Conventional Forecasting Models Research Articles

Prediction of Annual Rural Unemployment Rate in West Bengal using Grey Model

The rural unemployment rate is a critical economic indicator used to assess strength of rural economy in India. Annual estimates of rural UR are released in both usual status (ps+ss) as well as current weekly status (CWS) at the state and national level in India by National Statistics Office (NSO) through Periodic Labour Force Survey (PLFS). At present, the annual rural UR estimates are available for the state of West Bengal from the year 2017-18 to 2021-22. However, there is a notable delay in the publication of UR estimates as compared to the reference period. Therefore, accurate forecasting of the UR is crucial for timely and targeted interventions, and effective policy planning. Conventional forecasting models fail to provide accurate predictions of UR in these type of small time series due to the violation of requirement of number of data points. In contrast, the Grey model requires limited data to establish a differential forecasting model. In this study, application of grey model has been considered to forecast annual rural UR in West Bengal for different age groups as well as gender, and it was found that grey model provides satisfactory forecast.

Weather Forecasting: A Comprehensive Exploration of IoT and Machine Learning

Weather forecasting play an important role in human lives.It is impacting on various human activities such as agriculture and transportation.Changes in climate conditions often lead to unpredictable weather. Conventional forecasting models sometimes provide inaccurate predictions because they don't adapt well to the dynamic nature of climate.The integration of (IoT) and Machine Learning (ML) technologies has revolutionized weather forecasting methodologies.This paper explores how combining Machine Learning (ML) algorithms with Internet of Things (IoT) devices improves weather forecasting accuracy and efficiency. By analyzing real-time data and historical patterns, this paper shows how IoT and ML can offer more accurate and timely forecasts compare to the limitations of traditional methods.Accurate weather forecasts are really important for things like farming, transportation, saving energy.In this paper the effectiveness of the algorithm is evaluated using various performance metrics including r2 score comparison,mean square error comparison. Key Words: IOT,Machine Learning,Support Vector Machine

Spatio-temporal prediction of total energy consumption in multiple regions using explainable deep neural network

Energy consumption forecasting is essential for energy system integration and management. However, existing studies mainly focus on temporal features of energy consumption, which neglects the spatial correlation of variables with time information. Capturing the spatio-temporal relationships helps to improve forecasting accuracy and further promote energy dispatch. To tackle this problem, an explainable Convolutional Neural Network-Long Short Term Memory forecasting model is employed to effectively predict the total energy consumption by capturing the spatial and temporal features of multivariate time series. In the model, the autoencoder is used to achieve the nonlinear dimensionality reduction and transfer the data to a low-dimensional space. Furthermore, a Convolutional Neural Network is used to extract more effective features from the decoded data, and long short-term memory is employed to identify the temporal dependencies between extracted features and total energy consumption. Shapley additive explanation is introduced to interpret the outputs of the black-box model. The superior performance of the proposed method with high accuracy and good adaptability is verified by the comparisons with conventional forecasting models. This method provides an insight into the regional energy consumption analyzing contributions of weather variables to energy consumption, which helps administers in understanding regional energy performance for enhancing energy efficiency.

Short-Term EV Charging Demand Forecast with Feedforward Artificial Neural Network

The global increase in greenhouse gas emissions from automobiles has brought about the manufacture and usage of large quantities of electric vehicles (EVs). However, to ensure proper integration of EVs into the grid, there is a need to forecast the charging demand of EVs accurately. This paper presents a short-term electric vehicle charging demand forecast using a feedforward artificial neural network optimized with a modified local leader phase spider monkey optimization (MLLP-SMO) algorithm, a proposed variant of spider monkey optimization. A proportionate fitness selection is employed to improve the update process of the local leader phase of the spider monkey optimization. The proposed algorithm trains a feedforward neural network to forecast electric vehicle charging demand. The effectiveness of the proposed forecasting model was tested and validated with electric vehicle public charging data from the United Kingdom Power Networks Low Carbon London Project. The model's performance was compared to a feedforward neural network trained with particle swarm optimization, genetic algorithm, classical spider monkey optimization, and two conventional forecasting models, multi-linear regression and Monte Carlo simulation. The performance of the proposed forecasting model was assessed using the mean absolute percentage error of forecast and forecasting accuracy. The model produced a forecast accuracy and mean absolute percentage error of 99.88% and 3.384%, respectively. The results show that MLLP-SMO as a trainer predicted better than the other forecasting models and met industry standard forecast accuracy.

