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Examines trend rules in conjunction with other well‐known supplementary runs rules to assess their impact when used in control charting. Focuses on a set of 613 trend rules deemed as potential candidates to increase the sensitivity of the control chart. The examined rules are viewed in the light of a stable environment, which determines the false alarm rate, and then in an environment in which the process mean is subjected to drift. Results indicate that there are subsets of trend rules that aid in the detection of out‐of‐control conditions depending on the severity of the drift and the number of zonal‐based supplementary runs rules used.

This paper aims to contribute to the understanding of the concept of a trend and the discourse of trend analysis.

This paper concisely discusses the concept of trends, the value of trend analysis for strategic planning and hierarchical trend pyramids as a tool to scan and analyse trends.

The examples will be given of how specific mega, meso and micro trends are related within a hierarchic trend pyramid.

The tool of trend pyramids helps to structurally analyse and understand trends and developments. Such analysis and understanding are relevant for strategic foresight and scenario planning in leisure and tourism.

The literature on trend levels and pyramids is scarce and varies in interpretation. The aim of this paper is to integrate the various viewpoints into a useful instrument for the scanning and analysis of trends and developments.

This chapter aims at shedding light upon how transforming or detrending a series can substantially impact predictions of mixed causal-noncausal (MAR) models, namely dynamic processes that depend not only on their lags but also on their leads. MAR models have been successfully implemented on commodity prices as they allow to generate nonlinear features such as locally explosive episodes (denoted here as bubbles) in a strictly stationary setting. The authors consider multiple detrending methods and investigate, using Monte Carlo simulations, to what extent they preserve the bubble patterns observed in the raw data. MAR models relies on the dynamics observed in the series alone and does not require economical background to construct a structural model, which can sometimes be intricate to specify or which may lack parsimony. The authors investigate oil prices and estimate probabilities of crashes before and during the first 2020 wave of the COVID-19 pandemic. The authors consider three different mechanical detrending methods and compare them to a detrending performed using the level of strategic petroleum reserves.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

This chapter re-examines the determinants of health care expenditure (HCE), using a panel of 32 Organization for Economic Cooperation and Development (OECD) countries from 1990 to 2012. In particular, a panel semiparametric technique (i.e., a partially linear model) is employed, with cross-sectional dependence allowed. Beside the study of coefficients, this chapter investigates the trending functions of HCE. After the common and individual trends of HCE are estimated via semiparametric methods, the authors calibrate them with polynomial specifications, leading to out-of-sample forecasting. The validities of the calibration are tested as well. Contrary to those studies that do not take into account time series properties, our finding suggests that medical care is not a luxury commodity. Other determinants, such as public financing, and the supply of doctors, are all positively related to HCE. Moreover, the calibrated trending models perform well in out-of-sample forecasting.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

The role of trend inflation shocks for the U.S. macroeconomic dynamics is investigated by estimating two DSGE models of the business cycle. Policymakers are assumed to be concerned with a time-varying inflation target, which is modeled as a persistent and stochastic process. The identification of trend inflation shocks (as opposed to a number of alternative innovations) is achieved by exploiting the measure of trend inflation recently proposed by Aruoba and Schorfheide (2011). Our main findings point to a substantial contribution of trend inflation shocks for the volatility of inflation and the policy rate. Such contribution is found to be time dependent and highest during the mid-1970s to mid-1980s.

Climate change is a massive multidimensional shift. Temperature shifts, in particular, have important implications for urbanization, agriculture, health, productivity, and poverty, among other things. While much research has documented rising mean temperature levels, the authors also examine range-based measures of daily temperature volatility. Specifically, using data for select US cities over the past half-century, the authors compare the evolving time series dynamics of the average daily temperature (AVG) and the diurnal temperature range (DTR; the difference between the daily maximum and minimum temperatures). The authors characterize trend and seasonality in these two series using linear models with time-varying coefficients. These straightforward yet flexible approximations provide evidence of evolving DTR seasonality and stable AVG seasonality.