Strong Positive Autocorrelation Research Articles

Dynamic monitoring and analysis of ecological quality based on RSEI: A case study of Akkulam-Veli Lake Basin of Thiruvananthapuram City, Kerala, India

ABSTRACT The world today is experiencing rapid urbanization, leading to prominent urban ecological problems. Evaluating urban ecological quality is crucial for monitoring environment-centered initiatives. The Akkulam-Veli Lake Basin, in Thiruvananthapuram, Kerala, India, is threatened by rapid urbanization. The present study proposes a comprehensive evaluation of the ecological quality by the Remote-Sensing Ecological Index (RSEI), based on the four indexes: greenness (NDVI), wetness (WET), dryness (NDSBI), and heat (LST), from 2000 to 2023. The interrelationship between RSEI and land use has been studied to properly analyze human activities’ effects on the study region’s ecological quality. Results indicated that the mean values of RSEI experienced a drastic decline from 0.733 in 2000 to 0.645 in 2015, and further declined to 0.611 in 2023, indicating an overall deterioration in the status of ecological quality in the Akkulam-Veli Lake Basin. Moreover, Moran’s I index of 0.556 in 2000, 0.554 in 2015, and 0.552 in 2023 show that the sample RSEI values have a strong positive autocorrelation with adjacent values in the study area. The study provides evidence for the need for systematic urban planning and serves as a scientific reference for policymakers to manage the ecological qulaity of urban areas effectively.

Evaluation of landscape ecological risk in key ecological functional zone of South–to–North Water Diversion Project, China

The key ecological functional zone plays a significant role in maintaining ecosystem security, water conservation function and environmental protection. However, owing to rapid industrialization and urbanization, some ecological functional zones have undergone great changes in land use, which has changed the landscape pattern characteristics and resulted in ecological risks, affecting the regional ecological environment and water security. In this study, the core water source area of the Middle Route of China’s South–to–North Water Diversion Project is selected as the case study. A regional landscape ecological risk index (ERI) was constructed to evaluate the landscape ecological risk driven by land use transformation. Moreover, the ERI's spatiotemporal characteristics were investigated using a combination of geographic information systems and geostatistical techniques, which reveal the dominant land use function types associated with ecological risks and their causes. We found that (1) there was not a notable shift in land use, and the level of ecological risk increased slightly from 2010 to 2015. The conversion of previously unproductive land into places for industrial production land and agricultural productive land played a significant role in this phenomenon. From 2015 to 2020, the Danjiangkou Reservoir officially started operation. Furthermore, the improvement of residents’ awareness of environmental protection and natural forest land significantly reduced the ecological risk. (2) The ecological risk has a strong positive autocorrelation, exhibiting a pattern of high in the east and center, low in the west and periphery. (3) An obvious corresponding relation exists between the impacts of topography, soil, and climate on patterns of land use and ecological risk. Additionally, the strict ecological protection policies implemented by the Chinese government have realized remarkable achievements in promoting the improvement of ecological risks. Our study can provide a decision–making basis for the local authorities to conduct ecological risk prevention activities and ensure the sustainable northward flow of clean water.

An Approach to the Temporal and Spatial Characteristics of Vegetation in the Growing Season in Western China

Since the implementation of the great western development strategy in 2000, the ecological environment in the western region of China has been significantly improved. In order to explore the temporal and spatial characteristics of vegetation coverage in the western region, this paper adopted the method of Maximum Value Composite (MVC) to obtain the mean Normalized Difference Vegetation Index (NDVI) of vegetation on the basis of the Moderate-resolution Imaging Spector audiometer (MODIS) data of 2000/2005/2010/2015/2018. Thereafter, the spatio-temporal differentiation characteristics of vegetation in western China were analyzed. The results show that: (1) According to the time characteristics of vegetation coverage in the western region, the average annual NDVI value of vegetation coverage in the growing season in the western region fluctuated between 0.12 and 0.15, among which that of 2000 to 2010 fluctuated more greatly but did not show obvious change trend. (2) Based on Sen trend and Mann-Kendall test analysis, the area of vegetation coverage improvement in the western region from 2000 to 2018 was larger than that of significant vegetation degradation. (3) From the perspective of global autocorrelation coefficient, Moran’s I values were all positive from 2000 to 2018, which indicates that the vegetation coverage in the west showed strong positive autocorrelation in each period. According to the average value and coefficient of variation of vegetation coverage, the vegetation coverage was lower in 2000, its internal variation was smaller, and the vegetation coverage increased with time. According to the local spatial autocorrelation analysis, the vegetation coverage levels in different regions varied greatly. (4) The standard deviation ellipse method was used to study the spatial distribution and directional transformation of vegetation. It makes the result more intuitive, and the three levels of gravity center shift, direction shift, and angle shift were considered: the vegetation growth condition in the spatial aggregation area improved in 2015; the standard deviation ellipses in 2000 and 2018 overlapped and shifted eastward, which indicates that the vegetation coverage conditions in the two years were similar and got ameliorated.

