Deterministic Trend Research Articles

A large deformation finite element analysis of uplift behaviour for helical anchor in spatially variable clay

Helical anchors are emerging as an innovative foundation design option for offshore applications to resist uplift loading. Numerous studies have been conducted to investigate the uplift behaviour of helical anchor under different helical bearing plate configurations in clay, using field or model tests and numerical analyses. However, almost all of them are limited to deterministic analyses, ignoring the influence of inherent spatial variability of soil. This work conducts a 3D large deformation random finite element analysis to examine the uplift behaviour of helical anchor in spatially variable clay. Both the stochastic and deterministic trends are reflected in the 3D non-stationary random field adopted. It is found that the spatial variability of soil strength significantly influences the failure mechanism of helical anchor. Parametric studies indicate that the coefficient of variation and vertical scales of fluctuation of soil strength can much influence on the uplift capacity, while the effect of horizontal scales of fluctuation is trivial. The goodness-of-fit test of probability distribution suggests that random uplift capacities follow log-normal distribution, whereby the relationship between factor of safety and probability of failure is established. The findings of this paper might facilitate the safety design of helical anchor.

Estimating the Competitive Storage Model with Stochastic Trends in Commodity Prices

We propose a State-Space Model (SSM) for commodity prices that combines the competitive storage model with a stochastic trend. This approach fits into the economic rationality of storage decisions and adds to previous deterministic trend specifications of the storage model. For a Bayesian posterior analysis of the SSM, which is nonlinear in the latent states, we used a Markov chain Monte Carlo algorithm based on the particle marginal Metropolis–Hastings approach. An empirical application to four commodity markets showed that the stochastic trend SSM is favored over deterministic trend specifications. The stochastic trend SSM identifies structural parameters that differ from those for deterministic trend specifications. In particular, the estimated price elasticities of demand are typically larger under the stochastic trend SSM.

A multi-factor approach to modelling the impact of wind energy on electricity spot prices

We introduce a four-factor arithmetic model for electricity baseload spot prices in Germany and Austria. The model consists of a deterministic seasonality and trend function, both short- and long-term stochastic components, and exogenous factors such as the daily wind energy production forecasts, the residual demand and the wind penetration index. We describe the short-term stochastic factor by a Lévy semi-stationary (LSS) process, and the long-term component is modelled as a Lévy process with increments belonging to the class of generalised hyperbolic distributions.We derive the corresponding futures prices and develop an inference methodology for our multi-factor model. The methodology allows to infer the various factors in a step-wise procedure taking empirical spot prices, futures prices and wind energy production and total load data into account.Our empirical work shows that taking into account the impact of the wind energy generation on the prices improves the goodness of fit. Moreover, we demonstrate that the class of LSS processes can be used for modelling the exogenous variables including wind energy production, residual demand and the wind penetration index.

Testing stationarity of the detrended price return in stock markets

This paper proposes a generalized porous media equation with drift as the governing equation for stock market indexes. The proposed governing equation can be expressed as a Fokker–Planck equation (FPE) with a non-constant diffusion coefficient. The governing equation accounts for non-stationary effects and describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito’s Lemma, the FPE is associated with a stochastic differential equation (SDE) that models the time evolution of the price return in a fashion different from the classical Black–Scholes equation. Both FPE and SDE equations account for a deterministic part or trend and a stochastic part or q-Gaussian noise. The q-Gaussian noise can be decomposed into a Gaussian noise affected by a standard deviation or volatility. The presented model is validated using the S&P500 index’s data from the past 25 years per minute. We show that the price return becomes Gaussian, consequently stationary by normalizing the detrended data set. The normalization of the data is calculated by subtracting the trend and then dividing by the standard deviation of the detrended price return. The stationarity test consists of representing the power spectrum in terms of the time series’s autocorrelation. Additionally, this paper presents the multifractal analysis for the detrended and normalized price return to describe the Hurst exponent dynamics over the dataset.

