Examine the Reliability of Econometrics Software: An Empirical Comparison of Time Series Modelling

Researchers must understand that naively relying on the reliability of statistical software packages may result in suboptimal, biased, or erroneous results, which affects applied economic theory and the conclusions and policy recommendations drawn from it. To create confidence in a result, several software packages should be applied to the same estimation problem. This study examines the results of three software packages (EViews, R, and Stata) in the analysis of time-series econometric data. The time-series data analysis which presents the determinants of macroeconomic growth of Sri Lanka from 1978 to 2020 has been used. The study focuses on testing for stationarity, cointegration, and significant relationships among the variables. The Augmented Dickey-Fuller and Phillips Perron tests were employed in this study to test for stationarity, while the Johansen cointegration test was utilized to test for cointegration. The study employs the vector error correction model to assess the short-run and long-term dynamics of the variables in an attempt to determine the relationship between them. Finally, the Granger Causality test is employed in order to examine the linear causation between the concerned variables. The study revealed that the results produced by three software packages for the same dataset and the same lag order vary significantly. This implies that time series econometrics results are sensitive to the software that is used by the researchers while providing different policy implications even for the same dataset. The present study highlights the necessity of further analysis to investigate the impact of software packages in time series analysis of economic scenarios.

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is introduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to retrieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.

Time Series Models for Short Term Prediction of the Incidence of Japanese Encephalitis in Xianyang City, P R China

Objective To construct a model of Seasonal Autoregressive Integrated Moving Average （SARIMA） for forecasting the epidemic of Japanese encephalitis （JE） in Xianyang, Shaanxi, China, and provide valuable reference information for JE control and prevention. Methods Theoretically epidemiologic study was employed in the research process. Monthly incidence data on JE for the period from Jan 2005 to Sep 2014 were obtained from a passive surveillance system at the Center for Diseases Prevention and Control in Xianyang, Shaanxi province. An optimal SARIMA model was developed for JE incidence from 2005 to 2013 with the Box and Jenkins approach. This SARIMA model could predict JE incidence for the year 2014 and 2015. Results SARIMA （1, 1, 1） （2, 1, 1）12 was considered to be the best model with the lowest Bayesian information criterion, Akaike information criterion, Mean Absolute Error values, the highest R2, and a lower Mean Absolute Percent Error. SARIMA （1, 1, 1） （2, 1, 1）12 was stationary and accurate for predicting JE incidence in Xianyang. The predicted incidence, around 0.3/100 000 from June to August in 2014 with low errors, was higher compared with the actual incidence. Therefore, SARIMA （1, 1, 1） （2, 1, 1）12 appeared to be reliable and accurate and could be applied to incidence prediction. Conclusions The proposed prediction model could provide clues to early identification of the JE incidence that is increased abnormally （≥0.4/100 000）. According to the predicted results in 2014, the JE incidence in Xianyang will decline slightly and reach its peak from June to August.The authors wish to thank the staff from the CDCs from 13 counties of Xianyang, Shaanxi province, China, for their contribution to Japanese encephalitis cases reporting.

Emanation-Sedimentary Metallogenic Series and Models of the Proterozoic Rift in the Kangdian Axis

The Kangdian axis basement can be divided into two tectonic layers. The lower tectonic layer is the crystalline basement which is made up of the Archaean Dibadu Formation and early Proterozoic Dahongshan Group. The former is a kata-metamorphic basic volcano-sedimentary formation of the old geosyncline (old continental nucleus), and the latter is a medium-grade metamorphosed alkali-rich basic volcanic (emanation)-sedimentary formation of the Yuanjiang-Dahongshan marginal rift. They are in disconformable contact. The upper tectonic layer is the folded basement, and made up of the middle-late Proterozoic Kunyang Group. It is the result of Dongchuan-Yuanjiang intercontinental rifting with discordant contract with the underlying and overlying strata. Along with the evolution of Proterozoic from early to late, four types of emanation-sedimentary deposits in the Kangdian axis rift were formed in turn: emanation-sedimentary iron-copper-gold deposits related to basic volcanic rocks in the Yuanmou-Dahongshan marginal rift; emanation-sedimentary iron-copper deposits related to intermediate-basic volcanic rocks in the early stage of the Dongnchuan-Yuanjiang intercontinental rift; emanation-sedimentary copper deposits related to sedimentary rocks in the middle stage; copper deposits related to the late tectonic reworking. From early to late Proterozoic, with the evolution of the Kangdian axis rift and lowering volcanic basicity, the ore-forming elements also evolved from Fe, Cu and (Au) through Cu and Fe to Cu.

