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The main objective of this paper is to investigate the problem of estimating the trend function St = S(xt) for process satisfying stochastic differential equations of the type dX t = S ( X t ) dt + ε dB t H , K , X 0 = x 0 , 0 ≤ t ≤ T , {\rm{d}}{{\rm{X}}_{\rm{t}}} = {\rm{S}}\left( {{{\rm{X}}_{\rm{t}}}} \right){\rm{dt + }}\varepsilon {\rm{dB}}_{\rm{t}}^{{\rm{H,K}}},\,{{\rm{X}}_{\rm{0}}} = {{\rm{x}}_{\rm{0}}},\,0 \le {\rm{t}} \le {\rm{T,}} where { B t H , K , t ≥ 0 {\rm{B}}_{\rm{t}}^{{\rm{H,K}}},{\rm{t}} \ge {\rm{0}} } is a bifractional Brownian motion with known parameters H ∈ (0, 1), K ∈ (0, 1] and HK ∈ (1/2, 1). We estimate the unknown function S(xt) by a kernel estimator ̂St and obtain the asymptotic properties as ε → 0. Finally, a numerical example is provided.

We first establish, through a Berry–Esseen-type bound, the asymptotic normality of a local linear estimate of the regression function in a fixed design setting when the errors are stationary isotropic spatial random fields. On the other hand, we investigate the weak convergence of an empirical estimate of the variance of these errors in a general α-mixing setting.

Let X ( t ) = ( X 1 ( t ) , … , X d ( t ) ) , t ∈ [ 0 , S ] be a Gaussian vector process and let g ( x ) , x ∈ R d be a continuous homogeneous function. We are concerned with the exact tail asymptotic of the chaos process g ( X ( t ) ) , t ∈ [ 0 , S ] with a trend function h ( t ) . Both scenarios X ( t ) is locally-stationary and X ( t ) is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes.

We consider a model of deterministic one-time parameter change in a continuous time autoregressive model around a deterministic trend function. The exact discrete time analogue model is detailed and compared to corresponding parameter change models adopted in the discrete time literature. The relationships between the parameters in the continuous time model and the discrete time analogue model are also explored. Our results show that the discrete time models used in the literature can be justified by the corresponding continuous time model, with a only a minor modification needed for the (most likely) case where the changepoint does not coincide with one of the discrete time observation points. The implications of our results for a number of extant discrete time models and testing procedures are discussed.

The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.

The aim at the study is to examine the annual price fluctuation, and acreage response of rice in Bangladesh using the time series data for the period 1981-82 to 2010-11. Acreage response was estimated within the Nerlovian Partial Adjustment Model. The study estimates the growth rate of the area, production, yield and nominal price of rice and annual fluctuation on nominal and real prices of all the three rice seasons. The study was based on secondary data. Price fluctuation of Aus rice for nominal and real price was highest (-26.6 to 46.9) and (-29.4 to 37.2) in sub-period II (1991-92 to 2000-01). The fluctuation in nominal and real price of Aman rice was also highest (-27.0 to 40.7) and (-29.7 to 29.2) in the sub-period II (1991-92 to 2000-01). The fluctuation in nominal and real Boro rice price was also highest (-48.5 to 28.5) and (-34.4 to 28.4) in the sub-period II (1991-92 to 2000-01). Growth rates of area, production, yield and nominal price of three seasons of rice were estimated by fitting exponential trend function. Growth rates of area which were significantly negative for Aus, Aman that were -4.6 percent and -0.3 percent and positive for Boro rice it was 4.5 percent over the whole period. The growth rates of yield for Aus, Aman, and Boro were increased significantly at the rate of 2.2, 1.9 and 1.9 percent respectively during the entire time period. Farmer’s field-oriented policy should be developed for high yield and stable market.

We examine the effect of transport infrastructure on carbon dioxide (CO2) emissions in OECD countries over a period of almost 150 years. To do so, we employ both parametric and non-parametric panel data techniques. With the parametric estimates, we find mixed evidence of a statistically significant positive relationship between transport infrastructure and CO2 emissions, which is dependent on the specific long-run estimator used. Our non-parametric estimates suggest that the common trend function for CO2 emissions is rising for most of the period and that there is a time-varying relationship between transport infrastructure and CO2 emissions. The computed time-varying coefficient function of transport infrastructure has been positive since 1940, and the observed effect is most pronounced between 1940 and 1960.