Pricing efficiency and market efficiency of two bitcoin funds

ABSTRACT This study explores whether pricing inefficiency, or imperfect tracking in the market value of shares of a bitcoin fund of the fund’s net asset value (NAV), makes a significant impact on the fund’s market efficiency relative to the retail bitcoin market. Two bitcoin funds whose shares are traded at the exchanges which impose more stringent criteria for transparency compared to cryptocurrency exchanges are considered. The fund whose shares have been trading without significant premium or a discount relative to its NAV is found as weak-form efficient. The fund, whose shares have been trading at a significant premium over its NAV is found inefficient due to the presence of persistent and strong positive autocorrelation in its returns. Trading of shares in the inefficiently priced fund appears to be even more emotion-driven than the already volatile and emotional trading of bitcoin and exhibits a strong herding behaviour.

The structure of collaboration networks: Findings from three decades of co-invention patents in Chile

Abstract Collaboration networks have primarily been studied in developed economies. In this paper, we present a comprehensive analysis of co-inventor networks in a small but thriving OECD economy in Latin America: Chile. Using a dataset for patents granted in the country between 1989 and 2018, we study a variety of statistical properties for five different co-inventor networks. We show that these networks exhibit power-law, small-world, and preferential attachment properties, all of which have been used to describe networks in more advanced economies. We also highlight some apparent differences in collaboration patterns between networks (and inventors) and we reveal the precarious nature of the network of local inventors by confirming the community structure property. Evidence for strong positive autocorrelation between highly and lowly productive inventors is presented via methods used in spatial econometrics. Our results show that the inventor system in Chile is highly fragmented, which emphasizes the need for strong government intervention in steering research funding, and for more collaboration between inventors, especially local ones.

Measuring spatio-temporal autocorrelation in time series data of collective human mobility

ABSTRACTMassive spatio-temporal big data about human mobility have become increasingly available. Revealing underlying dynamic patterns from these data is essential for understanding people’s behavior and urban deployment. Spatio-temporal autocorrelation analysis is an exploratory approach to recognizing data distribution in space and time. The most widely used spatial autocorrelation measurements, such as Moran’s I and local indicators of spatial association (LISA), only apply to static data, so are powerless to spatio-temporal big data about human mobility. Thus, we proposed a new method by extending Moran’s I to measure the spatial autocorrelation of time series data. Then the method was applied to taxi ride data in Beijing, China to reveal the spatial pattern of collective human mobility. The result shows that there is strong positive spatio-temporal autocorrelation within the 5th Ring Road, weak negative spatio-temporal autocorrelation nearby the Sixth Ring Road, and almost no spatio-temporal autocorrelation between the roads. Local spatial patterns of taxi travel were also recognized. This method is useful for discovering underlying patterns from spatio-temporal big data to understand human mobility.

West Nile virus in Ontario, Canada: A twelve-year analysis of human case prevalence, mosquito surveillance, and climate data.

