There are several simple conclusions from the existence of periods of **linear** **trends** in the difference between the CPI and core CPI. First, prices for food and energy are driven by some forces effectively independent on those behind other goods and services. Second, there are “structural breaks” in these forces, which define time segments of different length. It is likely that these forces behind all major expenditure categories may have different characteristic periods. Third, having an initial interval for some next period of **linear** trend in the difference between the CPI and core CPI one can extrapolate the evolution of the index for food and energy at a horizon of about ten years. Forth, there exist some relatively short periods when current **linear** **trends** change to opposite ones. These periods are likely characterized by an elevated volatility.

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Two related papers (Clarke, 2002a, b) deal with the detection and estimation of **trends** in annual extremes of hydrological variables, where these are assumed, in the absence of trend, to follow Gumbel or Weibull distributions. The first paper casts the problem of estimating trend in data with underlying Gumbel distribution in the form of a Generalised **Linear** Model (GLM), and describes an iterative procedure for estimating trend parameters; the second paper modifies this iterative procedure to allow **trends** to be estimated, and tested for significance, in data with an underlying Weibull or a Generalised Extreme Value (GEV) distribution. The purpose of the present paper is to present an analytical result, and results of some simulations, that supplement and extend earlier results given for the Gumbel distribution; a second paper will present corresponding results for the Weibull distribution.

diagrams (Figure 2 and Figure 3) can be determined using the table values. Trend line and middle point for 70 occurrences in which a **linear** trend is re- vealed are shown in the diagram (Figure 2). Only the middle point is shown for the remaining 103 occurrences. The polygonal contour PC-98% is delineated. It includes about 98% of all middle points. The diagram shows that trend lines vary significantly in length. The horizontal span of the lines (the arithmetic difference δ 18 Оmax - δ 18 Оmin) ranges from 0.5‰ to 11‰, in 90% of cases it does not ex-

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Our results pinpoint a few economic insights. We first observe that in many cases structural breaks in the form of non-**linear** **trends** are present in the data. Second, for a number of countries, for instance the Czech Republic and Hungary, a **linear** trend is enough to approximate the data. This implies that the Bal- assa-Samuelson effect might be present, which makes economic sense given the process of catching-up with Western Europe during the transition period from communism to market economies. Finally, that in all cases of mean reversion, it occurs along with structural breaks. Comparing our results to those by Cushman (2008), although the results are not directly comparable, we can say that we find evidence of mean reversion using a lower order for the Chebyshev polynomials. A similar approach as the one presented here has been recently conducted in a paper by Caporale, Carcel, and Gil-Alana (2015), examining the inflation rates in five African countries: Angola, Lesotho, Bostwana, Namibia and South Africa, and evidence of non-linearities were found in the former two countries but not in the other three.

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The difference between the PPI of durables and nondurables is characterized by the presence of two distinct segments with sustainable quasi-**linear** **trends** between 1988 and 2008, with a turning period between 2000 and 2001. It is likely that the difference in the next 5 to 10 years will show similar behavior, i.e. a new robust trend will be observed. To match the previously observed pattern, the new trend should be characterized by a positive slope, which absolute value cannot be currently accurately determined.

The presence of **linear** **trends** in the difference between the PPI and the index for JJP is now a reliable observation. However, it describes the past rather than foresees the future evolution. So, the next step is less trivial and is based on an assumption that the presence of sustainable **trends** will last in the years to come.

Analysis of the difference between the headline CPI and such small individual subcategories as apples and oranges also revealed the presence of **linear** **trends** [10]. One of the studied subcategories was fuel oil for housing purposes, which was shown to be dependent primarily on oil price. All in all, the evolution of the price indices for even tiny subcategories relative to the CPI is not a stochastic process. This finding allows predicting prices of practically all goods and services. Such predictions include timing of the changes in **linear** **trends**.

We confirm here 21 of the 24 **trends** in Butler et al. (2006) to have FAPs below 1% (two others are in systems for which we have no data to test, and the third is HD 11964, discussed in x 6.3). We also confirm the trend in the 14 Her system, first announced in Naef et al. (2004) and analyzed more thoroughly in Goz´dziewski et al. (2006) and x 6.2. We confirm the finding of Endl et al. (2006) that the trend reported in Marcy et al. (2005b) for HD 45350b is not significant ( FAP ¼ 0:6 and 2 increases with the introduction of a trend ). We announce here the detection of statistically significant **linear** **trends** ( FAP < 1%) around four stars already known to harbor a single exoplanet: HD 83443, GJ 436 (=HIP 57087), HD 102117, and HD 195019. GJ 436 will be discussed more thor- oughly in an upcoming work ( Maness et al. 2007). In one addi- tional case, HD 168443, we detect a radial velocity trend with FAP < 1% in a system already known to have two exoplanets, indicating that a third, long-period companion may exist. We pre- sent the updated orbital solutions in Table 3.