In this contribution we are concerned with the asymptotic behaviour as $u\to \infty$ of $\mathbb{P}\{\sup_{t\in [0,T]} X_u(t)> u\}$, where $X_u(t),t\in [0,T],u>0$ is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns $\mathbb{P}\{\sup_{t\in [0,T]} (X(t)+ g(t))> u\}$ as $u\to\infty$, for $X$ a centered Gaussian process and $g$ some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest., 28 pages

We study the asymptotic properties of the least-squares estimator for the trend function of a particular class of locally stationary models, which are defined by considering a smooth variation of the trend function. Additionally, errors are assumed to be realizations from a long-range dependent stationary Gaussian process. Our findings are then illustrated through Monte Carlo simulations.

Goal – The main objective of the paper is to verify if the relation between the election cycles and the number of tax reliefs in Poland exists and – if it exists – what is its direction and strengh. Hypothesis – Election cycles affect the dynamics of introducing tax reliefs into the Polish Personal Income Tax. Research methodology – The research hypothesis was verified by assessing the cyclical fluctuations of the trend function describing the number of reliefs in the Polish Personal Income Tax. The study covers the years 1991-2018. The authors’ own calculations made on the basis of the legislative changes made in the studied period to the Act on Personal Income Tax of 26th July 1991 provide the source material for the research. Score – The study confirms positive relation between the election cycles and the dynamics of introducing tax reliefs into the Polish Personal Income Tax. The number of tax reliefs in personal tax cyclically fluctuates and, moreover, the total number of introduced tax reliefs is significantly higher in the election years and lower in the other accordingly.

Tests designed to detect increasing hazard ratio against the proportional hazards hypothesis are generally consistent for other alternatives also. This article provides a test of the null hypothesis of increasing hazard ratio. The test is based on the separation between an empirical version of the relative trend function and its greatest convex minorant. The proportional hazards model, the least favorable null model for large samples, is used to produce simulation based cutoffs. A simulation study shows reasonable performance of the proposed test in small samples. The analytical test, together with a graphical version, is illustrated through two real life examples.

This article examines the nonstationary properties of per capita real output in 28 sub-Saharan African (SSA) countries, covering the period 1960–2014. The sequential testing approach proposed by Kejriwal and Lopez (2013, Econometric Reviews 32(8), 892–927) is used to categorize SSA countries into growth shift, level shift and linear trend hypotheses based on the presence or not of breaks in slope and/or level of the trend function. The break dates are associated to major historical or economic events such as sociopolitical crisis, commodity price fluctuations on international market, the discovery and the exploitation of mineral deposits or unfavourable environmental and climatic conditions. The empirical evidences of appropriate unit root tests fail to reject the unit root hypothesis in all the countries, suggesting that a shock would have a permanent effect on growth process, and stabilization policies may be implemented in dealing with income fluctuations.

This paper revisits the catching-up hypothesis among the 29 transition countries using the time series approach to investigate income convergence. In this study, we propose a model which specifies a trend function incorporating both sharp and smooth breaks using dummy variables and Fourier functions, respectively. Our empirical results indicate that two convergence clubs are forming among the transition countries and one club is among the rich and the other club is among the poor countries, where most middle income countries will disappear and move into one of the two clubs. Also, our results indicate that the 1980s was an ominous decade for growth in the transition countries with income in most diverging from the USA. With recovery in the 1990s, we find that in the 2000s income per capita in most of these countries was catching up toward the USA.