A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

Modelling of Indian Monsoon Rainfall Series by Univariate Box-Jenkins Type of Models

The time domain approach, i.e. Autoregressive (AR) processes, of time series analysis is applied to the monsoon rainfall series of India and its two major regions, viz. North-West India and Central India. Since the original time series shows no modelable structure due to the presence of high interannual variability, a 3-point running filter is applied before exploring and fitting appropriate stochastic models. Out of several parsimonious models fitted, AR(3) is found to be most suitable. The usefulness of this fitted model is validted on an independent datum of 18 years and some skill has been noted. These models therefore can be used for low skill higher lead time forecasts of monsoon. Further the forecasts produced through such models can be combined with other forecasts to increase the skill of monsoon forecasts.

Estimation of permafrost thermal behavior using Fourier series model

Permafrost,being an important component of the cryosphere,is sensitive to climate change.Therefore,it is necessary to investigate the change of temperature within permafrost.In this study,we proposed a Fourier series model derived from the conduction equation to simulate permafrost thermal behavior over a year.The boundary condition was represented by the Fourier series and the geothermal gradient.The initial condition was represented as a linear function relative to the geothermal gradient.A comparative study of the different models(sinusoidal model,Fourier series model,and the proposed model)was conducted.Data collected from the northern Da Xing’anling Mountains,Northeast China,were applied for parameterization and validation for these models.These models were compared with daily mean ground temperature from the shallow permafrost layer and annual mean ground temperature from the bottom permafrost layer,respectively.Model performance was assessed using three coefficients of accuracy,i.e.,the mean bias error,the root mean square error,and the coefficient of determination.The comparison results showed that the proposed model was accurate enough to simulate temperature variation in both the shallow and bottom permafrost layer as compared with the other two Fourier series models(sinusoidal model and Fourier model).The proposed model expanded on a previous Fourier series model for which the initial and bottom boundary conditions were restricted to being constant.

Optimal Culture Capacity of White Shrimp (Litopenaeus vannamei) and Razor Clam (Sinonovacula constricta) in a New Series-Connection Culture Model

To construct an effective circular mix-culture model and investigate its culture capacity,we established one small and one large systems,with white shrimp(Litopenaeus vannamei)and razor clam(Sinonovacula constricta)cultured in separate ponds.The culture water from the L.vannamei was pumped to the S.constricta,and the culture water from the S.constricta overflowed back into the L.vannamei via gravity.In trial I,we tested four culture densities(groups 1–4),and monitored water quality,growth indices,and digestive and immune enzyme activities.From the results,the nitrogen and phosphorus levels generally increased then declined after 56 days,and were lower in groups 1 and 2.The specific growth rate of group 2 was the highest.After 56 days,activities of four digestive enzymes were increased in group 2,and lysozyme activity was significantly decreased in S.constricta in groups 1–4;Alkaline phosphatase activity of L.vannamei was increased in group 3,but decreased in S.constricta in groups 2–4;Acid phosphatase activity was significantly higher in groups 1–3(P<0.05),while SOD and CAT activities were significantly elevated in group 2(P<0.05).Thus,we applied group 2 density for trial II.In trial II,nitrogen and phosphorus concentrations declined significantly during the latter stages,and growth indices were higher than the control(P<0.05).The yields of L.vannamei and S.constricta were significantly higher than the control(P<0.05).The results revealed a good circular mix-culture system with the optimal culture capacity for L.vannamei(40 ind m^(−2))and S.constricta(300 ind m^(−2)),which provided a reference for the future culture of them.

Modelling time series properties of Australian lending interest rates

The purpose of this paper is to examine the time series properties of Australian residential mortgage interest rates, and in doing so, establish whether or not selected home loan rates （product-level monthly home loan interest rates for CBA） exhibit the expected cyclical and seasonal variations and whether seasonality, if present, is stochastic or deterministic. In particular, due to a well established presence of cyclicality in financial markets＇ interest rates and strong correlation between financial markets＇ interest rates and home loan interest rates, the paper presumes that cyclicality is also to be found in home loan interest rates. Furthermore, the paper tests the hypothesis that home loan interest rates, for selected products, exhibit the three identified （＂Spring＂, ＂Autumn＂ and ＂The end of the Financial Year＂） season-related interest rate reductions. The paper uses a structural time series modelling approach and product-level home loan interest rates data from one of the biggest banks in Australia, Commonwealth Bank of Australia （CBA）. As expected, the results overall confirm the existence of cyclicality in home loan interest rates. With respect to the seasonality of home loan interest rate, although most of the analysed variables show the presence of statistically significant seasonal factors, the majority of the statistically significant seasonal factors observed cannot be attributed to any of the three considered seasonal effects.