A regional solar forecasting approach using generative adversarial networks with solar irradiance maps

The intermittent and stochastic nature of solar resource hinders the integration of solar energy into modern power system. Solar forecasting has become an important tool for better photovoltaic (PV) power integration, effective market design, and reliable grid operation. Nevertheless, most existing solar forecasting methods are dedicated to improving forecasting accuracy at site-level (e.g. for individual PV power plants) regardless of the impacts caused by the accumulated penetration of distributed PV systems. To tackle with this issue, this article proposes a novel generative approach for regional solar forecasting considering an entire geographical region of a flexible spatial scale. Specifically, we create solar irradiance maps (SIMs) for solar forecasting for the first time by using spatial Kriging interpolation with satellite-derived solar irradiance data. The sequential SIMs provide a comprehensive view of how solar intensity varies over time and are further used as the inputs for a multi-scale generative adversarial network (GAN) to predict the next-step SIMs. The generated SIM frames can be further transformed into PV power output through a irradiance-to-power model. A case study is conducted in a 24 × 24 km area of Brisbane to validate the proposed method by predicting of both solar irradiance and the output of behind-the-meter (BTM) PV systems at unobserved locations. The approach demonstrates comparable accuracy in terms of solar irradiance forecasting and better predictions in PV power generation compared to the conventional forecasting models with a highest average forecasting skill of 10.93±2.35% for all BTM PV systems. Thus, it can be potentially used to assist solar energy assessment and power system control in a highly-penetrated region.

Evaluation of Various Machine Learning Methods to Predict Istanbul’s Freshwater Consumption

Planning, organizing, and managing water resources is crucial for urban areas and metropolitans. Istanbul is one of the largest megacities, with a population of over 15 million. The large volume of water demand and increasing scarcity of clean water resources make long-term planning necessary for this city, as sustained water supply requires large-scale investment projects. Successful investment plans require accurate projections and forecasting for freshwater demand. This study considers different machine learning methods for freshwater demand forecasting for Istanbul. Using monthly consumption data provided by the municipality since 2009, we compare forecasting accuracies of ARIMA, Holt-Winters, Artificial Neural Networks, Recursive Neural Networks, Long-Short Term Memory, and Simple Recurrent Neural Network models. We find that the monthly freshwater demand of Istanbul is best predicted by Multi-Layer Perceptron and Seasonal ARIMA. From the predictive modeling perspective, this result is another indication of the combined usage of conventional forecasting models and novel machine learning techniques to achieve the highest forecasting accuracy.

Multi-model approach applied to meteorological data for solar radiation forecasting using data-driven approaches

The accuracy of the solar forecasting model depends upon various factors such as attributes of the data, time horizon, time interval, length of the data, etc. This means attributes of data selection are an important feature of any solar forecasting model. A lot of research has been done on solar forecasting using deep learning and machine learning approaches, providing better accuracy for a particular type of model and data. However, how to accurately apply the multi-model techniques in the data-driven approaches of the solar radiation prediction model is still a challenging issue due to the complexity of the temporal resolution, length, and attribute selection of the data. This paper proposes a multi-model technique using data-driven approaches to get an improvised solar forecasting model with respect to the attributes of data. In this research, a multi-model method based on data-driven approaches is developed for short-term solar radiation forecasting. Three years of weather data with different temporal resolutions taken from reliable online sources were used for training and testing in this work. The weather data considered various input parameters such as temperature, humidity, pressure, wind speed, and wind direction; solar radiation data is considered the model’s target variable. This work is a two-stage process. In the first stage, multi-model methods are analyzed based on solar forecasts at different temporal resolutions, and best-performing models are selected. The optimization technique is applied to the best model in the second stage to obtain an improvised solar forecasting model. It is observed that the multi-model forecasts provide better accuracy in terms of R2, nRMSE, and MAE than the conventional forecasting model. In this work, the performance parameters of nRMSE = 0.34, MAE = 4.71, and R2 = 0.93 are obtained before optimization, and nRMSE = 0.25, MAE = 1.39 and R2 = 0.96 are obtained after optimization in the testing stage for an hourly dataset. For daily datasets, the performance parameters nRMSE = 0.24, MAE = 3.19, and R2 = 0.93 are obtained before optimization, and nRMSE = 0.16, MAE = 2.61, and R2 = 0.95 are obtained after optimization in the testing stage. As a result, the proposed algorithm focused on an efficient model to predict solar radiation. Accurate solar radiation prediction models are highly in demand in various smart grid applications. Therefore, the proposed work may help in suggesting a suitable model for solar energy forecasting.

