Home  About us  Contact
 

Smoothing Constant (smoothing + constant)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Estimating Trends with Percentage of Smoothness Chosen by the User

INTERNATIONAL STATISTICAL REVIEW, Issue 2 2008
Victor M. Guerrero
Summary This work presents a method for estimating trends of economic time series that allows the user to fix at the outset the desired percentage of smoothness for the trend. The calculations are based on the Hodrick-Prescott (HP) filter usually employed in business cycle analysis. The situation considered here is not related to that kind of analysis, but with describing the dynamic behaviour of the series by way of a smooth curve. To apply the filter, the user has to specify a smoothing constant that determines the dynamic behaviour of the trend. A new method that formalizes the concept of trend smoothness is proposed here to choose that constant. Smoothness of the trend is measured in percentage terms with the aid of an index related to the underlying statistical model of the HP filter. Empirical illustrations are provided using data on Mexico's GDP. Résumé Ce travail présente un méthode pour estimer les tendances des séries de temps économiques qui permet à l'usager fixer dès début le pourcentage désiré de douceur pour la tendance. Les calculs ont fondement en le filtre de Hodrick et Prescott que s'emploie généralement dans l'analyse de cycles économiques. La situation ici considéré n'a pas relation avec ce type d'analyse, mais comment la description du comportement dynamique des séries avec une courbe douce. Pour appliquer le filtre, l'usager a besoin de spécifier une constante de douceur que détermine le comportement dynamique de la tendance. Un nouveau méthode que formalise le concept de douceur de la tendance est ici proposé pour choisir la constante. La douceur de la tendance est mesuré en termes de pourcentage avec l'aide d'un index rapporté avec le modèle statistique après le filtre. Quelques illustrations empiriques sont munies avec données de l'économie mexicaine. [source]

Trend estimation of financial time series

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2010
Víctor M. Guerrero
Abstract We propose to decompose a financial time series into trend plus noise by means of the exponential smoothing filter. This filter produces statistically efficient estimates of the trend that can be calculated by a straightforward application of the Kalman filter. It can also be interpreted in the context of penalized least squares as a function of a smoothing constant has to be minimized by trading off fitness against smoothness of the trend. The smoothing constant is crucial to decide the degree of smoothness and the problem is how to choose it objectively. We suggest a procedure that allows the user to decide at the outset the desired percentage of smoothness and derive from it the corresponding value of that constant. A definition of smoothness is first proposed as well as an index of relative precision attributable to the smoothing element of the time series. The procedure is extended to series with different frequencies of observation, so that comparable trends can be obtained for say, daily, weekly or intraday observations of the same variable. The theoretical results are derived from an integrated moving average model of order (1, 1) underlying the statistical interpretation of the filter. Expressions of equivalent smoothing constants are derived for series generated by temporal aggregation or systematic sampling of another series. Hence, comparable trend estimates can be obtained for the same time series with different lengths, for different time series of the same length and for series with different frequencies of observation of the same variable. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On the exponentially weighted moving variance

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2009
Longcheen Huwang
Abstract MacGregor and Harris (J Quality Technol 25 (1993) 106,118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta-Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source]

Trend estimation of financial time series

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2010
Víctor M. Guerrero
Abstract We propose to decompose a financial time series into trend plus noise by means of the exponential smoothing filter. This filter produces statistically efficient estimates of the trend that can be calculated by a straightforward application of the Kalman filter. It can also be interpreted in the context of penalized least squares as a function of a smoothing constant has to be minimized by trading off fitness against smoothness of the trend. The smoothing constant is crucial to decide the degree of smoothness and the problem is how to choose it objectively. We suggest a procedure that allows the user to decide at the outset the desired percentage of smoothness and derive from it the corresponding value of that constant. A definition of smoothness is first proposed as well as an index of relative precision attributable to the smoothing element of the time series. The procedure is extended to series with different frequencies of observation, so that comparable trends can be obtained for say, daily, weekly or intraday observations of the same variable. The theoretical results are derived from an integrated moving average model of order (1, 1) underlying the statistical interpretation of the filter. Expressions of equivalent smoothing constants are derived for series generated by temporal aggregation or systematic sampling of another series. Hence, comparable trend estimates can be obtained for the same time series with different lengths, for different time series of the same length and for series with different frequencies of observation of the same variable. Copyright © 2009 John Wiley & Sons, Ltd. [source]