True Trend Research Articles

PREDICTION OF TEMPERATURE AND FLUE GASES FOR THE INCINERATION PROCESS USING MATHEMATICAL MODELING AND COMPUTER SIMULATION

Mathematical modeling and computer simulation for the municipal solid waste incineration process provides important understanding into the incinerator’s performance. The application of mathematical modeling for the incineration process will increase the incinerator operating efficiency. The broad objective of this study was to optimize the design of municipal solid waste incinerators using mathematical modeling and computer simulation. Computation Thermal Predictions (CTP) relations involving different types of incineration parameters such as temperature, density, velocity and species concentration were formulated based on theories of incineration process with various assumptions. The solution of the mathematical model developed was done and accomplished by Computational Fluid Dynamics (CFD). Finite element method of numerical analysis was applied to solve the temperatures in the simulated incinerator model as well as species/flue concentration at the end of its chimney. Dimensions used on the simulated model were applied to construct the physical incinerator for analysis. Tests were performed on the physical model incinerator and data used to validate the results obtained from the simulated model. Both simulated and experimental results showed that it is possible to forecast temperature and flue gases by the application of mathematical expressions. The incinerator CTP model was applied to simulate the incineration process and aid to regulate temperature at different locations and species/flue concentration at the end of incinerator chimney. The CTP results were very close to those obtained from experiment. The t-test method conducted revealed that simulated and experimental results did not differ significantly at 0.05 level of significance. Therefore, there is an agreement between the empirical model and experimental data as they show true trend of the incineration process.

Robust enhanced trend filtering with unknown noise

One important step in time series analysis is the extraction of an underlying trend. However, the true trend is often submerged by complex background noise, especially non-Gaussian noise or outliers. Accurate trend extraction against outliers from a raw signal is a challenging task. To address this challenge, this paper extends l1 trend filtering to a robust enhanced trend filtering called RobustETF by combining mix of Gaussian (MoG) and non-convex sparsity-inducing functions. We first model the noise as a MoG distribution to allow RobustETF to be robust in the presence of any type of non-Gaussian noise or outliers. After that, to handle the biased estimation of the l1 norm, we use the Gibbs distribution embedding smoothed and non-convex sparsity-inducing functions to faithfully preserve the amplitude of the trend. Furthermore, we design an extended EM algorithm to solve the resulting non-convex optimization problem. Finally, we show the results of experiments on both real-world and synthetic data to compare the performance of the proposed algorithm against other state-of-the-art methods. Finally, the corresponding Matlab codes are available at https://github.com/ZhaoZhibin/RobustETF.

Gastrointestinal Pathologies in a Center with Limited Resources: Pilot Study at the Bafoussam Regional Hospital, Cameroon.

Rationale: The pathology of the digestive tract is frequent in Cameroon. Despite this situation, studies of gastrointestinal pathology are rare. The pathological anatomy service is almost non-existent in the Cameroonian suburbs. Bafoussam in the west of the country is a semi-urban area and one of the rare ones to have a pathological anatomy department. This is why we decided to present the epidemiological data of the pathologies of the digestive tract of this locality. Methods: We carried out a prospective study over three months (October 2019 - January 2020), in the pathological anatomy department of the Bafoussam Regional Hospital in Cameroon with the aim of presenting the structural pathologies of the digestive tract listed in this institution. . Results: the pathology of the digestive tract has an incidence of approximately 400 in this locality, and represents 45.24% of all the pathologies identified in the pathological anatomy department of the Bafoussam Regional Hospital The age of our patients varies between 17 and 98 years old, with an average of 52.8. Women are slightly more represented (sex ratio M: F of 1: 1.3). Samples from the digestive tract represent 45% of all histological samples recorded in this department. The most common location, in decreasing order, is the stomach (84%), followed by the esophagus (5%), the colon and the rectum (4% each). On the other hand, other sites including the duodenum are rather rare. Of 100 samples of the digestive tract examined, 98 were pathological with a preponderance of inflammatory lesions (80.61%) against 19.39% of neoplastic nature. The inflammatory pathology was distributed uniformly in all age groups while the malignant pathologies were not observed until after 50 years. Malignant pathologies were more common in men (sex ratio M: F of 3: 1). Gastritis was the most common diagnosis (76.53%) and 94.66% of these gastritis were associated with Helicobacter pylori. Conclusion: The pathology of the digestive tract is important in our community and dominated by the inflammatory type. The most common site is the stomach, most of the lesions of which are linked to Helicobacter pylori. It would be desirable to actively seek out and eradicate Helicobacter pylori infection to decrease the incidence of digestive pathology. Further studies are recommended to establish the true epidemiological trend of gastrointestinal pathology in our community.