A novel integrated method for short-term wind power forecasting based on fluctuation clustering and history matching

The intermittent and randomness of wind power poses a great challenge to the safe and stable operation of power systems. Accurate wind power forecasting is a key to reduce the negative impact of uncertainty on the entire system. To this end, a novel integrated method for short-term wind power forecasting is proposed based on frequency analysis, fluctuation clustering and history matching. Through variational modal decomposition (VMD) and Pearson correlation coefficient between wind resource and wind power, the wind power sequence is decomposed into a trend component and a fluctuation component. Then both the two components are sequentially divided into time series segments with equal lengths, which are set as the variation period determined by fast Fourier transform (FFT). Time series segments of the trend component are clustered by feature extraction and fuzzy C-means (FCM) clustering method, and accordingly the segments of fluctuation component are clustered as well. The correlation consistency between trend components and fluctuation components is further studied. Finally, the trend component is forecasted by random forest (RF) model, and the fluctuation component is forecasted by matching its counterpart trend component from historical similar segments database based on the correlation consistency. The performance and effectiveness of the proposed method are verified by using four wind farms in Jilin Province, China. Results indicate that the forecasting accuracy of the proposed method is greatly improved compared with the conventional forecasting model, which proves the validity.

Analysis of Signs and Effects of Surgical Breast Cancer Patients Based on Big Data Technology.

Big data in health care has gained popularity in recent years for disease prediction. Breast cancer infections are the most common cancer in urban Indian women, as well as women internationally, and are impacted by many events across countries and regions. Breast malignant growth is a notable disease among Indian women. According to the WHO, it represents 14% of all malignant growth tumors in women. A couple of studies have been directed utilizing big data to foresee breast malignant growth. Big data is causing a transformation in healthcare, with better and more ideal results. Monstrous volumes of patient-level data are created by using EHR (Electronic Health Record) systems data because of fast mechanical upgrades. Big data applications in the healthcare business will assist with improving results. Conventional forecast models, then again, are less productive in terms of accuracy and error rate because the exact pace of a specific calculation relies upon different factors such as execution structure, datasets (little or enormous), and kinds of datasets utilized (trait-based or picture based). This audit article looks at complex information mining, AI, and profound learning models utilized for recognizing breast malignant growth. Since “early identification is the way to avoidance in any malignant growth,” the motivation behind this audit article is to support the choice of fitting breast disease expectation calculations, explicitly in the big information climate, to convey powerful and productive results. This survey article analyzes the precision paces of perplexing information mining, AI, and profound learning models utilized for distinguishing breast disease on the grounds that the exactness pace of a specific calculation relies upon different factors such as execution structure, datasets (little or enormous), and dataset types (quality based or picture based). The reason for this audit article is to aid the determination of suitable breast disease expectation calculations, explicitly in the big information climate, to convey successful and productive outcomes. Thus, “Early discovery is the way to counteraction in the event of any malignant growth.”

Hydrological time series forecasting via signal decomposition and twin support vector machine using cooperation search algorithm for parameter identification

• TSVM is introduced for hydrological forecasting for the first time. • CEEMDAN divides complex runoff into several stationary subseries. • TSVM optimized by CSA identify nonlinear relationship of each subseries. • Real-world applications prove the feasibility of the developed method. Accurate hydrologic forecasting is of vital importance for water resource management and reservoir operation under the changing environments. However, it is difficult for a standalone method to track the complex hydrological time series with highly nonlinear and nonstationary features. To improve the forecasting accuracy, this study proposes a hybrid model using compete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and twin support vector machine (TSVM) optimized by metaheuristic algorithm. Firstly, the CEEMDAN tool is chosen to divide the original runoff data into several relatively stable subcomponents with various resolutions and frequencies. Then, the TSVM forecasting model is established to extract the deep features of each subseries, while the emerging cooperation search algorithm is used to search for satisfying parameter combination. The final forecasting value for the original hydrological time series is formulated by aggregating the outputs of all TSVM models. Long-term streamflow data from several hydrological stations in China’s Yangtze River is used for simulation. Experimental results reveal that the hybrid model significantly outperforms several conventional forecasting models in prediction accuracy. For instance, the proposed method improves the root mean squared error and mean absolute error value with about 36.5% and 41.6% reductions compared with the traditional support vector machine at station B. Thus, a novel and effective evolutionary artificial intelligence model is developed for hydrological forecasting.

