Autocorrelated Errors Research Articles

The efficiency assessment of installation of a non-cash system in the public transport to combat the shadow economy

This article describes the shadow economy in the public passenger transport sphere in regions of Russia. The goal of the work is to evaluate the impact of a non-cash payment system on the shadow economy. The relevance is to obtain quantitative assessments of the effectiveness of contactless payments using debit, credit and/or transport cards as a tool to combat the concealment of income by transport organizations via hiding the data on passengers carried in regions of Russia. The author uses econometric analysis of panel data for the period 2015–2018, where the dependent variable is the number of passengers carried. Among the independent variables are such indicators as price for a ride, number of population, number of buses, income of population, and other indicators that reflect presence or absence of discount for paying for a ride via debit, credit and/or transport cards in regions in Russia. The model considers autocorrelation and heteroskedasticity of the error in the regression, but also endogeneity of the variable «Price for a ride». As the results of research, absence of discount via a debit/credit card and discount via a transport card leads to an increase of the number of passengers carried. Meanwhile, presence of discount via a debit/credit card and absence of discount via a transport card does not lead to an increase of the number of passengers carried. At the end of 2018 a non-cash system got the most proliferation in the municipal transport than in commercial one

The COVID-19 Pandemic and the Degree of Persistence of US Stock Prices and Bond Yields

This paper analyses the possible effects of the Covid-19 pandemic on the degree of persistence of US monthly stock prices and bond yields using fractional integration techniques. The model is estimated first over the period January 1966-December 2020 and then a recursive approach is taken to examine whether or not persistence has changed during the following pandemic period. We find that the unit root hypothesis cannot be rejected for stock prices while for bond yields the results differ depending on the maturity date and the specification of the error term. In general, bond yields appear to be more persistent, although there is evidence of mean reversion in case of 1-year yields under the assumption of autocorrelated errors. The recursive analysis shows no impact of the Covid-19 pandemic on the persistence of stock prices, whilst there is an increase in the case of both 10- and 1- year bond yields but not of their spread.

Persistence, seasonality, and fractional integration within a nonlinear framework: Evidence from US citizens’ overseas travel

This research note examines data on US citizens’ overseas air passenger travel with respect to the degree of persistence, seasonality, nonlinearities, and fractional integration. Based on seasonally differenced data with allowance for autocorrelated errors, we find evidence of nonlinearity with moderate persistence and mean reversion in US overseas air travel. The results suggest that shocks to US overseas air travel will dissipate over time, and as such, the observed persistence and nonlinearity can provide useful information in the modeling and forecasting of future behavior.

A comparison among Different Methods for Estimating Regression Parameters with Autocorrelation Problem under Exponentially Distributed Error

Multiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of cigarettes according to the US Federal Trade Commission.

Simulation Study of Autocorrelated Error Using Bayesian Quantile Regression


 The purpose of this study is to compare the ability of the Classical Quantile Regression method and the Bayesian Quantile Regression method in estimating models that contain autocorrelated error problems using simulation studies. In the quantile regression approach, the data response is divided into several pieces or quantiles conditions on indicator variables. Then, The parameter model is estimated for each selected quantiles. The parameters are estimated using conditional quantile functions obtained by minimizing absolute asymmetric errors. In the Bayesian quantile regression method, the data error is assumed to be asymmetric Laplace distribution. The Bayesian approach for quantile regression uses the Markov Chain Monte Carlo Method with the Gibbs sample algorithm to produce a converging posterior mean. The best method for estimating parameter is the method that produces the smallest absolute value of bias and the smallest confidence interval. This study resulted that the Bayesian Quantile method produces smaller absolute bias values and confidence intervals than the quantile regression method. These results proved that the Bayesian Quantile Regression method tends to produce better estimate values than the Quantile Regression method in the case of autocorrelation errors. 
 Keywords: Quantile Regression Method, Bayesian Quantile Regression Method, Confidence Interval, Autocorrelation.

Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

Effects of Correlation between the Error Term and Autocorrelation on Some Estimators in a System of Regression Equations

Seemingly unrelated regression model developed to handle the problem of correlation among the error terms of a system of the regression equations is still not without a challenge, where each regression equation must satisfy the assumptions of the standard regression model. When dealing with time-series data, some of these assumptions, especially that of independence of the regressors and error terms leading to multicollinearity and autocorrelation respectively, are often violated. This study examined the effects of correlation between the error terms and autocorrelation on the performance of seven estimators and identify the estimator that yields the most preferred estimates under the separate or joint influence of the two correlation effects considered by the researcher. A two-equation model was considered, in which the first equation had multicollinearity and autocorrelation problems while the second one had no correlation problem. The error terms of the two equations were also correlated. The levels of correlation between the error terms and autocorrelation were specified between -1 and +1 at interval of 0.2 except when it approached unity.