Characterization of basin-scale aquifer heterogeneity using transient hydraulic tomography with aquifer responses induced by groundwater exploitation reduction

This study exploits aquifer responses to the reduction of pumping rates at different locations in a synthetic groundwater basin as basin-scale hydraulic tomography (HT) surveys to estimate transmissivity (T) and storage coefficient (S) fields. This experiment mimics the situation of groundwater exploitation reduction in a pilot area of groundwater-overexploitation control in the North China Plain. The results of the study show that taking advantage of the groundwater exploitation reduction as HT surveys is a viable approach for basin-scale parameter estimations. Results also suggest that HT analysis should use accurate mean values of T and S for geological zones as initial guesses for the inversion of parameters. Further, we show that the T and S fields estimated from HT yield accurate predictions of the groundwater flow velocities and breakthrough curves (BTCs). However, the BTCs based on kriged and zonal mean fields are inaccurate. The predicted BTCs using homogeneous fields fail to capture the true trend of solute concentration over time. We advocate that utilizing aquifer responses induced by groundwater exploitation reduction could be a new paradigm for basin-scale aquifer characterization.

Long-term reliability of the Figaro TGS 2600 solid-state methane sensor under low-Arctic conditions at Toolik Lake, Alaska

Abstract. The TGS 2600 was the first low-cost solid-state sensor that shows a response to ambient levels of CH4 (e.g., range ≈1.8–2.7 µmol mol−1). Here we present an empirical function to correct the TGS 2600 signal for temperature and (absolute) humidity effects and address the long-term reliability of two identical sensors deployed from 2012 to 2018. We assess the performance of the sensors at 30 min resolution and aggregated to weekly medians. Over the entire period the agreement between TGS-derived and reference CH4 mole fractions measured by a high-precision Los Gatos Research instrument was R2=0.42, with better results during summer (R2=0.65 in summer 2012). Using absolute instead of relative humidity for the correction of the TGS 2600 sensor signals reduced the typical deviation from the reference to less than ±0.1 µmol mol−1 over the full range of temperatures from −41 to 27 ∘C. At weekly resolution the two sensors showed a downward drift of signal voltages indicating that after 10–13 years a TGS 2600 may have reached its end of life. While the true trend in CH4 mole fractions measured by the high-quality reference instrument was 10.1 nmolmol-1yr-1 (2012–2018), part of the downward trend in sensor signal (ca. 40 %–60 %) may be due to the increase in CH4 mole fraction because the sensor voltage decreases with increasing CH4 mole fraction. Weekly median diel cycles tend to agree surprisingly well between the TGS 2600 and reference measurements during the snow-free season, but in winter the agreement is lower. We suggest developing separate functions for deducing CH4 mole fractions from TGS 2600 measurements under cold and warm conditions. We conclude that the TGS 2600 sensor can provide data of research-grade quality if it is adequately calibrated and placed in a suitable environment where cross-sensitivities to gases other than CH4 are of no concern.

Oracally efficient estimation and testing for an ARCH model with trend

This article investigates an ARCH model with trend and proposes a two-step estimation method and develops an ARCH effect test. The trend is estimated by the linear B-spline method, and then the least squares estimation (LSE) and a Lagrange multiplier (LM) test based on the residuals are presented. Under mild conditions, it is shown that the proposed LSE and the test statistic enjoy the oracle properties; namely, they perform as well as if the true trend function were known and then removed to obtain the ARCH errors. Simulation studies assess the finite-sample performance of the LSE and the test statistic. An empirical example on the US gross private saving series is analyzed to illustrate the usefulness of our procedure.