Recognition and Investigation of Covid-19 with Artificial Intelligence and Deep Learning Approaches

Machine learning (ML)-based forecasting techniques have demonstrated their use in predicting perioperative outcomes and improving decision-making about future actions. Many application domains that required the detection and prioritization of adverse aspects of a threat have long used machine learning models. To deal with forecasting challenges, a variety of prediction approaches are widely utilized. This investigation illustrates the ability of machine learning models to forecast the number of patients who would be afflicted by COVID-19, which is now regarded as a possible threat to humanity. In this work, four conventional forecasting models were utilized to forecast the dangerous situation: linear regression (LR), least absolute shrinkage and selection operator (LASSO), support vector machine (SVM), and exponential smoothing (ES).

Clustering analysis of the Sargassum transport process: application to beaching prediction in the Lesser Antilles

Abstract. The massive Sargassum algae beachings observed over the past decade are a new natural hazard currently impacting the island states of the Caribbean region (human health, environmental damages, and economic losses). This study aims to improve the prediction of the surface current dynamic leading to beachings in the Lesser Antilles using clustering analysis methods. The input surface currents were derived from the Mercator model and the Hybrid Coordinate Ocean Model (HYCOM) outputs in which we integrated the windage effect. Past daily observations of Sargassum beaching on Guadeloupe coasts and satellite-based Sargassum offshore abundance were also integrated. Four representative current regimes were identified for both Mercator and HYCOM data. The analysis of the current sequences leading to beachings showed that the recurrence of two current regimes is related to the beaching peaks respectively observed in March and August. The performance score of the predictive model showed that the HYCOM data seem more suitable to assess coastal Sargassum hazard in the Lesser Antilles. For 1 year of tests (i.e., 2021), the decision tree accuracy respectively reached 70.1 % and 58.2 % for HYCOM and Mercator with a temporal uncertainty range ±3 d around the forecast date. The present clustering analysis predictive system, requiring lower computational resources compared to conventional forecast models, would help improve this risk management in the islands of the region.

Use of supervised machine learning algorithms for state wise COVID-19 forecasting

The Covid Techniques for predicting have demonstrated their value in anticipating perioperative outcomes for the objective of improve future decision-making activities. The designs have existed for a long time. Utilized in a large number of possible uses where unfavorable variables for a danger required be identifying and prioritizing. To take care of forecasting challenges, a large number of prediction approaches are widely utilized. This study demonstrates the model’s ability to estimate how many patients will be COVID-19 is a virus that affects people. Currently assumed to be a possibility danger to the human race. In this case, study; four conventional forecasting models were put to use to foresee the hazardous elements of COVID-19: LR, least LASSO, SVM, and ES.Each of the models makes 3 sorts of forecasts for the next ten days: the no. of freshly infected cases, the no.of newly infected cases, the no. of newly infected cases, the no. of newly fatalities, and the no. of recoveries. The study’s findings show that using these strategies in the present situation COVID-19 pandemic scenario is a promising mechanism.

Deep Learning for Demand Forecasting in the Fashion and Apparel Retail Industry

Compared to other industries, fashion apparel retail faces many challenges in predicting future demand for its products with a high degree of precision. Fashion products’ short life cycle, insufficient historical information, highly uncertain market demand, and periodic seasonal trends necessitate the use of models that can contribute to the efficient forecasting of products’ sales and demand. Many researchers have tried to address this problem using conventional forecasting models that predict future demands using historical sales information. While these models predict product demand with fair to moderate accuracy based on previously sold stock, they cannot fully be used for predicting future demands due to the transient behaviour of the fashion industry. This paper proposes an intelligent forecasting system that combines image feature attributes of clothes along with its sales data to predict future demands. The data used for this empirical study is from a European fashion retailer, and it mainly contains sales information on apparel items and their images. The proposed forecast model is built using machine learning and deep learning techniques, which extract essential features of the product images. The model predicts weekly sales of new fashion apparel by finding its best match in the clusters of products that we created using machine learning clustering based on products’ sales profiles and image similarity. The results demonstrated that the performance of our proposed forecast model on the tested or test items is promising, and this model could be effectively used to solve forecasting problems.