This paper presents a multi-model Gaussian process (MMGP) approach for predicting the RUL of lithium-ion batteries. The proposed MMGP approach incorporates multiple candidate capacity fade models, as the trend functions of a Gaussian process (GP) model, to capture the multi-stage capacity fade trend of the batteries. First, the hypothetical capacities at a predefined number of future cycles are predicted at the current cycle based on the offline data using similarity-based extrapolation. Then, the active fade model is selected by comparing the hypothetical capacities with the GP model-projected capacities using each candidate fade model and the active model is employed as the trend function of the GP model. Finally, the distribution of the RUL is estimated by determining when the projected capacity curves using the GP model down-cross a pre-defined capacity threshold. The MMGP approach was used for the RUL prediction of eight lithiumion battery cells that show multi-stage capacity fade behavior when cycled with a daily current rate (i.e., C/24). The capacities of these cells initially degrade rapidly, followed by a reduced fade rate and then a faster linear fade rate. The RUL prediction results suggest that the proposed MMGP approach can adaptively select proper trend functions for the GP model at different capacity fade stages throughout the lifetime, as well as adapting the models to accommodate variations in the capacity fade performance among different cells.

This article provides evidence that the forward premium involves structural changes in the trend function, which might affect the predictability of currency excess returns to be dependent on the choice of the sample period. Accounting for the shifts in trend for the forward premium reveals that currency excess returns for the Canadian dollar, Swiss franc, euro and pound against the US dollar are significantly predictable irrespective of the sample period selected. Another advantage of detrending the forward premium is that we can obtain more consistent slope coefficient estimates in the predictive regression, which enables us to make more consistent, dependable inferences about the excess return predictability.

This paper proposes an IV-based panel unit root test that is general enough to accommodate general error serial and cross-section dependence, and a potentially nonlinear deterministic trend function. These allowances make the new test one of the most general around. It is also very simple to implement. Indeed, the IV statistic is asymptotically invariant to not only to all nuisance parameters characterizing the dependence of the errors and the true trend function, but also the deterministic specification of the fitted test regression.

Trend models are important in describing nonstationary behavior of a time series. In this paper we propose valid tests for the trend coefficients in a multivariate system with mixed stationary, integrated or nearly integrated errors. Cross-sectional and serial dependence in innovations are left unspecified beyond regularity assumptions. We consider two sets of tests based on OLS and SUR estimation of the transformed system. A modified SUR estimator corrected for serial correlation of unknown form is shown to be asymptotically efficient. The standard tests under stationarity are also analyzed and potential misleading inferences are demonstrated. The framework is general allowing for linear and nonlinear trend functions. Asymptotic theory, simulations and an empirical application are provided.

Purpose – The purpose of this paper is to examine the time series behavior of Greek labor market series by providing an empirical perspective on trend breaks and unit roots. Trend breaks represent aggregate behavior responses to “infrequent” changes in economic fundamentals, including changes in fiscal or labor market conditions, as have been perceived in Greece during the last years. Unit roots reveal whether “regular” shocks have significant effects on the level of the series over a specified finite horizon. Design/methodology/approach – The authors employ recent procedures that deal with the “circular testing problem” between tests on the parameters of the trend function and unit root tests that often arises in empirical applications. These techniques assess trend function stability and are robust regardless of whether the noise component is stationary or having a unit root. Then, conditional on the presence of breaks, the authors test whether the series can be characterized by a stochastic trend. Findings – The analysis provides evidence of “infrequent” trend breaks that appear to coincide with the recent global economic crisis and the implementation of the counteraction (fiscal) measures to the Greek debt crisis. Allowing for trend breaks does not lead to a rejection of the unit root hypothesis, which might reflect the low flexibility of the country’s labor market operation. Practical implications – The procedures employed can be viewed as new tools that might help empirical researchers to explore more accurately the characteristics of individual time series and to find reasonable approximations to the true processes of the time series examined. Originality/value – The paper provides new information on the presence of structural changes in the Greek labor market, and on whether the “aggressive” and “occasional” nature of fiscal measures can be approximated by infrequent changes in the slope of the trend function.

The main goals of our study of the women’s javelin throw were twofold:. first, to analyse the dynamics of female javelin throw results variability as a function of time (time period 1946-2014), second, to create a predictive model of the results during the upcoming 4 years. The study material consisted of databases covering the female track and field events obtained from the International Association of Athletics Federations. Prior to predicting the magnitude of results change dynamics in the time to follow, the adjustment of trend function to empirical data was tested using the coefficients of convergence. Phase II of the investigation consisted of the construction of predictive models. The greatest decreases in result indexes were noted in 2000 (9.4%), 2005-2006 (8.7%) and 2009 (7.4%). The trend increase was only noted in the years 2006-2008. In general, until 1998 the mean result improved by 54.6% (100% - results of 1946) whereas from 1999 through 2011 the result only increased by 1.3%. Based on data and results variability analysis it might be presumed that, in the nearest future (2015-2018), results variability will increase by approximately 9.7%. Percent improvement of javelin throw distance calculated on the basis of the 1999 raw input data is 1.4% (end of 2014).