West Nile Virus (WNV) first arrived in Ontario, Canada in 2001 and has since spread throughout most of the province, causing disease in humans. The provincial government established a province-wide surveillance program to monitor WNV transmission throughout the 36 regional health units. Here we have acquired records of WNV human and mosquito surveillance from 2002 to 2013 to describe seasonal and geographic trends in WNV activity in southern Ontario. Additionally, we obtained climate data from seven municipalities to investigate how temperature and precipitation affect WNV transmission dynamics. We identified a strong quadratic relationship between the number of confirmed human cases and positive Culex mosquito pools recorded at the end of each year (R2 = 0.9783, p < 0.001). Using Spearman rank correlation tests, we identified that the minimum infection rate of Culex pipiens/restuans pools are the strongest predictor of human cases at a 1 week lag period. We also identified positive correlations between minimum infection rates, temperature, vector abundance, and cumulative precipitation. Global Moran’s I index indicates strong positive autocorrelation and clustering of positive Culex pool counts in southern Ontario. Local indicators of spatial association tests revealed a total of 44 high-high and 1 high-low trap locations (n = 680). In the current work we have identified when and where hot spots of WNV activity have occurred in southern Ontario. The municipalities surrounding the western shore of the Lake Ontario and Windsor-Essex County have the largest records of positive mosquitoes and human cases. We identified that positive mosquitoes are a strong indicator of human cases to follow in the coming weeks. An epidemic action threshold of cumulative positive Culex pools was established, allowing Ontario public health officials to predict an epidemic at epidemiological week 34 (rho = 0.90, p < 0.001). These data have the potential to contribute to more efficient larvicide programs and awareness campaigns for the public.

Assessment of spatio-temporal variations in air quality of Jaipur city, Rajasthan, India

This paper presents the evaluation of air quality in different wards of Jaipur city. Geo-spatial and geo-statistical techniques were utilized to estimate the seasonal and temporal variations (2004–2015) of gaseous and particulate pollutants. Data of six fixed monitoring stations was collected from Central Pollution Control Board (CPCB) and Rajasthan Pollution Control Board (RPCB) and the relationship between air quality and local weather parameters were also analyzed for the Jaipur city. It was found that SPM and PM10 is the major contributor to the deterioration of air quality in Jaipur city, while NOX and SO2 concentrations were below the CPCB standards. Results show that the concentrations of the air pollutants are high in winter and summer in comparison to the monsoon. The spatio-temporal distribution of Air Quality Index (AQI) clearly depicts the severe air pollution in Vidhyadhar nagar, Civil lines, Hawa Mahal, Kishanpole and Aadarsh Nagar area of Jaipur city. Ordinary least square (OLS) regression reveals good correlation between AQI and weather conditions (temperature, relative humidity and wind speed) for summer and winter seasons. The spatial analysis was also conducted to ascertain the degree of spatial association between AQI and weather conditions in different wards of Jaipur city using bivariate Moran’s I and LISA (Local Indicator of Spatial Association). Moran’s I results imply strong positive autocorrelation between AQI and relative humidity followed by temperature and wind speed. The combination of GIS and statistical analyses contributes to characterize the spatial influences of weather conditions on air pollutants and provide a quick view of the relatively critical areas that need more attention from decision makers to initiate the policies geared towards developing appropriate strategies for reducing air pollution.