Intensive long-term monitoring of soil organic carbon and nutrients in Northern Germany

Since 2003, the regional long-term soil monitoring network (SMN) Schleswig–Holstein (SH) includes an intensive monitoring program (I-BDF) with (sub-)annual measurements at four sites. This is the first study investigating the benefits of this SMN where study sites are no experiments but managed by independent farmers. The main objective of this study was to investigate whether, and under which circumstances, annual soil carbon and nutrient measurements are more beneficial within a soil monitoring network than common five- to ten-year measurements using modeling and nutrient balances. Soil measurements (stocks of soil organic carbon (SOC), Ntot, P and Mg), weekly leachate-NO3–N and management data were used for comparison. C and N changes were modeled with DNDC (DeNitrification–DeComposition); P and Mg were calculated as full nutrient balances and compared to the observations using performance metrics. The results show that DNDC could reproduce the long-term trend of SOC and Ntot well, but this could also be by coincidence as the type of trendline depended on the starting year. The model results could not depict measured short-term variations in soil which were due to field heterogeneities caused by farm management. NO3-N leaching was strongly overestimated when organic fertilization and stronger rainfall occurred. Comparing stock changes with nutrient balances revealed that, in several cases, long-term trends could be shown to a limited extent and reproduced only very few short-term changes and variations. The results suggest that only annual soil property measurements can depict the soil’s variability and contribute to the identification of the true long-term trend.

A trend analysis approach for air quality network data

Trend analysis of air pollutant concentrations becomes problematic when applied to data from air quality monitoring networks containing time series of differing lengths. The average trend from such data can be misleading due to biases in the monitoring network. For example, if new monitoring sites located in more polluted locations are added to a network, the introduction of these time series can leverage the trend upwards. A method for resolving this problem was developed, using rolling window regression to recursively calculate the change in pollutant concentration as a function of time, which can be used as a proxy for the true trend. The efficacy of the method was established by conducting simulations with known trends. The rolling change trend was shown to more accurately reflect the true trend than simply averaging the time series. Application of the technique to estimate trends in NOx, NO2 and NO2/NOx concentrations at London roadside monitoring sites over the period 2000–2017 revealed clear differences from the simple average. In particular, a significant monotonic downward trend in NOx concentration was observed, in stark contrast to the average trend, which suggested little change in NOx concentration had occurred over the same period. By accurately representing trends using time series of different lengths, this method has the benefit of being able to describe changes in air quality for locations and time periods with otherwise insufficient data.

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Inline detection of Denial of Service Attacks in Software Defined Networking using the Hotelling Chart

Software Defined Network (SDN) has become the true trend of the IT service model offering a cost-effective and scalable processing solution. Although central control is the major asset of the SDN, it is also a single point of failure if it is made inaccessible by a distributed denial of service (DDoS) attack. Despite the number of existing traditional detection solutions, DDoS attacks continue to increase in frequency, volume and severity. This paper provides an analysis of the problem by examining the impact on security, particularly for distributed denial of service (DDoS) attacks that is still a threat to SDN software-defined networks and suggests the proposal and implementation of a DDoS attack detection algorithm. Based on an architecture that integrates highly programmable network monitoring and a flexible control structure to enable fast and specific attack detection. To cope with the new architecture, we propose an attack detection system based on a statistical model that can address the problem of flooding attack and bandwidth attack. The simulation results show that our architecture can effectively address the security challenges posed by the new network paradigm and our attack detection system can effectively signal various attacks using real-world network traffic.

Trend estimation for complex survey designs of water chemistry indicators from Sierra Nevada Lakes

Surveys for long-term monitoring programs managing natural resources often incorporate sampling design complexity. However, design weights are often ignored in trend models of data from complex sampling designs. Generalized random tessellation stratified samples of a simulated population of lakes are selected with various levels of survey design complexity, and three trend approaches are compared. We compare an unweighted trend model, linear regression models of the trend in design-based estimates of annual status, and a probability-weighted iterative generalized least squares (PWIGLS) approach with a linearization variance. The bias and confidence interval coverage of the trend estimate and the size and power of the trend test are used to evaluate weighted and unweighted approaches. We find that the unweighted approach often outperforms the other trend approaches by providing high power for trend detection and nominal confidence interval coverage of the true trend regression parameter. We also find that variance composition and revisit design structure affect the performance of the PWIGLS estimator. When a subpopulation exhibiting an extreme trend is sampled disproportionately to its occurrence in the population, the unweighted approach may produce biased estimates of trend with poor confidence interval coverage. We recommend considering variance composition and potential subpopulation trends when selecting sampling designs and trend analysis approaches.