A key feature of Flexible Fourier Form (FFF) is that the essential characteristics of multiple structural changes can be captured using a small number of low frequency components from a Fourier approximation. We introduce a variant of the FFF into the trend function of US real GDP in order to allow for gradual effects of unknown numbers of structural changes occurring at unknown dates. We find that the hypothesis of no changes can be rejected, and the Fourier components are significant. Our new cycle matches the NBER chronology very well, especially for the Great Recession of 2009.

Based on consistency and asymptotic normality of a nonparametric kernel trend estimation in the context of locally stationary processes, validity of a hybrid wild bootstrap approach for estimating the distribution of the nonparametric estimator is established. Simulations are presented. © 2015 Elsevier B.V. 101 54 63 Cited By :1

This paper tests the hysteresis hypothesis in Spanish regional unemployment using quarterly data over the 1976–2014 period using a large battery of univariate unit root tests allowing for two breaks in the trend function of the series. The evidence strongly supports the hysteresis hypothesis for each of the 17 Spanish regions, since we consistently fail to reject the unit root null hypothesis. When the analysis is extended to allow for five structural breaks, the conclusion remains unaltered. The results call for policy measures to reduce the sluggishness in the adjustment of the labour market to adverse shocks.

Purpose– The purpose of this paper is to use quarterly time series data from Canada and the Canadian provinces to determine if the unemployment rates in the Canadian provinces are converging to the national rate of unemployment.Design/methodology/approach– First, the authors check for existence of stochastic convergence using recent unit root statistics, see Perron and Rodríguez (2003) and Rodríguez (2007). Second, the authors verify existence of convergence using methods proposed by Volgelsang (1998) and Bai and Perron (1998, 2003). All these methods allows for structural break(s) in the data.Findings– Results from different unit root tests, without and with structural breaks, confirm that stochastic convergence exists in all provinces. The other results show strong evidence that deterministic convergence exists and the unemployment rates of the Canadian provinces are converging to the unemployment rate of Canada. This conclusion is stronger when multiple breaks are allowed in the trend function using the approach of Bai and Perron (1998, 2003).Practical implications– Since the authors have verified the existence of stochastic convergence, any intervention in the labor markets of the Canadian provinces to control the provincial unemployment rate would have a temporary effect and these policies will not have a permanent influence on the unemployment rates. However, existence ofβ-convergence in the Canadian provinces shows that general policies toward lowering the national unemployment rate would decrease the provincial unemployment rates as well.Originality/value– To the best of the knowledge, the paper attempts to study the unemployment rate convergence in the Canadian provinces using the above-mentioned approaches. These approaches allow the authors to take into consideration the possibility of structural breaks in order to get results that are more accurate.

We give expansions about the Gumbel distribution in inverse powers of n and log n for Mn, the maximum of a sample size n or n+1 when the j-th observation is \(\mu (\tfrac{j} {n}) + e_j \), µ is any smooth trend function and the residuals {ej} are independent and identically distributed with $$P(e > r) \approx \exp ( - \delta x)x^{d_0 } \sum\limits_{k = 1}^\infty {c_k x^{ - k\beta } } $$ as x→∞. We illustrate practical value of the expansions using simulated data sets.

In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. As a by-product we solve a minimization problem related to the norm of the trend function., 17 pages

This paper addresses the statistical uncertainties associated with the estimation of a depth-dependent trend function and spatial variation about the trend function using limited site-speci...

