Iterative Plug-in Research Articles

Data-driven local polynomial for the trend and its derivatives in economic time series

ABSTRACTThe main purpose of this paper is the development of data-driven iterative plug-in algorithms for local polynomial estimation of the trend and its derivatives under dependent errors. Furthermore, a data-driven lag-window estimator for the variance factor in the bandwidth is proposed so that the nonparametric stage is carried out without any parametric assumption on the stationary errors. Analysis of the residuals using an ARMA model is further discussed. Moreover, some computational features of the data-driven algorithms are discussed in detail. Practical performance of the proposals is confirmed by a simulation study and a comparative study, and illustrated by quarterly US GDP and labour force data. An R package called ‘smoots’ (smoothing time series) for smoothing the trend and its derivatives in short-memory time series is developed based on the proposals of this paper.

Steady state adjusting trends using a data-driven local polynomial regression

Economic variables usually follow a dynamic trend pattern. However, it is difficult to estimate this trend precisely as numerous economically- and statistically-based estimation methods exist. This contribution proposes a data-driven nonparametric trend that is local polynomial, to improve arbitrary trend estimations of commonly used methods concerning the selection of the smoothing parameter and the dependence structure. An iterative plug-in (IPI) algorithm determines the bandwidth endogenously and allows a theory-based interpretation of the length of growth processes. This length of the bandwidth reflects the lengths of the steady state periods. Consequently, the bandwidth identifies the time period of stable economic conditions and can detect economic changes. To demonstrate the power of this estimation approach, an extensive simulation study is performed. Furthermore, examples using US and UK GDP data along with a guide for the optimal choice of algorithms for empirical applications are provided. This proposed method yields new insights for growth dynamics, cyclical movements and their dependence.

Secular stagnation? Is there statistical evidence of an unprecedented, systematic decline in growth?

So far it is difficult to establish firm evidence that the recent decline in growth is indeed systematic, unprecedented, and significant. In order to provide more statistical evidence of a decline in economic growth, we use a data-driven nonparametric estimation approach which improves boundary estimators, using an extended iterative plug-in (IPI) algorithm to determine the bandwidth endogenously. We identify continuously Moving Trends (MT) with a length of 18 years for US GDP. Two introduced tests demonstrate a persistent decline in US trends and growth rates since the dot.com bubble. Hence, the 2008 financial crisis merely revealed that GDP, labor, and multi-factor productivity trends were already stagnating.

Growth Trends and Systematic Patterns of Booms and Busts‐Testing 200 Years of Business Cycle Dynamics

AbstractWe study the dynamic pattern of business cycles using US GDP data between 1790 and 2015. To address difficulties in trend and cycle decomposition, we introduce a semiparametric estimation approach with an iterative plug‐in (IPI) algorithm for endogenous bandwidth selection. This algorithm identifies continuously moving growth trends with trend‐supporting growth periods. A simulation study demonstrates the value‐added of our trend identification. Afterwards, nonlinear SETAR models are fitted parametrically. Further, we test the trend using a recently developed test and the estimated SETAR models against their linear alternatives. The results indicate asymmetric characteristics during booms and busts.

Slow Booms and Deep Busts: 160 Years of Business Cycles in Spain

Abstract This paper introduces an economically important new idea for detrending macroeconomic time series and examines the Spanish business cycle pattern with respect to potential asymmetries. To address difficulties in the trend and cycle decomposition, a nonparametric trend estimation approach is introduced and exemplary applied to the Spanish GDP data for the period 1850 to 2015. The application of an iterative plug-in (IPI) algorithm for endogenous bandwidth selection solves the problem of choosing an adequate smoothing parameter for nonparametric regression. The algorithm identifies continuously Moving Trends (MT) with a time length of 34 years. After we estimate the trend nonparametrically, we fit several time series models to the residuals for further analysis. Although asymmetry during expansion and recession phases is indicated, it is not unambiguous.

On the iterative plug-in algorithm for estimating diurnal patterns of financial trade durations

ABSTRACTThis paper discusses the detailed performance of an iterative plug-in (IPI) bandwidth selector for estimating the diurnal duration pattern in a Semi-ACD (semiparametric autoregressive conditional duration) model. For this purpose a large simulation study was carried out. The effects of different factors, which affect the selected bandwidth are discussed in detail. The simulated results and data examples show that the proposed IPI algorithm works very well in practice and that the Semi-ACD model in general is clearly superior to the parametric ACD model, if there is a deterministic trend in the duration data. It is also shown that the bandwidth selection, and the estimation of the diurnal pattern and the model parameters will all be clearly improved, if the sample size is enlarged. According to the goodness-of-fit of the estimated diurnal pattern, a best combination of the above-mentioned factors is found. Moreover, a comparative study shows that our proposal usually outperforms the commonly used cubic spline.

An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method

We propose a fast data-driven procedure for decomposing seasonal time series using the Berlin Method, the procedure used, e.g. by the German Federal Statistical Office in this context. The formula of the asymptotic optimal bandwidth h A is obtained. Methods for estimating the unknowns in h A are proposed. The algorithm is developed by adapting the well-known iterative plug-in idea to time series decomposition. Asymptotic behaviour of the proposal is investigated. Some computational aspects are discussed in detail. Data examples show that the proposal works very well in practice and that data-driven bandwidth selection offers new possibilities to improve the Berlin Method. Deep insights into the iterative plug-in rule are also provided.

Iterative Plug-In Algorithms for SEMIFAR Models—Definition, Convergence, and Asymptotic Properties

This article proposes data-driven algorithms for fitting SEMIFAR models. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. Convergence and asymptotic properties of the proposed algorithms are investigated. A large simulation study illustrates the practical performance of the methods.

Local Bandwidth Choice in Kernel Regression Estimation

This article gives a short overview on proposals for locally adaptive kernel regression estimation. Computational and algorithmic aspects of a new variant and generalization of the iterative plug-in rule by Brockmann, Gasser, and Herrmann are described in detail. This new bandwidth selector adapts to heteroscedasticity and can also be used for nonequidistant design. A simulation study supplements the article. Classical approaches to nonparametric regression estimation use such linear methods as kernel smoothing, orthogonal series, or smoothing spline methods with adaptation of a global smoothing parameter to the data at hand. More refined proposals adapt the smoothing parameters locally. Recently, interest in local methods has increased through research on locally adaptive wavelet methods. These wavelet methods enjoy nearly optimal asymptotic behavior over broad risk and function classes. Nevertheless, classical methods, such as local variable bandwidth kernel estimators, can compete with these new methods, at least in practical terms. This might be due to great experience and refined algorithmic versions which have been developed. (Some theoretical aspects are discussed by Fan, Hall, Martin, and Patil.) Additionally, classical methods can easily be modified for more general regression models without losing their typical structure as is demonstrated by the proposal in this article.