The Impact of Terms of Trade on the Export Structure of Manufactured Products in Different Economic Developing Status

The Prebisch-Singer Hypothesis states that in structural time series analysis, the terms of trade between primary products and manufacturers have a negative deterministic trend. Many researchers argued that the deterioration in trade is the type of country in which the products are exported, regardless of whether the types of products exported by such countries are primary or manufactured products. This paper employs a development-differentiated model to analyze the correlation between various terms of trade and the export proportion of manufactured products on different economies of development status. In the long run, stable co-integration relations exist between terms of trade and the export proportion of manufactured products for development status. Furthermore, the increased proportion of manufactured products exports is the Granger casualty for the worse terms of trade for several economies of development status. The results demonstrated that changing the terms of trade is significantly influenced by structured changes in the export proportion of manufactured products for the development status of economies.

Cotrending: Testing for common deterministic trends in varying means model

In a varying means model, the temporary evolution of a p-vector system is determined by p deterministic nonparametric functions superimposed by error terms, possibly dependent cross sectionally. The basic interest is in linear combinations across the p dimensions that make the deterministic functions constant over time. The number of such linearly independent linear combinations is referred to as a cotrending dimension, and their spanned space as a cotrending space. This work puts forward a framework to test statistically for cotrending dimension and space. Connections to principal component analysis and cointegration are also considered. Finally, a simulation study to assess the finite-sample performance of the proposed tests, and applications to several real data sets are also provided.

Counterfactual Analysis With Artificial Controls: Inference, High Dimensions, and Nonstationarity

Recently, there has been growing interest in developing statistical tools to conduct counterfactual analysis with aggregate data when a single “treated” unit suffers an intervention, such as a policy change, and there is no obvious control group. Usually, the proposed methods are based on the construction of an artificial counterfactual from a pool of “untre ated” peers, organized in a panel data structure. In this article, we consider a general framework for counterfactual analysis for high-dimensional, nonstationary data with either deterministic and/or stochastic trends, which nests well-established methods, such as the synthetic control. We propose a resampling procedure to test intervention effects that does not rely on postintervention asymptotics and that can be used even if there is only a single observation after the intervention. A simulation study is provided as well as an empirical application. Supplementary materials for this article are available online.

Digital mapping of zinc in urban topsoil using multisource geospatial data and random forest

This study aimed to map the spatial patterns of Zn in urban topsoil by using multisource geospatial data and machine learning method. Geological map, digital elevation models, and Landsat images were used to extract data related to geology, relief, and land use types and a vegetation index. Urban functional types were derived from the fusion of Systeme Probatoire d'Observation de la Terre 5 images, points of interest, and real-time Tencent user data. A geodetector was adopted to select key environmental covariates. Random forest (RF) and geographically weighted regression (GWR) were employed to model and map Zn concentrations in urban topsoil. The results showed that urban functional type, geology, NDVI, elevation, slope, and aspect were key environmental covariates. Compared with land use types, urban functional types could better reflect the spatial variation in Zn. The RF and GWR models were established using the key environmental covariates, with leave-one-out cross-validated R values of 0.68 and 0.58 and root mean square errors of 0.51 and 0.57, respectively. The results indicated that digital mapping of Zn in urban topsoil by using multisource geospatial data and RF was feasible. RF might be more suitable to fit the stochastic characteristics of Zn in urban topsoils than GWR, which considers deterministic trends in modeling.

The nature of the trend in global and hemispheric temperatures

AbstractThe aim of this note is to provide evidence about the existence or non‐existence of a stochastic trend in the global temperatures time series by using standard unit root tests. Three sets of data are considered in this paper: global, Northern Hemisphere and Southern Hemisphere monthly temperature anomalies. Our main finding is that there is not a stochastic trend in the temperatures time series and they are stationary around a deterministic trend.