Predictability of Analyst Earnings Forecast Errors and Institutional and Individual Investors’ Reactions to Earnings News

We decompose analysts’ earnings forecast error into predictable and unpredictable components and investigate individual vis-à-vis institutional investors’ reactions to each of these components. We find that in the immediate post-earnings announcement window, only individuals under-react to the predictable component, while both individuals and institutions under-react to the unpredictable component. The price drift in this window is driven primarily by investors’ under-reaction to the unpredictable component. This drift remains highly significant in larger firms and intensifies in firms with complex financial reports, suggesting that it likely represents the slow and noisy process of price discovery. Around the next quarterly earnings announcement, only individuals under-react to the previous quarter’s predictable component, and this fixation drives the entire price drift in this window. This drift disappears in larger firms and gets exacerbated in firms with greater forecast error autocorrelations, suggesting that it is likely attributable to incomplete processing of earnings information by individuals.

Accounting for erroneous model structures in biokinetic process models

In engineering practice, model-based design requires not only a good process-based model, but also a good description of stochastic disturbances and measurement errors to learn credible parameter values from observations. However, typical methods use Gaussian error models, which often cannot describe the complex temporal patterns of residuals. Consequently, this results in overconfidence in the identified parameters and, in turn, optimistic reactor designs. In this work, we assess the strengths and weaknesses of a method to statistically describe these patterns with autocorrelated error models. This method produces increased widths of the credible prediction intervals following the inclusion of the bias term, in turn leading to more conservative design choices. However, we also show that the augmented error model is not a universal tool, as its application cannot guarantee the desired reliability of the resulting wastewater reactor design.

Modeling Nigerian Covid-19 cases: A comparative analysis of models and estimators.

COVID-19 remains a major pandemic currently threatening all the countries of the world. In Nigeria, there were 1, 932 COVID-19 confirmed cases, 319 discharged cases and 58 deaths as of 30th April 2020. This paper, therefore, subjected the daily cumulative reported COVID-19 cases of these three variables to nine (9) curve estimation statistical models in simple, quadratic, cubic, and quartic forms. It further identified the best of the thirty-six (36) models and used the same for prediction and forecasting purposes. The data collected by the Nigeria Centre for Disease Control for sixty-four (64) days, two (2) months and three (3), were daily monitored and eventually analyzed. We identified the best models to be Quartic Linear Regression Model with an autocorrelated error of order 1 (AR(1)); and found the Ordinary Least Squares, Cochrane Orcutt, Hildreth-Lu, and Prais-Winsten and Least Absolute Deviation (LAD) estimators useful to estimate the models' parameters. Consequently, we recommended the daily cumulative forecast values of the LAD estimator for May and June 2020 with a 99% confidence level. The forecast values are alarming, and so, the Nigerian Government needs to hastily review her activities and interventions towards COVID-19 to provide some tactical and robust structures and measures to avert these challenges.

Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator

This study tests for the sandwich-form asymptotic covariance matrices entailed by conditionally heteroskedastic and/or autocorrelated regression errors or conditionally uncorrelated homoskedastic errors. In doing so, we enable the empirical researcher to estimate the asymptotic covariance matrix of the quasi-maximum likelihood estimator by supposing a possibly misspecified model for error distribution. Accordingly, we provide test methodologies by extending the approaches in Cho and White (in: Chang Y, Fomby T, Park JY (eds) Advances in econometrics: essays in honor of Peter CB Phillips. Emerald Group Publishing Limited, West Yorkshire, 2014) and Cho and Phillips (J Econ 202:45–56, 2018a) to detect the influence of heteroskedastic and/or autocorrelated regression errors on the asymptotic covariance matrix. In particular, we establish a sequential testing procedure to achieve our goal. We affirm the theory on our test statistics through simulation and apply the test statistics to energy price growth rate data for illustrative purposes; here, we also apply our test methodology to test the fully correct model hypothesis.

A combined mixed-s-skip sampling strategy to reduce the effect of autocorrelation on the X̄ scheme with and without measurement errors

In order to reduce the effect of autocorrelation on the monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size n. It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.