A partial replacement of resin binder in epoxy mortars by PET waste based glycolyzates makes these building materials ecologically and economically interesting. The article presents the results of the first phase of research on epoxy mortars modified with poly(ethylene terephthalate) (PET) glycolyzates. Changes of some chosen mortar parameters (weight change, appearance of mortar specimens) due to the effect of the solutions of five aggressive media were monitored for twelve months. It was established that unlike ordinary cement mortars, the building composites that were obtained showed very good chemical corrosion resistance. The results of the investigation were presented as the trend function.

This paper investigates the stability of the steady-state growth process in East Asian region using a novel panel stationarity test, which allows us to control for (a) unobserved heterogeneity in form and date of potential structural breaks in a trend function, (b) the cross-sectional dependence among countries in the panel bootstrapping methods, and (c) the serially correlated errors. Evidence shows that a large majority of countries exhibit slowdowns in economic growth after their structural breaks and thus could not recover from negative shocks and return original balanced growth path.

Based on index system of mining area ecosystem management is set on, on the basis of ecosystem health in mining area, constructs the ecological environment in mining area level, management of mineral resources, mining area economic and social development level as the criterion layer multi-level evaluation index system of index of quantitative method, combined with the change trend of volatility and changes in indicators of the direction and speed, puts forward the trend function and grey prediction method is applied to dynamic evaluation model of mining area ecosystem management, and in a certain mining area, the inspection case study conclusion shows that the mining area ecological system management is in medium level, need to strengthen management, and proposed the corresponding countermeasure and the suggestion.

Degradation signals are sensor-based signals that are correlated with degradation processes of engineering components. In this article, we present a flexible modeling framework for characterizing degradation signals that can only be observed up to a prespecified failure threshold. The underlying assumption of this framework is that the engineering components degrade according to a similar trend, referred to as the common shape function, but at different degradation rates. Under this assumption, the degradation signals of different components are synchronized using a random time warping process that transforms the common trend function into degradation processes that progress at varying rates. Our primary objective is to obtain real-time predictions for the residual lifetime of components deployed in the field. In the initial step, the historical degradation signals are used to recover the distribution of the degradation processes under the assumptions of the proposed time warping model. Next, the distribu...

Summarization: We conduct a spatiotemporal geostatistical analysis of groundwater level data using space–time Residual Kriging (STRK). We compare the performance of three spatiotemporal variogram models in mapping groundwater level data. All models involve the same space–time trend function; the first model is a separable product variogram that involves Matérn space and time functions, while the second and third use non-separable functions. The non-separable models include a diffusive space–time variogram and a spatiotemporal extension of the Spartan variogram. The non-separable models are applied for the first time to groundwater level data. Our analysis shows that the Spartan and the non-separable diffusive variograms fit the experimental variogram of the residuals better than the separable Matérn model and improve the cross-validation results. The Spartan model provides the best cross validation measures among the three models. We also generate maps of groundwater level which illustrate the spatiotemporal variability in the basin. Παρουσιάστηκε στο: Spatial Statistics

Adulthood trajectories of outcomes such as depression and the sense of control measure aspects of the human condition that Americans may view as objects of change. Social science should provide information on that progress, or its absence. Whether these trajectories change their shape, and how and why if they do, is important theoretically too. A range of birth cohorts coexist in time, place, and social relationship. Each cohort, as it goes through adulthood, follows in aggregate a path left by older ones, reshaping that path as it goes. The shapes of the trajectories, and the trends reshaping them, represent two inseparable aspects of the same phenomenon. This report describes methods for mapping aging trajectories and intercohort trends, using linear latent-growth models of relatively brief follow-up data (six years in the examples). The author reviews shared research ideals that led to the model: put theory into modeling, go where the data lead, use what you have, go beyond where you have been, and risk being precisely wrong.

This paper proposes a new unit root test that is general enough to accommodate a potentially non-linear deterministic trend function, making it one of the most general tests around. However, the main advantage lies with its simple implementation. In particular, the asymptotic critical values are shown to be “almost” independent of the deterministic trend function, and as a result the test can be implemented without the need for model-specific critical values. The new test is applied to a sample consisting of monthly prices of four precious metals for a number of Asian countries.