Likelihood ratio test for the mean of asymptotic spatial regression with the Brownian sheet noise

Likelihood ratio test (LR-test) is frequently applied in regression analysis when the observations are normally distributed. However, when the normality assumption is violated, such a test can not be directly adopted in practice. In this work, we propose an approach by firstly transforming the observations to a set-indexed partial sums process. The limit model under this transformation is presented as a deterministic trend plus a random noise given by the set-indexed Brownian sheet. We show that the problem of testing the appropriateness of a model can be handled step-wise by testing the validity of the trend in the limit model by defining an LR-test based on the ratio between the likelihood function under H 0 and under H 0 ∪ H 1. The rejection region as well as the power of the size α LR-test are obtained based on the Cameron-Martin-Girsanov formula of the Radon-Nikodym derivative of the set-indexed partial sums limit process of the observation with respect to the set-indexed Brownian sheet. Simulation study shows that the proposed test behaves as a consistent test in that it maximizes the power when H 1 is true. Application of the method to real data can help in detecting valid regression model describing the variability of the maximum height of corn plants over the experimental region.

Regional Investigation for Economies of Development Status on Changes in Export Structure of Deterioration Terms of Trade

The theory of Deterioration Terms of Trade states that the terms of trade between primary commodities and manufactures have a negative deterministic trend. However, the terms of trade for primary commodities have improved significantly because of higher prices of raw materials and natural resources due to the rapid development of some emerging developing countries. Literatures argued that the deterioration in terms of trade is the type of country in which the goods are exported rather than the types of goods exported by such countries are primary or manufactured goods. This paper employs regression models of alternative economies to analyze the correlation between terms of trade and manufactured goods export ratio. Results demonstrated that the Prebisch-Singer Hypothesis holds for all the economies except the developed ones, and the ITTs are worsened by increases in the proportion of manufactured goods for all the economies.

EFFICIENCY OF THE LOGISTICS CHAIN AS A FACTOR OF ECONOMIC SECURITY OF ENTERPRISES

Abstract. The basis of economic and financial security of the enterprise is effective financial and economic activity, stable financial condition, rational use of financial resources, the ability to counter threats to the internal and external environment. One of the factors of effective financial and economic activity and economic security of enterprises is the formation of effective logistics chains that provide its participants with opportunities to counter threats to the internal and external environment. Formation of effective logistics chains on the basis of taking into account the economic interests of its participants causes changes in the results of their financial and economic activities and creates the basis for their financial independence, socio-economic efficiency and stability. The purpose of the article is to form approaches to assessing the efficiency of the logistics chain on the basis of economic and financial security of enterprises. The article investigates scientific approaches to evaluating the efficiency of the logistics chain of enterprises, identifies their strengths and weaknesses, analyzes their methodology. An approach to evaluating the efficiency of the logistics chain of industrial enterprises, the use of which will reconcile the economic interests of the participants in the logistics chain, reduce their financial costs, ensure effective economic activity, form the basis for their financial and economic security. The scientific novelty of the article is the formation of a modern approach to evaluating the efficiency of the logistics chain, which, in contrast to existing ones, involves the use of an indicator of the efficiency of logistics activities of enterprises, the proposed indicator is the stationarity of ratio of operating results to logistics costs relative to the mean or deterministic trend over time, and identification of potential models of logistics efficiency of enterprises, which would ensure economic and financial security of enterprises. It is proved that efficiency of the logistics chain is achieved under the condition that the financial result from the operating activities of the enterprises united by the logistics chain in relation to their costs for logistics activities will not change for a long time or will naturally change with a reliable forecast and possibility economic forecasting of further cooperation. The expediency of using this approach was confirmed on the basis of the analysis of the efficiency of logistics chains of selected enterprises. The initial data for the construction of this model were the logistics costs as a component of the company’s operating expenses and the financial result from operating activities. The deficiencies in the use of existing accounting standards and regulations that govern the integrated assessment of the enterprise’s logistics costs have been established. It is proposed to use the Davis databases, which are formed on the basis of a web-survey of enterprises regarding the value of their logistic costs. It is noted that the actual stability of the logistics chains for each enterprise and the optimal ratio of their results to costs are determined by the current market conditions. An idea of the efficiency of connections in the logistics chain is formulated. It was concluded that the existence of a long-term stable equilibrium in the form of vector co-integration for all subjects of the logistics chain can be considered optimal. Prospects for further research are the development of a scientific approach to the formation of a logistics cluster as a basis for financial and economic security of enterprises. Keywords: economic security, financial security, financial costs, financial results, efficiency, the logistics chain, logistics activities. JEL Classіfіcatіon С22, D22, D61, O30 Formulas: 5; fig.: 2; tabl.: 2; bibl.: 15.