Evaluation of Syndrome Algorithms for Detecting Pneumonia Emergency Department Visits

ObjectiveTo validate and improve the syndromic algorithm used to describe pneumonia emergency department (ED) visit trends in New York City (NYC).IntroductionThe NYC Department of Health and Mental Hygiene (DOHMH) uses ED syndromic surveillance to monitor near real-time trends in pneumonia visits. The original pneumonia algorithm was developed based on ED chief complaints, and more recently was modified following a legionella outbreak in NYC. In 2016, syndromic data was matched to New York State all payer database (SPARCS) for 2010 through 2015. We leveraged this matched dataset to validate ED visits identified by our pneumonia algorithm and suggest improvements. An effective algorithm for tracking trends in pneumonia could provide critical information to inform and facilitate public health decision-making.MethodsThe DOHMH syndromic surveillance system includes daily ED data from 53 NYC hospitals. Most syndrome algorithms rely solely on chief complaint, which has historically been reported more consistently than discharge diagnosis. For this analysis, the validation dataset was restricted to matched visits with consistent age (plus or minus two years) and sex between the syndromic and SPARCS datasets.The original pneumonia algorithm used a basic text search function to identify any mention of ICD-9-CM and ICD-10-CM diagnosis codes indicating pneumonia or key words “PNEUMON” or “MONIA” within the chief complaint only. The updated algorithm additionally searches the chief complaint for any mention of key words specific to legionella (“LEGIONA”, “LEGIONN”, “LEGIONE”) and also searches for pneumonia ICD codes in the discharge diagnosis field. Syndrome sensitivity and positive predictive value (PPV) were evaluated by comparing visits identified by each algorithm to visits identified by billing diagnosis codes. A true SPARCS pneumonia ED visit was defined to contain an admitting or principal diagnosis billing code indicating pneumonia.Alternate algorithms were created using regular expressions, which allowed for more flexible and accurate pattern matching. The algorithms were further revised based on additional inclusion and exclusion key words identified using the validation dataset.ResultsBetween 2010 and 2015, there were a total of 204,101 true pneumonia visits based on the SPARCS billing records. Evaluation of the original algorithm found a sensitivity of 15.6% (31,771/204,101) and a PPV of 55.6% (31,771/57,180). Over the same time period, syndromic surveillance identified a total of 127,560 pneumonia visits using the updated algorithm; 86,590 of the 127,560 syndromic cases identified were determined to be a true visit based on the billing diagnosis codes, resulting in an algorithm sensitivity of 42.4% and PPV of 67.9%. Of the 127,560 cases identified by the updated algorithm, 19 cases were classified as a pneumonia visit solely due to the presence of legionella key words in the chief complaint. Regular expression usage as opposed to the basic text search on the updated algorithm found similar sensitivity (42.4%, 86,561/204,101) and PPV (68.0%, 86,561/127,238).Among all true pneumonia visits with a non-blank discharge diagnosis field, 65.3% (68,001/104,223) had mention of a pneumonia diagnosis code. Use of the discharge diagnosis code field in addition to the chief complaint found the algorithm to be almost three times more sensitive and 1.2 times greater in PPV than an algorithm without use of discharge diagnosis. Seasonal trends captured with and without use of discharge diagnosis were both similar to the true pneumonia trend indicated by SPARCS.Among the 117,540 pneumonia cases missed by the updated algorithm, 58.6% had fewer than three words in the chief complaint. With the most popular key words among the missed cases being highly non-specific (i.e., “fever”, “cough”, “pain”), inclusion of these key words in addition to regular expression and discharge diagnosis field usage elevated algorithm sensitivity at a severe cost to the PPV. Including “fever” in the list of pneumonia key words resulted in a sensitivity of 56.5% (115,280/204,101) and a PPV of 9.0% (115,280/1,282,342), while addition of the key word combination “fever” and “cough” led to a sensitivity of 46.7% (95,264/204,101) and a PPV of 29.8% (95,264/319,876).As we were unable to identify novel key word indicators that were good markers for pneumonia events, regular expression search functionality was the best improvement to the pneumonia syndrome algorithm. This revised, new algorithm maintained sensitivity (42.4%, 86,561/204,101) and provided slight improvements to PPV (68.0%, 86,561/127,219).However, performance of the updated algorithm varied across age groups. The algorithm was most effective in identifying younger cases (43.9% sensitivity, 80.4% PPV for those 17 years and younger), while it performed the worst among those 65 years and older (39.6% sensitivity, 58.7% PPV).ConclusionsBased on our evaluation of the pneumonia syndromic surveillance algorithm, we found that search of the discharge diagnosis field greatly improved algorithm sensitivity and PPV and usage of regular expressions increased PPV slightly. Including additional words possibly indicating pneumonia did not substantially improve sensitivity or PPV. However, integration of the ED chief complaint triage notes which are not currently utilized could further enhance the effectiveness of the pneumonia syndrome algorithm and better characterize daily pneumonia trends in NYC.