基于ArcGIS的下辽河平原地下水脆弱性评价及空间结构分析

PDF HTML阅读 XML下载 导出引用 引用提醒 基于ArcGIS的下辽河平原地下水脆弱性评价及空间结构分析 DOI: 10.5846/stxb201403280580 作者: 作者单位: 辽宁师范大学城市与环境学院,辽宁师范大学城市与环境学院 作者简介: 通讯作者: 中图分类号: 基金项目: 教育部高等学校博士点基金(2012123611000);国家自然科学基金(40501013) An ArcGIS-based analysis of groundwater spatial structure and groundwater vulnerability in the lower reaches of the Liaohe River Plain Author: Affiliation: College of Urban and Environment,Liaoning Normal University,College of Urban and Environment,Liaoning Normal University Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:以下辽河平原为研究区,通过选取1991、2000和2010年3个代表年的相关参数,在DRASTIC模型基础上构建评价指标体系进行地下水脆弱性评价,并以地下水中氮元素浓度为响应指标通过显著性检验,在此基础上借助GS+、ArcGIS和Geoda095i等软件的制图功能和空间统计分析功能,对下辽河平原地下水脆弱性的空间分布特征、变异规律以及空间关联格局进行研究分析,结果表明:①1991-2010年下辽河平原地下水脆弱性总体上呈先增后减趋势,空间分布上以沈阳市为中心的地下水高脆弱区向南部沿海方向扩散;②1991-2010年研究区地下水脆弱性Moran's I表现为较强正相关现象,且关联程度呈略微下降趋势;③1991-2010年研究区地下水脆弱性局部空间自相关和显著性水平均发生了明显的变化;④研究区内地下水脆弱性受结构性因素和随机性因素共同作用,且随机性因素在3个时期内有逐步上升趋势。研究成果反映了研究区地下水脆弱性空间结构的变异规律及驱动机制,为决策者在未来地下水污染防治方面提供相关参考依据。 Abstract:High-quality groundwater bodies with relatively stable water volumes, good water quality, and a high resistance to pollution are widely distributed throughout the world. They play an important role in, among other things, the domestic water supply, economic development, and maintaining the integrity of the geological environment and ecological balance. However, with rapid socio-economic development, increasing human demand for water has resulted in increasing pressure on, and unreasonable use of, groundwater bodies. Consequently, groundwater systems throughout the world are subject to varying degrees of pollution and destruction, one result of which is an increasing disequilibrium between the supply of and demand for water resources.The field of international hydrogeology is concerned with evaluation of groundwater vulnerability, which is considered a basic task in the development and protection of groundwater resources. Currently, groundwater vulnerability is thought to result from characteristics of the groundwater system itself and anthropogenic factors; research into groundwater vulnerability can support groundwater protection. GIS, together with the contraposed index method, is the most popular tool for calculating groundwater vulnerability indices. Because the hydrogeological environment is not under the complete control of human activities, a thorough understanding of groundwater vulnerability and the causes of its variation is necessary for environmental managers to enact preventive and pollution control measures.This study was based on the DRASTIC model. Groundwater parameters for 3 years (1991, 2000, and 2010) were used to calculate the distribution of groundwater vulnerability in the lower reaches of the plain of the Liaohe River, using ArcGIS. Groundwater nitrogen concentration was used as a response index to test the reliability of results. Using the mapping and spatial statistical analysis functions in GS+, ArcGIS, and Geoda095i, we evaluated and analyzed the spatial distribution, variation, and spatial correlation patterns of groundwater vulnerability in the tested area. Results showed that:1) Overall groundwater vulnerability initially decreased but then showed a trend of increase from 1991 to 2010, and high-vulnerability areas were distributed from the regions around Shenyang to the south coast. 2) From 1991 to 2010, groundwater vulnerability showed a strong positive autocorrelation (Moran's I), the degree of which showed a slight downward trend. 3) Over the study period, marked changes have occurred in local spatial autocorrelation of groundwater vulnerability and its significance levels. 4) Groundwater vulnerability in the study area was influenced by a combination of structural and random factors. While the random factors have gradually increased over time, structural factors remain important. This study highlights the causes of variation in groundwater vulnerability and the mechanisms that drive its spatial structure in the study area and can provide a reference for policy makers to support development of groundwater pollution control and protection plans. 参考文献 相似文献 引证文献

Long-term and seasonal dynamics of dengue in Iquitos, Peru.

IntroductionLong-term disease surveillance data provide a basis for studying drivers of pathogen transmission dynamics. Dengue is a mosquito-borne disease caused by four distinct, but related, viruses (DENV-1-4) that potentially affect over half the world's population. Dengue incidence varies seasonally and on longer time scales, presumably driven by the interaction of climate and host susceptibility. Precise understanding of dengue dynamics is constrained, however, by the relative paucity of laboratory-confirmed longitudinal data.MethodsWe studied 10 years (2000–2010) of laboratory-confirmed, clinic-based surveillance data collected in Iquitos, Peru. We characterized inter and intra-annual patterns of dengue dynamics on a weekly time scale using wavelet analysis. We explored the relationships of case counts to climatic variables with cross-correlation maps on annual and trimester bases.FindingsTransmission was dominated by single serotypes, first DENV-3 (2001–2007) then DENV-4 (2008–2010). After 2003, incidence fluctuated inter-annually with outbreaks usually occurring between October and April. We detected a strong positive autocorrelation in case counts at a lag of ∼70 weeks, indicating a shift in the timing of peak incidence year-to-year. All climatic variables showed modest seasonality and correlated weakly with the number of reported dengue cases across a range of time lags. Cases were reduced after citywide insecticide fumigation if conducted early in the transmission season.ConclusionsDengue case counts peaked seasonally despite limited intra-annual variation in climate conditions. Contrary to expectations for this mosquito-borne disease, no climatic variable considered exhibited a strong relationship with transmission. Vector control operations did, however, appear to have a significant impact on transmission some years. Our results indicate that a complicated interplay of factors underlie DENV transmission in contexts such as Iquitos.

