ArticlePDF Available

The Trilemma Between Accuracy, Timeliness and Smoothness in Real-Time Signal Extraction

Authors:
Marc Wildi at Zurich University of Applied Sciences
Marc Wildi
Tucker Mcelroy at U.S. Census Bureau
Tucker Mcelroy
Download full-text PDFDownload full-text PDF
Read full-text
Download citation

Abstract and Figures

The evaluation of economic data and monitoring of the economy is often concerned with an assessment of mid-and long-term dynamics of time series (trend and/or cycle). Frequently, one is interested in the most recent estimate of a target signal, a so-called real-time estimate. Unfortunately, real-time signal extraction is a difficult prospective estimation problem which involves linear combinations of one-and possibly infinitely many multi-step ahead forecasts of a series. We here address performances of real-time designs by proposing a generic Direct Filter Approach (DFA). We decompose the ordinary MSE into Accuracy, Timeliness and Smoothness error components, and we propose a new two-dimensional tradeoff between these conflicting terms, the so-called ATS-trilemma. With this formalism, we are able to derive a general class of optimization criteria that allow the user to address specific research priorities, in terms of the Accuracy, Timeliness and Smoothness properties of the resulting real-time filter.
Figures - uploaded by the authors
Content may be subject to copyright.
54b6818a0cf2bd04be3218
f4.pdf
Content uploaded by Tucker Mcelroy
Author content
All content in this area was uploaded by Tucker Mcelroy on Jan 14, 2015
Content may be subject to copyright.
new_short_trilemma_12-25-
13.pdf
Content uploaded by Marc Wildi
Author content
All content in this area was uploaded by Marc Wildi on Jan 01, 2014
Content may be subject to copyright.
A preview of the PDF is not available
... Based on this contrast, we may infer that MBA is likely to outperform DFA if the transformed series is subject to a permanent and slowly varying level-shift; preferences for either filter design may be adopted, depending on whether log-returns of the data are deemed to follow such a non-stationary pattern 8. A comprehensive treatment of frequency-domain characteristics is provided in Wildi and McElroy (2014), where the authors derive a generic optimization criterion addressing noise-suppression, timeliness, and accuracy of real-time designs. for understanding the U.S. economy-both retail and housing are key facets of consumption and production activity in advanced economies. ...
... Our treatment is illustrated through two main examples: trend estimation from a retail series, and seasonal adjustment of a construction series. Other work-the subject of the companion paper Wildi and McElroy (2014) further explores the design of filters, taking into account their frequency domain properties (described via the gain and phase delay functions) directly in the DFA criterion. ...
Optimal Real-Time Filters for Linear Prediction Problems
Article
Full-text available
  • Dec 2013
The classic model-based paradigm in time series analysis is rooted in the Wold decomposition of the data-generating process into an uncorrelated "white noise" process. By design, this uni-versal decomposition is indifferent to particular features of a specific prediction problem (e.g., forecasting or signal extraction) – or features driven by the priorities of the data-users. A single optimization principle (one-step ahead forecast error minimization) is proposed by this classical paradigm to address a plethora of prediction problems. In contrast, this paper proposes to rec-oncile prediction problem structures, user priorities, and optimization principles into a general framework whose scope encompasses the classic approach. We introduce the linear prediction problem (LPP), which in turn yields an LPP objective function. Then one can fit models via LPP minimization, or one can directly optimize the linear filter corresponding to the LPP, yielding the Direct Filter Approach. We provide theoretical results and practical algorithms for both applications of the LPP, and discuss the merits and limitations of each. Our empirical illustrations focus on trend estimation (low-pass filtering) and seasonal adjustment in real-time, i.e., constructing filters that depend only on present and past data.
View
... Another possible extension is motivated by Wildi and McElroy (2019) , which develops a still more general error criterion allowing for customization of filters -so that a practitioner can directly accomodate specific user-priorities of having a smoother real-time estimate of the signal, versus having a more timely estimate (i.e., less phase delay). ...
The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions
Article
  • Apr 2020
Numerous contexts in macroeconomics, finance, and quality control require real-time estimation of trends, turning points, and anomalies. The real-time signal extraction problem is formulated as a multivariate linear prediction problem, the optimal solution is presented in terms of a known model, and multivariate direct filter analysis is proposed to address the more typical situation where the process’ model is unknown. It is shown how general constraints – such as level and time shift constraints – can be imposed on a concurrent filter in order to guarantee that real-time estimates have requisite properties. The methodology is applied to petroleum and construction data.
View
View
View
Optimal Real-Time Filters for Linear Prediction Problems
Article
Full-text available
  • Dec 2013
The classic model-based paradigm in time series analysis is rooted in the Wold decomposition of the data-generating process into an uncorrelated "white noise" process. By design, this uni-versal decomposition is indifferent to particular features of a specific prediction problem (e.g., forecasting or signal extraction) – or features driven by the priorities of the data-users. A single optimization principle (one-step ahead forecast error minimization) is proposed by this classical paradigm to address a plethora of prediction problems. In contrast, this paper proposes to rec-oncile prediction problem structures, user priorities, and optimization principles into a general framework whose scope encompasses the classic approach. We introduce the linear prediction problem (LPP), which in turn yields an LPP objective function. Then one can fit models via LPP minimization, or one can directly optimize the linear filter corresponding to the LPP, yielding the Direct Filter Approach. We provide theoretical results and practical algorithms for both applications of the LPP, and discuss the merits and limitations of each. Our empirical illustrations focus on trend estimation (low-pass filtering) and seasonal adjustment in real-time, i.e., constructing filters that depend only on present and past data.
View
Multi-step-ahead estimation of time series models
Article
Full-text available
  • Jul 2013
  • INT J FORECASTING
We study the fitting of time series models via the minimization of a multi-step-ahead forecast error criterion that is based on the asymptotic average of squared forecast errors. Our objective function uses frequency domain concepts, but is formulated in the time domain, and allows the estimation of all linear processes (e.g., ARIMA and component ARIMA). By using an asymptotic form of the forecast mean squared error, we obtain a well-defined nonlinear function of the parameters that is proven to be minimized at the true parameter vector when the model is correctly specified. We derive the statistical properties of the parameter estimates, and study the asymptotic impact of model misspecification on multi-step-ahead forecasting. The method is illustrated through a forecasting exercise, applied to several time series.
View
View
Forecasting, Structural Time Series Models and the Kalman Filter
Article
Full-text available
  • Dec 2002
In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.
View
View
View
View
View
View