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are responsible for current neutralizing effect, but in the future they (alkaline elements) can increase the intensity of physico-chemical sorption of soil resulting in decrease in soil pH KCl . Biochar is very stable in soil compared to other organic matter ad- ditions [Fischer and Glaser 2012]. Management practices such as addition of labile C (e.g. slurry) to soil significantly increased biochar mineraliza- tion [Kuzyakov et al. 2009]. After addition to soils, non-aromatic C fractions in biochar are potentially oxidized [Nguyen et al. 2010], which leads to sub- sequent decline in soil pH [Joseph et al. 2010]. Additionally, nitrification may also contribute to the decrease in pH [Horák et al. 2017]. Above mentioned findings confirms our results (Table 2). The dynamics of soil pH KCl showed a decreasing trend with time in all treatments including control according to the results of the Mann-Kendall test. Statistically significant **linear** **trends** were observed in treatments with applied biochar in both rates as well as in treatment with applied lower dose of biochar with combination of higher dose of N and opposite in treatment with applied higher dose of biochar with lower N fertilization.

The paper discusses the role of stochastic **trends** in DSGE models and effects of stochastic detrending. We argue that explicit structural assumptions on trend behavior is convenient, namely for emerging countries. In emerging countries permanent shocks are an impor- tant part of business cycle dynamics. The reason is that permanent shocks spill over the whole frequency range, potentially, including business cycle frequencies. Applying high- or band-pass filter to obtain business cycle dynamics, however, does not eliminate the influence of permanent shocks on comovements of time series. The contribution of the paper is to provide a way how to calculate the role of permanent shocks on the de- trended/filtered business cycle population dynamics in a DSGE model laboratory using the frequency domain methods. Since the effects of permanent shocks pervade the cycli- cal part of a time series, a stationary ‘gap’ versions of DSGE model must have hard times to explain the comovement of the data. For a special case of Hodrick-Prescott and band- pass filter we provide analytical results, reinterpreting some of their features. We also give a guidance for model-builders why detrending may complicate the policy analysis with DSGE models and how to avoid the need for detrending.

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We used scatter plots to visualize the data and **linear** re- gression to examine **trends** across the U.S. News Rankings and to observe relationships between the percentage of fe- male applicants and other factors that may influence where applicants apply. We tested gender-by-U.S. News Rank interaction terms to determine whether U.S. News Ranking had a stronger association with applications from male compared to female applicants. Next, we tested if the number of female students in a given program or fe- male matriculants in 2016 had an association with U.S. News ranking, as a surrogate for applicant success rate. Fi- nally, we tested for an association between the percentage of current female students and the rate of female appli- cants to the various programs. **Linear** regression models between genders were compared using an interaction term in the regression model. All analyses were conducted using Stata version 14.0 (StataCorp. 2015. Stata Statistical Software: Release 14. College Station, TX: StataCorp LP).

The satellite images were acquired keeping in consideration that the satellite images should be free from cloud cover. The layers of the acquired data was then stacked and a subset of the study area (Multan city) was extracted and some im- age enhancements were applied for the clarification of the data. The pre-processing also includes radiometric and geometric correction so that the classified images must be free from errors. This spatial resolution along with spectral bands was good enough to provide accurate information regarding expansion of the Mul- tan city. Moreover, another type of dataset, LandScan, has been used in this study to visualize the population growth **trends** from 1998 to 2015 (subjected to data availability).

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So what has the cohort component method got going for it? A definite strength is that it forces us to take a stance on each of the factors influencing population change. Of course this is difficult but it means that we have to nail our colours to the mast on all the components. We have to take a view on fertility rates – whether at the national level they will continue to fall in line with the European experience and whether at a regional level we will see continued convergence. We have to pronounce on how quickly Ireland will converge towards the life expectancies of other European countries while observing that there is little variation at regional level within the State. More critically we have to pronounce on the magnitude and direction of migration flows – both internal and international. This has proved to be the most difficult component to predict in past projections and will doubtless continue to be so in future projections. In the final analysis, if our projections turn out to be wrong we can at least say which of the factors is at fault. In the alternatives examined in the paper we will not be able to explain away differences except to state that the overall population **trends** have not faithfully followed those which were experienced in the past.