The evolution of predictive adaptive responses in humans: response

The evolution of predictive adaptive responses in humans: response

Climate Change is Likely to Worsen the Public Health Threat of Diarrheal Disease in Botswana

Diarrheal disease is an important health challenge, accounting for the majority of childhood deaths globally. Climate change is expected to increase the global burden of diarrheal disease but little is known regarding climate drivers, particularly in Africa. Using health data from Botswana spanning a 30-year period (1974–2003), we evaluated monthly reports of diarrheal disease among patients presenting to Botswana health facilities and compared this to climatic variables. Diarrheal case incidence presents with a bimodal cyclical pattern with peaks in March (ANOVA p < 0.001) and October (ANOVA p < 0.001) in the wet and dry season, respectively. There is a strong positive autocorrelation (p < 0.001) in the number of reported diarrhea cases at the one-month lag level. Climatic variables (rainfall, minimum temperature, and vapor pressure) predicted seasonal diarrheal with a one-month lag in variables (p < 0.001). Diarrheal case incidence was highest in the dry season after accounting for other variables, exhibiting on average a 20% increase over the yearly mean (p < 0.001). Our analysis suggests that forecasted climate change increases in temperature and decreases in precipitation may increase dry season diarrheal disease incidence with hot, dry conditions starting earlier and lasting longer. Diarrheal disease incidence in the wet season is likely to decline. Our results identify significant health-climate interactions, highlighting the need for an escalated public health focus on controlling diarrheal disease in Botswana. Study findings have application to other arid countries in Africa where diarrheal disease is a persistent public health problem.

The spatial food environment of the DC metropolitan area: Clustering, co-location, and categorical differentiation

The objective was to analyze the spatial food environment of the Washington, DC metropolitan area. Poorer food sources (convenience stores, fast food, and pharmacies) were the most spatially clustered. Co-Location results suggest strong positive autocorrelation among food environment establishment categories, and competitive effects between pharmacies and convenience stores. Grocery stores were present throughout the region. Changes in the retail food environment, a measure potentially important for diet-related health, occurred through the changing ratio of restaurants to fast food as well as the increased presence of convenience stores.

Modeling Short-Term Spatial and Temporal Variability of Groundwater Level Using Geostatistics and GIS

Continuous depletion of groundwater levels from deliberate and uncontrolled exploitation of groundwater resources lead to the severe problems in arid and semi-arid hard-rock regions of the world. Geostatistics and geographic information system (GIS) have been proved as successful tools for efficient planning and management of the groundwater resources. The present study demonstrated applicability of geostatistics and GIS to understand spatial and temporal behavior of groundwater levels in a semi-arid hard-rock aquifer of Western India. Monthly groundwater levels of 50 sites in the study area for 36-month period (May 2006 to June 2009; excluding 3 months) were analyzed to find spatial autocorrelation and variances in the groundwater levels. Experimental variogram of the observed groundwater levels was computed at 750-m lag distance interval and the four most-widely used geostatistical models were fitted to the experimental variogram. The best-fit geostatistical model was selected by using two goodness-of-fit criteria, i.e., root mean square error (RMSE) and correlation coefficient (r). Then spatial maps of the groundwater levels were prepared through kriging technique by means of the best-fit geostatistical model. Results of two spatial statistics (Geary’s C and Moran’s I) indicated a strong positive autocorrelation in the groundwater levels within 3-km lag distance. It is emphasized that the spatial statistics are promising tools for geostatistical modeling, which help choose appropriate values of model parameters. Nugget-sill ratio (<0.25) revealed that the groundwater levels have strong spatial dependence in the area. The statistical indicators (RMSE and r) suggested that any of the three geostatistical models, i.e., spherical, circular, and exponential, can be selected as the best-fit model for reliable and accurate spatial interpolation. However, exponential model is used as the best-fit model in the present study. Selection of the exponential model as the best-fit was further supported by very high values of coefficient of determination (r2 ranging from 0.927 to 0.994). Spatial distribution maps of groundwater levels indicated that the groundwater levels are strongly affected by surface topography and the presence of surface water bodies in the study area. Temporal pattern of the groundwater levels is mainly controlled by the rainy-season recharge and amount of groundwater extraction. Furthermore, it was found that the kriging technique is helpful in identifying critical locations over the study area where water saving and groundwater augmentation techniques need to be implemented to protect depleting groundwater resources.