Amending the heston stochastic volatility model to forecast local motor vehicle crash rates: A case study of Washington, D.C.

Modelling crash rates in an urban area requires a swathe of data regarding historical and prevailing traffic volumes and crash events and characteristics. Provided that the traffic volume of urban networks is largely defined by typical work and school commute patterns, crash rates can be determined with a reasonable degree of accuracy. However, this process becomes more complicated for an area that is frequently subject to peaks and troughs in traffic volume and crash events owing to exogenous events – for example, extreme weather – rather than typical commute patterns. One such area that is particularly exposed to exogenous events is Washington, D.C., which has seen a large rise in crash events between 2009 and 2020. In this study, we adopt a forecasting model that embeds heterogeneity and temporal instability in its estimates in order to improve upon forecasting models currently used in transportation and road safety research. Specifically, we introduce a stochastic volatility model that aims to capture the nuances associated with crash rates in Washington, D.C. We determine that this model can outperform conventional forecasting models, but it does not perform well in light of the unique travel patterns exhibited throughout the COVID-19 pandemic. Nevertheless, its adaptability to the idiosyncrasies of Washington, D.C. crash rates demonstrates its ability to accurately simulate localised crash rates processes, which can be further adapted in public policy contexts to form road safety targets.

Efficient Energy Management Based on Convolutional Long Short-Term Memory Network for Smart Power Distribution System

An efficient energy management system is integrated with the power grid to collect information about the energy consumption and provide the appropriate control to optimize the supply–demand pattern. Therefore, there is a need for intelligent decisions for the generation and distribution of energy, which is only possible by making the correct future predictions. In the energy market, future knowledge of the energy consumption pattern helps the end-user to decide when to buy or sell the energy to reduce the energy cost and decrease the peak consumption. The Internet of things (IoT) and energy data analytic techniques have provided the convenience to collect the data from the end devices on a large scale and to manipulate all the recorded data. Forecasting an electric load is fairly challenging due to the high uncertainty and dynamic nature involved due to spatiotemporal pattern consumption. Existing conventional forecasting models lack the ability to deal with the spatio-temporally varying data. To overcome the above-mentioned challenges, this work proposes an encoder–decoder model based on convolutional long short-term memory networks (ConvLSTM) for energy load forecasting. The proposed architecture uses encode consisting of multiple ConvLSTM layers to extract the salient features in the data and to learn the sequential dependency and then passes the output to the decoder, having LSTM layers to make forecasting. The forecasting results produced by the proposed approach are favorably comparable to the existing state-of-the-art and better than the conventional methods with the least error rate. Quantitative analyses show that a mean absolute percentage error (MAPE) of 6.966% for household energy consumption and 16.81% for city-wide energy consumption is obtained for the proposed forecasting model in comparison with existing encoder–decoder-based deep learning models for two real-world datasets.

An Innovative Hourly Water Demand Forecasting Preprocessing Framework with Local Outlier Correction and Adaptive Decomposition Techniques

Accurate forecasting of hourly water demand is essential for effective and sustainable operation, and the cost-effective management of water distribution networks. Unlike monthly or yearly water demand, hourly water demand has more fluctuations and is easily affected by short-term abnormal events. An effective preprocessing method is needed to capture the hourly water demand patterns and eliminate the interference of abnormal data. In this study, an innovative preprocessing framework, including a novel local outlier detection and correction method Isolation Forest (IF), an adaptive signal decomposition technique Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and basic forecasting models have been developed. In order to compare a promising deep learning method Gated Recurrent Unit (GRU) as a basic forecasting model with the conventional forecasting models, Support Vector Regression (SVR) and Artificial Neural Network (ANN) have been used. The results show that the proposed hybrid method can utilize the complementary advantages of the preprocessing methods to improve the accuracy of the forecasting models. The root-mean-square error of the SVR, ANN, and GRU models has been reduced by 57.5%, 27.8%, and 30.0%, respectively. Further, the GRU-based models developed in this study are superior to the other models, and the IF-CEEMDAN-GRU model has the highest accuracy. Hence, it is promising that this preprocessing framework can improve the performance of the water demand forecasting models.