F. Scott Fitzgerald and the American Scene

F. Scott Fitzgerald and the American Scene

Synoptically classified lake-effect snowfall trends to the lee of Lakes Erie and Ontario

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 74:1-13 (2017) - DOI: https://doi.org/10.3354/cr01480 Synoptically classified lake-effect snowfall trends to the lee of Lakes Erie and Ontario Zachary J. Suriano*, Daniel J. Leathers Department of Geography, University of Delaware, Newark, DE 19716, USA *Corresponding author: zsuriano@udel.edu ABSTRACT: Recent research has indicated that snowfall in portions of the North American Great Lakes region subject to lake-effect snow has undergone a trend reversal, with snowfall declining in recent decades. This study examines the seasonal variability and trends specifically in synoptically classified lake-effect snow across the eastern Great Lakes region, and investigates the mechanisms responsible for observed changes. Using a synoptic climatological approach, days are identified where the synoptic-scale conditions are conducive to lake-effect snowfall and the associated snowfall is analyzed. Seven synoptic types over the November to March snowfall season are identified with characteristics of lake-effect conditions. Snowfall from these 7 lake-effect synoptic types represents between 45 and 53% of the seasonal snowfall total along the eastern shores of Lakes Erie and Ontario, with snowfall totals being highest during January. Lake-effect snowfall exhibits a 60 yr increasing trend downwind of Lakes Erie and Ontario; however, through examination over shorter 30 yr periods, a change in the trend of snowfall is observed around 1980. While a true trend reversal is not detected, lake-effect snowfall significantly increases from 1950-1979 before exhibiting no significant trend from 1980-2009. The inter-annual variability of seasonal lake-effect snowfall is highly related to the frequency of lake-effect synoptic types where an increase (decrease) in synoptic type occurrence leads to enhanced (diminished) lake-effect snowfall totals. Depending on the period examined, long-term changes in the frequency of lake-effect synoptic types and snowfall rates represent between 89 and 95% of the observed changes in lake-effect snow. KEY WORDS: Great Lakes · Synoptic classification · Snowfall variability · Climate change · Lake effect Full text in pdf format NextCite this article as: Suriano ZJ, Leathers DJ (2017) Synoptically classified lake-effect snowfall trends to the lee of Lakes Erie and Ontario. Clim Res 74:1-13. https://doi.org/10.3354/cr01480 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 74, No. 1. Online publication date: October 16, 2017 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2017 Inter-Research.

Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness

This paper studies the effect of autocorrelation on the smoothness of the trend of a univariate time series estimated by means of penalized least squares. An index of smoothness is deduced for the case of a time series represented by a signal-plus-noise model, where the noise follows an autoregressive process of order one. This index is useful for measuring the distortion of the amount of smoothness by incorporating the effect of autocorrelation. Different autocorrelation values are used to appreciate the numerical effect on smoothness for estimated trends of time series with different sample sizes. For comparative purposes, several graphs of two simulated time series are presented, where the estimated trend is compared with and without autocorrelation in the noise. Some findings are as follows, on the one hand, when the autocorrelation is negative (no matter how large) or positive but small, the estimated trend gets very close to the true trend. Even in this case, the estimation is improved by fixing the index of smoothness according to the sample size. On the other hand, when the autocorrelation is positive and large the simulated and estimated trends lie far away from the true trend. This situation is mitigated by fixing an appropriate index of smoothness for the estimated trend in accordance to the sample size at hand. Finally, an empirical example serves to illustrate the use of the smoothness index when estimating the trend of Mexico’s quarterly GDP.