Using Hybrid Wavelet-Exponential Smoothing Approach for Streamflow Modeling

Considering the three intrinsic components (of autoregressive, seasonality, and error) of streamflow time series, the overall performance of the streamflow modeling tool is associated with the correct estimation of these components. In this study, a new hybrid method based on the wavelet transform (WT) as a multiresolution forecasting tool and exponential smoothing (ES) method, with two presented scenarios (WES1 and WES2), was introduced. To this end, the performance of the proposed method was investigated versus four conventional methods of the autoregressive integrated moving average (ARIMA), ES ad-hoc, artificial neural network (ANN), and wavelet-ANN (WANN) for daily and monthly streamflow modeling of West Nishnabotna and Trinity River watersheds with different hydro-geomorphological conditions. In the presented WES technique, firstly, WT is employed for decomposing the observed signal to one approximation (deterministic trend) and more diverse components of subseries (each at a specific frequency). Then, for the first scenario (WES1), only two subseries are introduced to the model as input parameters; however, for the second scenario (WES2), decomposed subseries are separately used as the inputs of ES models. The obtained results indicated that combining WT with the ES method and ANN led to more accurate modeling. The proposed methodology (WES2) that used all decomposed subseries separately improved the efficiency of models up to 30% and 10% for the daily dataset and up to 88% and 57% for the monthly dataset, respectively, for the West Nishnabotna and Trinity Rivers.

Efficient tapered local Whittle estimation of multivariate fractional processes

The semiparametric estimation of multivariate fractional processes based on the tapered periodogram of the differenced series is considered in this paper. We construct multivariate local Whittle estimators by incorporating the maximal efficient taper developed by Chen (2010). The proposed estimation method allows a wide range of potentially nonstationary long-range dependent series, being invariant to the presence of deterministic trends with the same extent of the differencing order, without a two-step procedure. We establish the consistency and asymptotic normality of the proposed estimators, which have no discontinuities, and show that the asymptotic variance is the same as that of the nontapered local Whittle estimation by increasing the order of a taper to infinity with a moderately slow rate. We examine the finite sample behavior of the proposed estimators through a simulation experiment.

On the Shape of a High Excursion of a Gaussian Stationary Process

We investigate the shape of an excursion above a high level u by a stationary Gaussian process. The shape depends on the conditioned mean and covariances of the underlying process. The paths vary slightly around a deterministic trend. The probability of such event can be determined asymptotically exactly for u → ∞.

Impact of Private Investment, Economic Growth and Financial Development on Environmental Degradation: Evidence from Pakistan

Private investment plays an important role in the process of economic growth and also impact natural environment of a country. The main purpose of the present study is to empirically analyze the impact of private investment and other macro economic variables on environmental degradation of Pakistan. For the purpose, time series data is collected for the years 1975 to 2017. The study used Linear regression model for analyzing the impact of private investment, energy consumption, financial development and economic growth on environmental degradation. Augmented Dickey Fuller (ADF) test and Phillips Perron (PP) test is used for identifying the unit root of the variables; first with an intercept then, with an intercept and a linear deterministic trend. Akaike Information Criterion (AIC) is used for selection of optimum lag whereas Johansen cointegration test is adopted for analyzing long run association in the variables. The results of linear regression model show that energy consumption and economic growth have a positive and statistically significant impact on CO2 emissions whereas the impact of private investment on CO2 emissions is negative. It means that in Pakistan, private investment is environment friendly. Based on study results, it is recommended that when formulating policies for economic growth and development, motivation should be given to private inverters in order to increase private investment.