Smart energy forecasting strategy with four machine learning models for climate-sensitive and non-climate sensitive conditions

Developing a reliable and robust algorithm for accurate energy demand prediction is indispensable for utility companies for various applications, e.g., power dispatching, market participation and infrastructure planning. However, this is challenging because the performance of a forecasting algorithm may be affected by various factors, such as data quality, geographic diversity, forecast horizon, customer segmentation and the forecast origin. Furthermore, an approach that performs well in one region may fail in other regions, and similarly, a model that forecasts accurately in one horizon may fail to produce an accurate prediction for other horizons. To overcome the above challenges such as rough data quality, different forecasting horizons, different kinds of loads and forecasting for different regions, this study proposes four machine learning/supervised learning models. These models are applied to improve the generalization of the network and reduce forecasting. These models are intended to simplify or demystify terms, complex concepts and data granularity used in energy forecasting. Two different data sites and four forecasting horizons are used to validate the proposed models. The coefficient of variation and mean absolute percentage error are 50% higher as compared with the existing model. The proposed supervised learning models ensure a generalization ability, robustness and high accuracy for building and utilities energy consumption forecasting. The forecasting results help to improve and automate the predictive modeling process while covering the knowledge-gaps between machine learning and conventional forecasting models.

Dynamic Inversion of Inland Aquaculture Water Quality Based on UAVs-WSN Spectral Analysis

The inland aquaculture environment is an artificial ecosystem, where the water quality is a key factor which is closely related to the economic benefits of inland aquaculture and the quality of aquatic products. Compared with marine aquaculture, inland aquaculture is normally smaller and susceptible to pollution, with poor self-purification capacity. Considering its low cost and large-scale monitoring ability, many researches have developed spectrum sensor on-board satellite platforms to allow remote monitoring of inland water surface. However, there remain many problems, such as low image resolution, poor flexible data acquisition, and anti-interference. Apart from that, the conventional forecasting model is of weak generalization ability and low accuracy. In our study, we combine unmanned aerial vehicles system (UAVs) with the wireless sensor network (WSN) to design a new ground water quality parameter and drone spectrum information acquisition approach, and to propose a novel dynamic network surgery-deep neural networks (DNS-DNNs) model based on multi-source feature fusion to forecast the distribution of dissolved oxygen (DO) and turbidity (TUB) in inland aquaculture areas. The result of using fused features, including characteristic spectrum, Gray-level co-occurrence matrix (GLCM) texture feature, and convolutional neural network (CNN) texture feature to build a model is that the characteristic spectrum+ CNN texture fusion features were the best input items for DNS-DNNs when forecasting DO, with the determination coefficient R 2 of the vertical set arriving at 0.8741, while the characteristic spectrum+ GLCM texture+ CNN texture fusion features were the best for TUB, with the R 2 reaching 0.8531. Compared with a variety of conventional models, our model had a better performance in the inversion of DO and TUB, and there was a strong correlation between predicted and real values: R 2 reached 0.8042 and 0.8346, whereas the root mean square error (RMSE) were only 0.1907 and 0.1794, separately. Our study provides a new insight about using remote sensing to rapidly monitor water quality in inland aquaculture regions.

Considering seasonal fluctuations on balancing time series with the use of artificial neural networks when forecasting US imports from the PRC

The paper’s objective is to propose a particular methodology to be used to regard seasonal fluctuations on balancing time series while using artificial neural networks based on the example of imports from the People's Republic of China (PRC) to the USA (US). The difficulty of forecasting the volume of foreign trade is usually given by the limitations of many conventional forecasting models. For the improvement of forecasting it is necessary to propose an approach that would hybridize econometric models and artificial intelligence models. Data for an analysis to be conducted are available on the World Bank website, etc. Information on US imports from the PRC will be used. Each forecast is given by a certain degree of probability which it will be fulfilled with. Although it appeared before the experiment that there was no reason to include the categorical variable to reflect seasonal fluctuations of the USA imports from the PRC, the assumption was not correct. An additional variable, in the form of monthly value measurements, brought greater order and accuracy to the balanced time series.