance σ t .…”

Section: B the Barndorff-nielsen And Shephard Model-based Estimator Omentioning

confidence: 99%

Volatility estimation via hidden Markov models

Rossi

Gallo

2006

Journal of Empirical Finance

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We propose a stochastic volatility model where the conditional variance of asset returns switches across a potentially large number of discrete levels, and the dynamics of the switches are driven by a latent Markov chain. A simple parameterization overcomes the commonly encountered problem in Markov-switching models that the number of parameters becomes unmanageable when the number of states in the Markov chain increases. This framework presents some interesting features in modelling the persistence of volatility, and that, far from being constraining in data fitting, it performs comparably well as other popular approaches in forecasting short-term volatility.

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Section: B the Barndorff-nielsen And Shephard Model-based Estimator Omentioning

confidence: 99%

Volatility estimation via hidden Markov models

Rossi

Gallo

2006

Journal of Empirical Finance

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“…Within this second approach the pseudo-spectrum seems to describe "the distribution (over the frequency range) of the energy (per unit time) or variance (possibly infinite) of the process" [24], in a similar way as the spectrum does in the stationary case. Hence, we find that sometimes the term "spectrum" is, in fact, used to denote this type of pseudospectrum [25].…”

Section: The Incomplete Generalization To the Non-stationary Casementioning

confidence: 99%

“…In addition, the Extended Fourier Transform F is defined so that for any sequence that satisfies (24), that is, any sequence Ψ such that…”

Section: Spectrum Ormentioning

confidence: 99%

Mathematical Framework for Pseudo-Spectra of Linear Stochastic Difference Equations

Bujosa

Garcı́a-Ferrer

2015

IEEE Trans. Signal Process.

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Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous mathematical extension of the classic Fourier spectrum to the case in which there are AR roots in the unit circle, ie, the transfer function of the linear time-invariant filter has poles on the unit circle. To achieve it we: embed the classical problem in a wider framework, extend the Discrete Time Fourier Transform and defined a new Extended Fourier Transform pair pseudo-covariance function/pseudo-spectrum. Our approach is a proper extension of the classical spectral analysis, within which the Fourier Transform pair auto-covariance function/spectrum is a particular case. Consequently spectrum and pseudo-spectrum coincide when the first one is defined.Keywords Spectral analysis, time series, non-stationarity, frequency domain, pseudocovariance function, linear stochastic difference equations, partial inner product, Extended Fourier Transform. JL Classification C00, C22This working paper has been accepted for publication in a future issue of IEEE Transactions on Signal Processing. Content may change prior to final publication. Abstract-Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous mathematical extension of the classic Fourier spectrum to the case in which there are AR roots in the unit circle, ie, the transfer function of the linear time-invariant filter has poles on the unit circle. To achieve it we: embed the classical problem in a wider framework, extend the Discrete Time Fourier Transform and defined a new Extended Fourier Transform pair pseudocovariance function/pseudo-spectrum. Our approach is a proper extension of the classical spectral analysis, within which the Fourier Transform pair auto-covariance function/spectrum is a particular case. Consequently spectrum and pseudo-spectrum coincide when the first one is defined.

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“…In other words, if there exists an admissible decomposition, we need to determine what is called a canonical decomposition. A detailed examination of these two problems of admissible and canonical decompositions are outside the scope of this paper and has been solved elsewhere (Hillmer and Tiao 1982;Maravall and Planas 1999;Fiorentini and Planas 2001). In Sect.…”

Section: Principles Behind Seatsmentioning

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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Estimation error and the specification of unobserved component models

Cited by 11 publications

References 27 publications

Volatility estimation via hidden Markov models

Volatility estimation via hidden Markov models

Mathematical Framework for Pseudo-Spectra of Linear Stochastic Difference Equations

On some remarks about SEATS signal extraction

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