Reconstructing historical forest fire risk in the non-satellite era using the improved forest fire danger index and long short-term memory deep learning-a case study in Sichuan Province,southwestern China

Historical forest fire risk databases are vital for evaluating the effectiveness of past forest management approaches,enhancing forest fire warnings and emergency response capabilities,and accurately budgeting potential carbon emissions resulting from fires.However,due to the unavailability of spatial information technology,such databases are extremely difficult to build reliably and completely in the non-satellite era.This study presented an improved forest fire risk reconstruction framework that integrates a deep learning-based time series prediction model and spatial interpolation to address the challenge in Sichuan Province,southwestern China.First,the forest fire danger index(FFDI)was improved by supplementing slope and aspect information.We compared the performances of three time series models,namely,the autoregressive integrated moving average(ARIMA),Prophet and long short-term memory(LSTM)in predicting the modified forest fire danger index(MFFDI).The bestperforming model was used to retrace the MFFDI of individual stations from 1941 to 1970.Following this,the Anusplin spatial interpolation method was used to map the distributions of the MFFDI at five-year intervals,which were then subjected to weighted overlay with the distance-to-river layer to generate forest fire risk maps for reconstructing the forest fire danger database.The results revealed LSTM as the most accurate in fitting and predicting the historical MFFDI,with a fitting determination coefficient(R^2)of 0.709,mean square error(MSE)of0.047,and validation R^2 and MSE of 0.508 and 0.11,respectively.Independent validation of the predicted forest fire risk maps indicated that 5 out of 7 historical forest fire events were located in forest fire-prone areas,which is higher than the results determined from the original FFDI(2 out of 7).This proves the effectiveness of the improved MFFDI and indicates a high level of reliability of the historical forest fire risk reconstruction method proposed in this study.

Comparison of performance of statistical models in forecasting monthly streamflow of Kizil River,China

This paper presents the application of autoregressive integrated moving average （ARIMA）, seasonal ARIMA （SARIMA）, and Jordan-Elman artificial neural networks （ANN） models in forecasting the monthly streamflow of the Kizil River in Xinjiang, China. Two different types of monthly streamflow data （original and deseasonalized data） were used to develop time series and Jordan-Elman ANN models using previous flow conditions as predictors. The one-month-ahead forecasting performances of all models for the testing period （1998-2005） were compared using the average monthly flow data from the Kalabeili gaging station on the Kizil River. The Jordan-Elman ANN models, using previous flow conditions as inputs, resulted in no significant improvement over time series models in one-month-ahead forecasting. The results suggest that the simple time series models （ARIMA and SARIMA） can be used in one-month-ahead streamflow forecasting at the study site with a simple and explicit model structure and a model performance similar to the Jordan-Elman ANN models.

Analysis of seasonal position variation for selected GNSS sites in Poland using loading modelling and GRACE data

In this study we compared weekly GNSS position time series with modelled values of crustal deformations on the basis of Gravity Recovery and Climate Experiment （GRACE） data. The Global Navigation Satellite Systems （GNSS） time series were taken from homogeneously reprocessed global network solutions within the International GNSS Service （IGS） Reprucessing 1 project and from regional solutions performed by Warsaw University of Technology （WUT） European Permanent Network （EPN） Local Analysis Center （LAC） within the EPN reprocessing project. Eight GNSS sites from the territory of Poland with observation timespans between 2.5 and 13 years were selected for this study. The Total Water Equivalent （TWE） estimation from GRACE data was used to compute deformations using the Green＇s function formalism. High frequency components were removed from GRACE data to avoid aliasing problems. Since GRACE observes mainly the mass transport in continental storage of water, we also compared GRACE deformations and the GNSS position time series, with the deformations computed on the basis of a hydrosphere model. We used the output of Water GAP Hydrology Model （WGHM） to compute deformations in the same manner as for the GRACE data. The WGHM gave slightly larger amplitudes than GNSS and GRACE. The atmospheric non-tidal loading effect was removed from GNSS position time series before comparing them with modelled deformations. The results confirmed that the major part of observed seasonal variations for GNSS vertical components can be attributed to the hy- drosphere loading. The results for these components agree very well both in the amplitude and phase. The decrease in standard deviation of the residual GNSS position time series for vertical components corrected for the hydrosphere loading reached maximally 36% and occurred for all but one stations for both global and regional solutions. For horizontal components the amplitudes are about three times smaller than for vertical components therefore the comparison is much more complicated and the conclusions are ambiguous.