Recursive update of channel information for reliable history matching of channel reservoirs using EnKF with DCT

Ensemble Kalman filter (EnKF) is one of the promising reservoir characterization schemes for history matching. It has been widely researched due to its excellence in recursive data processing and dependable uncertainty quantification. However, EnKF has critical limitations for applying to non-Gaussian distribution fields such as channel reservoirs.In this study, we propose a novel scheme to characterize channel reservoirs reliably. The scheme, recursive update of channel information (RUCI), updates key channel information such as facies ratio and permeabilities of each rock facies as components of the state vector. Since permeabilities assimilated by EnKF follow a Gaussian distribution, EnKF itself is not adequate to preserve channel structure. To overcome this limitation, we use cumulative distribution function mapping to maintain its bimodal distribution. In addition to RUCI, discrete cosine transform (DCT) is utilized to preserve clear channel continuities by figuring out essential channel trend.The proposed method, RUCI in EnKF with DCT, is applied to three different channel reservoir cases and is compared with typical three methods: EnKF, EnKF with DCT, and EnKF with normal score transform (NST). Both of conventional EnKF and EnKF with DCT show overshooting and fail to present channel details. Furthermore, their permeability distributions have a tendency to follow a Gaussian, not a typical bimodal distribution of sand and shale. Even if EnKF with NST maintains a bimodal distribution after updates, it cannot figure out overall channel trend. The proposed method not only prevents overshooting but also preserves a bimodal distribution of permeability. It can clearly characterize true channel trend even though initial reservoir models are poorly made. In addition, it gives better estimation of future oil and water productions than the other 3 methods by reducing uncertainties and matching true performances.

Impact of Population Aging on Household Savings and Portfolio Choice in Japan

We examine whether Japanese households have begun to dissave and reduce their holdings of risky assets because of population aging over the period 2000–14. While there is little doubt that household savings have decreased, the true trend without a negative income shock in the early 2000s would have been declining more smoothly and moderately. The average share of risky assets in household portfolios increases with age and barely decreases even for retired households. The main sources of increasing household wealth are the increasing wealth of the elderly and the increasing proportion of the wealthier elderly population.

Steps roughening in thermal relaxation and low-coverage growth of sloped Pt(110) and Ir(110) surfaces: A numerical study

The dynamical roughening of [001] steps on sloped Pt (110) and Ir (110) surfaces is investigated by kinetic Monte Carlo simulations. Our model includes deposition, diffusion and fully reversible aggregation on these surfaces with both anisotropic barriers and anisotropic attachment. The barriers for the diffusion processes have been calculated by means of classical molecular dynamics simulations where both metals are modeled by realistic many-body potentials. The roughness is evaluated through calculations of the step width in thermal relaxation of the surface and low-coverage growth conditions. Results indicated a non-trivial behavior of the width in time during relaxation. In growth, power-law behavior is recovered for both metal surfaces. Defects population on terraces is investigated through calculations of adatom and island densities. It is found that at very low temperature (T = 200K for Pt and 400K for Ir and below), a power-law behavior with the growth time is got. Beyond, fluctuations in generated data become important and do not allow to correctly access the true trend of both quantities. Their behavior with the diffusion length at low temperature is singled out.

An IV Test for a Unit Root in Generally Trending and Correlated Panels

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.

Oracally Efficient Estimation and Consistent Model Selection for Auto-Regressive Moving Average Time Series with Trend

Summary Most time series that are encountered in practice contain non-zero trend, yet textbook approaches to time series analysis are typically focused on zero-mean stationary auto-regressive moving average (ARMA) processes. Trend is often estimated by ad hoc methods and subtracted from time series, and the residuals are used as the true ARMA noise for data analysis and inference, including parameter estimation, lag selection and prediction. We propose a theoretically justified two-step method to analyse time series consisting of a smooth trend function and ARMA error term, which is computationally efficient and easy for practitioners to implement. The trend is estimated by B-spline regression, and the maximum likelihood estimator based on residuals is shown to be oracally efficient in the sense that it is asymptotically as efficient as if the true trend function were known and then removed to obtain the ARMA errors. In addition, consistency of the Bayesian information criterion for model selection is established for the detrended residual sequence. Finite sample performance of the procedure is illustrated by simulation studies and real data analysis.