In this paper, we compare different ways to construction of the degradation models with random effects. Such models are based on the degradation index's dependence on time, which is called trend in this work. Using the constructed model, we can predict time of the failure, in other words, non-failure time of the tested items. The two ways are considered: it is a Wiener degradation model with covariates, which includes the normal distribution as a distribution of the increments of the degradation index, and semi-parametric model with random effects. Using the computer simulation methods, we conduct the research on accuracy of the trend construction, which coincides the considering models, regarding true trend function.

The paper considers the construction of a confidence band for the trend function of a stationary time series. An explicit formula is derived based on polynomial splines and Sunklodas (1984). The performance of the confidence band is illustrated by simulation studies. The proposed method is applied to the analysis of the annual yields of wheat in the United States.

The framework of stationarity testing is extended to allow a generic smooth trend function estimated nonparametrically. The asymptotic behavior of the pseudo-Lagrange Multiplier test is analyzed in this setting. The proposed implementation delivers a consistent test whose limiting null distribution is standard normal. Theoretical analyses are complemented with simulation studies and some empirical applications.

This paper empirically examines whether there exists stochastic convergence of income inequality among 48 contiguous states within the US over the 1916–2005 period. For that purpose, we employ the recently developed panel stationarity test of Carrion-i-Silvestre, Del Barrio-Castro and Lopez-Bazo (2005), which assumes a highly flexible trend function by incorporating an unknown number of structural breaks. In addition, the issues of cross-sectional dependence as well as control for finite-sample bias are accommodated through bootstrap methods. Overall, for the US case, our analysis provides strong evidence in support of the hypothesis of inter-state inequality convergence. Moreover, the results are robust to alternative inequality measures applied, different notions of stochastic convergence defined, and alternative panel stationary test employed.

SUMMARY We present an accurate modeling technique that exploits standard space mapping (SM) as a trend function and the correction layer implemented with kriging. The kriging process allows us to efficiently utilize all available fine model data (not possible in the standard SM approach) and to obtain accuracy better than both the SM and recently published combinations of SM and radial basis function interpolation and fuzzy systems. We present application examples of design optimization and statistical analysis of several microwave filters. Copyright © 2011 John Wiley & Sons, Ltd.

We employ a unique data set and new time-series techniques to reexamine the existence of trends in relative primary commodity prices. The data set comprises 25 commodities and provides a new historical perspective, spanning the seventeenth to the twenty-first centuries. New tests for the trend function, robust to the order of integration of the series, are applied to the data. Results show that eleven price series present a significant and downward trend over all or some fraction of the sample period. In the very long run, a secular, deteriorating trend is a relevant phenomenon for a significant proportion of primary commodities. © 2010 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Seasonality analysis is one of the classic topics in time series. This paper studies techniques for seasonality analysis when the trend function is unspecified. The asymptotic properties of the semiparametric estimators are derived, and an estimation algorithm is provided. The techniques are applied to making inference for the monthly global land–ocean temperature anomaly indexes.

Trend–cycle decompositions for US real GDP such as the unobserved components models, the Beveridge–Nelson decomposition, the Hodrick–Prescott filter and others yield very different cycles which bear little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycle, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of a change in the slope of the trend function. Once this is accounted for, all methods yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. The cycle is more important in magnitude than previously reported and it accords well with the NBER chronology. Our results are corroborated using an alternative trend–cycle decomposition based on a generalized unobserved components models with errors having a mixture of normals distribution for both the slope of the trend function and the cyclical component.

This paper investigates the hypothesis of a unit root in inflation for 13 OECD countries over the period 1957–2005, taking into account cross-sectional dependence and multiple mean shifts. We conduct unit root testing with the more powerful unit root tests with cross-dependence proposed by Smith et al. [Smith, L. V., Leybourne, S., Kim, T., & Newbold, P. (2004). More powerful panel data unit root tests with an application to the mean reversion in real exchange rates. Journal of Applied Econometrics , 19 (2), 147–170] and a bootstrap version of the panel stationarity test of Hadri [Hadri, K. (2000). Testing for stationarity in heterogeneous panel data. The Econometrics Journal , 3 (2), 148–161.], which provide inconclusive evidence on the time series properties of OECD inflation rates. To shed some light on this issue, we employ the recently developed panel stationarity test of Carrion-i-Silvestre et al. [Carrion-i-Silvestre, J. L., Del Barrio, T., & Lopez-Bazo, E. (2005). Breaking the panels: An application to the GDP per capita. The Econometrics Journal , 8 (2), 159–175] that assumes a highly flexible trend function by incorporating an unknown number of breaks in level. Overall, our confirmatory analysis renders clear-cut evidence in favor of regime-wise stationarity. Furthermore, the breaks in inflation detected are closely associated with macroeconomic shocks and changes in monetary policy.