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Although it has been originally introduced and widely ap- plied in econometrics, in the last years, an increasing number of applications of QR to geoscientific problems has been re- ported. In a time series analysis context, variations in the distribution of temperature and precipitation records have been studied by various authors (Koenker and Schorfheide, 1994; Draghicescu, 2002; Zhou and Wu, 2009; Timofeev and Sterin, 2010; Cannon, 2011; Barbosa et al., 2011). Besides time as a unique predictor, problems interrelating different geoscientific variables with each other have been extensively discussed, including the effect of meteorological variables on ozone concentration (Baur et al., 2004), the modelling of tropical cyclone intensity based on an additive QR model with different climatic covariates (Elsner et al., 2008; Jag- ger and Elsner, 2009), or the soil-moisture impact on hot ex- tremes in southeastern Europe (Hirschi et al., 2011). Kysel´y et al. (2010) used QR for obtaining threshold values for time- dependent extreme value analysis of climate simulations. In the context of sea-level research, Barbosa (2008) studied **linear** QR models for selected tide gauge records from the Baltic Sea. Park et al. (2010) investigated the interrelation- ships between local extreme sea-level in Florida and the At- lantic Multidecadal Oscillation (AMO). In addition to many other applications as well as intensive methodological work mainly done in the econometrics community, these examples demonstrate the wide applicability of QR. To our knowledge, there are no other conceptually different methods for estimat- ing conditional quantiles available so far that perform equally well – or even better – for the purpose of estimating quantile **trends**.

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This paper explored the use of generalised **linear** and nonlinear mixed regression methods that explicitly models the correlation in longitudinal data in quantifying **trends** in incidence rates. The availability of functions in easily accessible software such as R to fit generalised **linear** and nonlinear mixed models is leading to increasing and wide implementation of these methods. However there are caveats associated with usage. For instance, while parameters in Poisson regression models are readily interpretable, the in- flexibility of Poisson regression in modelling the variance can result in poor inference. On the other hand, the negative binomial model maintains much of the interpretation of the Poisson model and allows a more flexible variance structure but, as confirmed in the work here, is computationally much more difficult to fit in practice.

Next, we studied the statistics of obtained p-values, checking for departure from a uniform distribution that either indicates inflation (genomic control lw1) or deflation (genomic control lv1) of the respective methods (Figure 2d and Supplementary Figure S8 for corresponding Q-Q-plots). All methods except for ICE yielded an inflated p-value distribution. Notably, this observation also applies to the ideal model where the effect of confounders had been perfectly removed. Thus, in settings with Figure 1. Illustration of the PANAMA model. (a) Representation of the **linear** model used by PANAMA to correct for the effect of confounding factors. (b) Alternative settings of confounders in relation to true genetic signals: First, orthogonality between confounders and genetics. The variation in the gene expression levels (green arrow) can be better explained by the SNP (blue arrow). Second, statistical overlap between variation explained by confounders and the genetic variation as often found in trans hotspots. Gene expression variation can be equally well explained as genetic or due to a confounding factor. Previous methods focus in the first setting, while PANAMA is able to handle both situations. (c) PANAMA applied to the yeast eQTL dataset. Pronounced trans regulators that overlap with the learnt confounding factors are highlighted in red.

A further question is whether to include a time trend in the models. Reinhart and Rogoff do not, and thus effectively only consider the raw association between the two variables. However, it could be that the association is in part the result of long-run changes over time, in debt ratios, growth rates, or both, which are not related to the growth-debt causal pathway. We also want to test whether that trend is global, across all countries, or more local, varying between countries – if the latter occurs, then those local **trends** need to themselves be controlled for. This is done by comparing the model’s fit where the year effect is (a) a ssumed

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Labour productivity indices for employees in industry and energy producing materials during the period 1997 2001 are given in Table 1. Parameters of the models of la- bour productivity development **trends** indices for employees in industry and energy producing materials in the period 19972001 are given in Table 2. Models of

To fill these gaps, population censuses and nationally representative household sample surveys have been widely used as two principal methods of data collection. These two data sources have contributed significantly to providing data required for the estimation of the vital rates (crude birth and death rates, general, age-specific and total fertility rates, gross and net reproduction rates, life expectancy, etc). These approaches have brought to light the much needed information on levels, patterns, and **trends** in fertility and mortality (NPopC , 2010).

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The third-order nonlinear optical properties of a series of 15 unmetallated and metallated 1,4,8,11,15,18,22,25- octaalkylphthalocyanines have been investigated. The palladium-metallated compound is the strongest nonlinear absorber of the series, but, due to its comparatively high **linear** absorption coefficient, it exhibits a relatively low ratio of excited- to ground-state absorption cross-sections (k) when compared to the other compounds. The highest values for k were found for derivatives metallated with indium and lead. The nickel- metallated compounds are the weakest nonlinear absorbers, indicating that they are unsuitable as potential materials for practical passive optical limiters. Phenomenologically, the data for k and the saturation energy density (F sat ) were found to follow **trends** dependent upon the **linear** absorption coefficient. This may have