On Mixed Model for Improvement in Stock Price Forecasting

Stock market trading is an activity in which investors need fast and accurate information to make effective decisions.But the fact is that forecasting stock prices by using various models has been suffering from low accuracy,slow convergence,and complex parameters.This study aims to employ a mixed model to improve the accuracy of stock price prediction.We present how to use a random walk based on jump-diffusion,to obtain stock predictions with a good-fitting degree by adjusting different parameters.Aimed at getting better parameters and then using the time series model to predict the data,we employed the time series model to smooth the sequence utilizing logarithm and difference,which successfully resulted in drawing the auto-correlation figure and partial the auto-correlation figure.According to the comparative analysis,which focuses on checking the mean absolute error,including root mean square error and R square evaluation index,we have drawn a clear conclusion that our mixed model prediction effect is relatively good.In the context of Chinese stocks,the hybrid random walk model is very suitable for predicting stocks.It can“interpret”the randomness of stocks very well,and it also has an unparalleled prediction effect compared with other models.Based on the time series model’s application in this paper,the abovementioned series is more suitable for predicting trends.

Modelling the unsteady melt flow under a pulsed magnetic field

A numerical model for the unsteady flow under a pulsed magnetic field of a solenoid is developed, in which magnetohydrodynamic flow equations decouple into a transient magnetic diffusion equation and unsteady Navier–Stokes equations in conjunction with two equations of the k–ε turbulent model. A Fourier series method is used to implement the boundary condition of magnetic flux density under multiple periods of a pulsed magnetic field （PMF）. The numerical results are compared with the theoretical or experimental results to validate the model under a time-harmonic magnetic field; it is found that the toroidal vortex pair is the dominating structure within the melt flow under a PMF. The velocity field of a molten melt is in a quasi-steady state after several periods; changing the direction of the electromagnetic force causes the vibration of the melt surface under a PMF.

Sensitivity Test and Data Analysis for Storage Reliability Assessment of Explosive Initiator

The explosive initiator is one kind of sensitivity products with long life and high reliability.In order to improve the storage reliability assessment,the method of storage reliability assessment for explosive initiator was proposed based on time series model using the sensitivity test data.In the method,the up and down test was used to estimate the distribution parameters of threshold.And an approach to design the up and down test was present to draw better estimations.Furthermore,the method of shrinkage estimation was introduced to get a better estimation of scale parameter by combining the sample information with prior information.The simulation result shows that the shrinkage estimation is better than traditional estimation under certain conditions.With the distribution parameters estimations,the time series models were used to describe the changing trends of distribution parameters along with storage time.Then for a fixed storage time,the distribution parameters were predicted based on the models.Finally,the confidence interval of storage reliability was obtained by fiducial inference.The illustrative example shows that the method is available for storage reliability assessment of the explosive initiator with high reliability.

LAI scale effect research based on compact airborne spectrographic imager data in the Heihe Oasis

As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.

INDUSTRIAL PRODUCTION IN GERMANY AND AUSTRIA:A CASE STUDY IN STRUCTURAL TIME SERIES MODELLING

Industrial production series are volatile and often cyclical. Time series models can be used toestablish certain stylized facts, such as trends and cycles, which may be present in these series. Incertain situations, it is also possible that common factors, which may have an interesting interpretation,can be detected in production series. Series from two neighboring countries with close economicrelationships, such as Germany and Austria, are especially likely to exhibit such joint stylized facts.

Basic Earth＇s Parameters as estimated from VLBI observations

The global Very Long Baseline Interferometry observation for measuring the Earth rotation＇s parameters was launched around 1970 s. Since then the precision of the measurements is continuously improving by taking into account various instrumental and environmental effects. The MHB2000 nutation model was introduced in 2002, which is constructed based on a revised nutation series derived from 20 years VLBI observations（1980-1999）. In this work, we firstly estimated the amplitudes of all nutation terms from the IERS-EOP-C04 VLBI global solutions w.r.t. IAU1980, then we further inferred the BEPs（Basic Earth＇s Parameters） by fitting the major nutation terms. Meanwhile, the BEPs were obtained from the same nutation time series using a BI（Bayesian Inversion）. The corrections to the precession rate and the estimated BEPs are in an agreement, independent of which methods have been applied.