We analyze the issue of the impact of multiple breaks on monetary neutrality results, using a long annual international data set. We empirically verify whether neutrality propositions remain addressable (and if so, whether they hold or not), when unit root tests are carried out allowing for multiple structural breaks in the long-run trend function of the variables. It is found that conclusions on neutrality are sensitive to the number and location of breaks. In order to interpret the evidence for structural breaks, we introduce a notion of deterministic monetary neutrality, which naturally arises in the absence of permanent stochastic shocks to the variables.

This paper examines the existence of stochastic and deterministic convergence of carbon dioxide (CO2) emissions in 23 countries over the period 1960–2002. For that purpose, we conduct unit root testing by employing the recently developed panel stationarity test of Carrion-i-Silvestre et al. [Carrion-i-Silvestre, J-L, del Barrio-Castro, T., Lopez-Bazo, E., 2005. Breaking the panels: An application to the GDP per capita. Econometrics Journal 8, 159–175] which assumes a highly flexible trend function by incorporating an unknown number of structural breaks. We accommodate general forms of cross-sectional dependence as well as control for finite-sample bias through bootstrap methods. Overall, our analysis provides strong evidence supporting both stochastic and deterministic convergence in CO2 emissions, thus confirming Strazicich and List [Strazicich, M.C., List, J.A., 2003. Are CO2 emission levels converging among industrial countries? Environmental and Resource Economics 24, 263–271] and Westerlund and Basher [Westerlund, J., Basher, S.A., 2007. Testing for convergence in carbon dioxide emissions using a century of panel data. Environmental and Resource Economics, forthcoming] findings of convergence.

Excel spreadsheets have been used in many classrooms to teach modeling and analysis of real business problems. This can be done with relative ease but often the modeling approach may be inappropriate and the analysis results not easily implemented. In this article, we illustrate these difficulties with the modeling of the number of equipment required in future years, given demand (historical and projected) and the amount of equipment held. We show how the desired output can be, and needs to be related to the given input. For this purpose, we apply the TREND function to predict data into future years. The real learning of this article comes from deriving actionable implementation solutions from the modeling results. We discuss this in terms of converting future equipment numbers into an equipment acquisition plan.

This work examines the behaviour of the input and output measures of the R&D process in the United States, Germany, France and the United Kingdom, in the second half of the 20th century. The researcher and idea stock series can be construed as stationary fluctuations around a trend function, with a main breakpoint at the end of the 1960s. All the countries exhibit slower growth after their last breaks than during the decades preceding their first breaks. In this connection, the United States and Germany appear to represent the end points in the range of incidence.

Este trabalho investiga a estacionariedade da razão consumo-renda para 11 países da América Latina e os Estados Unidos no período de 1951 a 2010. Inicialmente, testa-se a existência de múltiplas quebras estruturais em datas desconhecidas na função tendência da razão consumo-renda. O teste utilizado, sugerido por Perron e Yabu (2009) e Kejriwal e Perron (2010), é robusto ao fato do componente de ruído da série temporal ser estacionário ou integrado. Em seguida, empregam-se os testes de raiz unitária propostos por Carrion-i-Silvestre et al. (2009), que permite múltiplas quebras no nível e na inclinação da função tendência. Os resultados indicam a presença de duas quebras na função tendência da razão consumo-renda para a maior parte das economias analisadas. As exceções são a Colômbia e o Paraguai, que apresentam apenas uma quebra. No caso dos Estados Unidos, a hipótese de ausência de quebra estrutural dos parâmetros da função tendência da propensão média a consumir não pode ser rejeitada. Com relação à ordem de integração da razão consumo-renda, os resultados indicam que essa variável é não estacionária para todos os países da amostra, com exceção do Peru.