Short-Term Time Wind Speed Forecasting Based on Spatio-Temporal Geostatistical Approach and Kriging Method

Short-term wind speed prediction is an essential task for wind resource and wind energy planning. However, most of this literature does not take into account the spatio-termporal correlation of wind data from the geographical field. For this reason, we propose an integrated spatio-temporal kriging and functional kriging strategy to exploit such spatio-temporal correlation into the wind speed prediction. First, the deterministic trend component in wind data is estimated to be removed. The residuals are used for spatio-temporal modeling and prediction. Based on the spatio-temporal kriging framework, four spatio-temporal covariance models (product-sum model, separable exponential product model, separable and nonseparable Gneiting models) are considered which describe the spatio-temporal correlation of wind data. In particular, the flexibility of using the nonseparable Gneiting model is highlighted. More specifically, four spatio-temporal random fields are modeled from the 12 wind monitoring stations over Ireland. We also use an involved weighted least squares method for estimating parameters of the four covariance models involved in the spatio-temporal kriging strategy. We apply the fitted covariance models to generate day-ahead wind speed predictions at both observed and nonobserved locations where wind station already exist but also to nearby locations. Leave-one-out cross-validation is applied to check the significance of the difference among the four models, these spatio-temporal ordinary kriging (STOK), functional ordinary kriging (FOK) and autoregressive integrated moving average (ARIMA) methods are compared for day-ahead wind speed predictions. Forecasting results indicate that the predicting accuracy is improved almost 33.5% using FOK compared with three approaches which confirm the effectiveness of the functional kriging method in the paper.

Bootstrap unit-root test for random walk with drift: The bsrwalkdrift command

In this article, we introduce the command bsrwalkdrift, which is primarily intended to perform a bootstrap unit-root test under the null hypothesis of random walk with drift. The method implemented in this command is considerably more precise than the corresponding case of the conventional augmented Dickey–Fuller test, which can be inaccurate when the true value of the drift term is small relative to the standard deviation of the innovations. The command also has an option to account for deterministic linear trend and another option to perform bootstrap unit-root tests under the null hypothesis of random walk without drift.

Estimating persistence for irregularly spaced historical data

This paper introduces to the literature on Economic History a measure of persistence which is particularly useful when the data are irregularly spaced. An illustration to ten historical unevenly spaced data series for Holland of 1738 to 1779 shows the merits of the methodology. It is found that the weight of slave-based contribution in that period has grown with a deterministic trend pattern.

Detection of type of trends in surface air temperature in China

Detection of the type of trend in temperature data, by distinguishing between deterministic and stochastic trends, has important implications for understanding climate change. The Unit root tests (URTs) have been widely used for detecting the type of trend, but they do not consider the possibility of fractional integration and its influences. In this study, we detected the type of trends in observed surface air temperature during 1960–2019 at 558 stations across China, by considering fractional integration. The whole period was divided into three sub-periods by two structural breakpoints (denoted as SBP1 and SBP2). The fractional differencing parameter d was estimated by the Local Whittle (LW) function, and then three URTs (namely PP, KPSS, and ZA) were used to detect the type of trends in the temperature data during different sub-periods. The results indicated that the de-seasoned monthly temperature (DMT) series were fractionally integrated and, thus, exhibited long-range dependence characteristics, which significantly influenced the estimation of the slope of trend and detection of the type of trend. Compared with the LW function, the ordinary least squares method yielded biased estimation of the slope of trend, as it could not eliminate the influence of long-range dependence of the DMT series. The DMT series with weak long-range dependence or anti-persistent characteristics during 1960–SBP1, SBP1–SBP2, and SBP2–2019 were accurately detected as deterministic trends. However, the DMT series with strong long-range dependence during SBP1–2019 and 1960–2019 were detected to have stochastic trends by the KPSS test. Following the results of the fractional integration and URTs together, temperature over short periods in China were detected to have deterministic trends, but those at long periods were detected to have a combination of long-range dependence and deterministic trends.