The KPSS Test Using Fixed-b Critical Values: Size and Power in Highly Autocorrelated Time Series

In this paper we consider the KPSS test. We derive the asymptotic distribution of the statistic under the null of stationarity and under the unit root alternative under the "fixed-b" assumption that the ratio of the number of lags in the long run variance estimate to the sample size is fixed. Regardless of how the number of lags is actually chosen, the fixed-b asymptotic theory provides a better approximation to the finite sample distribution of the statistic than the traditional KPSS asymptotics. If the series being tested is stationary but has strong positive autocorrelation, the KPSS test has substantial size distortions (overrejections). We show that this problem can be more or less solved by using a larger number of lags than has traditionally been used. Using more lags costs power, but using the fixed-b critical values minimizes the power loss.

The effect of seasonal anomalies of seawater temperature and salinity on the fluctuation in yields of small yellow croaker, Pseudosciaena polyactis, in the Yellow Sea

To include the effects of environmental factors on the production of small yellow croaker, Pseudosciaena polyactis Bleeker, in the Yellow Sea, we applied time series analysis to the commercial catch and salinity and temperature data for the period 1970 to 1988. Residuals from a weighted least‐squares regression of log‐transformed catches against year and month were calculated to remove not only seasonal factors but also long‐term trends in catches. The residuals of mean and standard deviation (SD) of temperature and salinity were calculated and used for autocorrelation, cross‐correlation and first‐order autoregression analysis (AR(1)) using maximum likelihood. The landings showed a decreasing pattern across years with a conspicuous seasonal cycle within years. Catch residuals showed a strong positive autocorrelation and a conspicuous time‐lagged cross‐correlation with the residuals of mean and SD of seawater temperature at 75␣m. AR(1) revealed that positive anomalies of mean temperature were associated with positive anomalies in the production of small yellow croaker with a one year time lag. The decrease in the residual of SD of temperature appears to be related to the high production 0.5–1.0 year later. The effect of salinity was negligible compared with that of temperature. Therefore, the warm spawning period and homogeneous temperature condition of previous years for young fish may cause the increase in the following year's yield of this fish species. When used to predict catches in 1989 and 1990, the AR(1) model explained 40% of the variances of the observed landings.

The exact powers of some autocorrelation tests when the disturbances are heteroscedastic

Abstract This paper considers the exact finite sample powers of some popular tests for AR(1) disturbances when heteroscedasticity is also present. Although test sizes are found to be robust, severe reductions in power are found, particularly under strong positive autocorrelation. Factors influencing these power reductions are identified analytically.

Components of short-horizon individual security returns

In this paper, we present a simple model which relates security returns to three components: an expected return, a bid-ask error, and white noise. The relative importance of the various components is empirically assessed, and the model's ability to explain the various time-series properties of individual security and portfolio returns is tested. Time-varying expected returns and bid-ask errors are found to explain substantial proportions (up to 24%) of the variance of security returns. We also reconcile the typically negative autocorrelation in security returns with the strong positive autocorrelation in portfolio returns.

Wages and profits: A comment

Clark's (1979) model for the levels of aggregate wages and profits is respecified and reestimated using modern econometric techniques. One result is a more efficient estimate of the capital-labor substitution elasticity. In addition, the presence of very strong positive autocorrelation in one of the equations sheds doubt on Clark's assertion that a model for the levels of these variables is more appropriate than a model for their year-to-year changes.

A TIME SERIES ANALYSIS OF POST‐ACCORD INTEREST RATES: COMMENT

In order to avoid distorting the spectrum and introducing spurious coherency, time series shouid be filtered until they approximate white noise.2 Smith and Marcis filter interest rates by detrending with linear regression. Trend, however, is not the major problem in most economic time series. Even in the absence of trend, most economic time series contain strong positive autocorrelation and, as a result, most of the power is concentrated in the low frequencies. First differencing converts most economic time series to a reasonable approximation of white noise. Figures 1 and 2 show that detrending interest rates does not effectively eliminate the concentration of power in the low frequencies while first differencing does eliminate the concentration. Using regression techniques to remove trend also involves applying different filters to the two series, which tends to distort the phase estimates.3 In addition, from a purely practical standpoint, it generally is easier to interpret the spectrum for economic time series after the series have been converted to approximately white noise by first differencing.