The Effect of Spatiotemporal Resolution Degradation on the Accuracy of IMERG Products over the Huai River Basin

AbstractThe rapid development of the Integrated Multisatellite Retrievals for Global Precipitation Measurement (IMERG) precipitation product provides new opportunities for a wide range of Earth system and natural hazard applications. Spatiotemporal averaging is a common method for IMERG users to acquire suitable resolutions specific to their research or application purpose and has a direct impact on the overall quality of IMERG precipitation estimates. Here, three different IMERG, version 06 (V06), latency run products (i.e., early, late, and final) are assessed against a ground-based benchmark along a continuous series of spatiotemporal resolutions over the Huai River basin (HuaiRB) between June 2014 and May 2017. In general, IMERG products better capture the spatial pattern of precipitation, and demonstrate better reliability, in the southern portion of the HuaiRB relative to its northern region. Furthermore, the degradation of spatiotemporal resolution is associated with better rain/no-rain determination and the consistent improvement of rainfall product performance metrics. This improvement is more pronounced for IMERG products at fine spatiotemporal resolution. However, due to the presence of autocorrelated errors, the performance improvement associated with the degradation of spatiotemporal resolution is less than theoretical expectations assuming purely uncorrelated errors. Component analysis indicates that while both temporal and spatial aggregation do not mitigate temporally autocorrelated errors, temporal averaging can remove spatially autocorrelated error. Hence, temporal averaging is found to be more effective than spatial averaging for improving the quality of IMERG products. These results will inform users of the reliability of IMERG products at different spatiotemporal scales and assist in unifying former disparate validation assessments applied at different scales within the literature.

SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

Fully modified least absolute devotions and fully modified M in estimating regression model with non-stationary explanatory variable and auto correlated random errors

The research is concerned with the adoption of two robust estimation methods: The fully modified least absolute devotions method (FM-LAD) and the fully modified M method (FM-M), in estimating the parameters of regression model with non-stationary explanatory variable and autocorrelated random errors which can be modeled according to one of the mixed models, autoregressive and moving average (ARMA). The research aims to make a comparison between these two methods based on the results of their estimation using simulation experiments prepared for this purpose. The results of the simulation experiment showed the advantage of the fully modified M method over the second method depending on the trade-off criterion mean squared error (MSE).

Iterative estimation correcting for error auto-correlation in short panels, applied to lagged dependent variable models

An iterative estimation procedure incorporating error serial correlation in short panels is presented. Neglecting serial correlation might both result in inconsistent variance estimates and in inconsistent parameter estimates, for example in (structural) models containing (functions of) lagged dependent variables. Lagged disturbances and/or lagged innovations are treated as unobserved or latent variables, and their estimates are included as supplementary regressors. Iterating until convergence results in consistent estimates of all model parameters. In addition, the asymptotic distribution of the proposed estimator, which can accommodate auto-regressive errors without any assumptions regarding starting values is presented. The main advantage of the proposed method is the maximal reuse of existing (cross-sectional) code, which can simply be adapted to serially correlated disturbances. As such, this “quick fix” estimator seems to be a promising avenue for applied researchers suspecting serial correlation in their data, but only willing to perform a moderate amount of coding (i.e. the iterative loop & the adaptation of the variance estimation), without having to develop, code and debug a full own model. The proposed method is applied to panel data models with lagged dependent variables with and without fixed effects.

Estimation of Error Variance-Covariance Parameters Using Multivariate Geographically Weighted Regression Model

The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector ε that distributed as a multivariate normally with zero vector mean and variance-covariance matrix Σ at each location ui,vi, which Σ is sized qxq for samples at the i-location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures.

Improved day ahead heating demand forecasting by online correction methods

Novel control strategies to reduce the heating and cooling energy consumption of buildings and districts are constantly being developed. Control on higher system levels, for example demand side management, usually requires forecasts for the future energy demand of buildings or entire districts. Such forecasts can be done with Artificial Neural Networks. However, the prediction performance of Artificial Neural Networks suffers from high variance. This means that two parameter-wise identical networks fitted to the same training data set perform differently well in forecasting the testing set. Here, we use two correction methods, one based on the forecasting error autocorrelation, and one based on online learning, to obtain reliable forecasting models. The approach is tested in the frame of day-ahead sub-hourly heating demand forecasting in a case study of a complex building, which has properties of a district heating system. It is demonstrated that the methods significantly reduce variance in prediction performance and also increase average prediction accuracy. When compared to other grey-box and black-box forecasting models, the approach performs well.

Spatial dependence model with feature difference

AbstractThis paper presents a new spatial dependence model with an adjustment of feature difference. The model accounts for the spatial autocorrelation in both the outcome variables and residuals. The feature difference adjustment in the model helps to emphasize feature changes across neighboring units, while suppressing unobserved covariates that are present in the same neighborhood. The prediction at a given unit incorporates components that depend on the differences between the values of its main features and those of its neighboring units. In contrast to conventional spatial regression models, our model does not require a comprehensive list of global covariates necessary to estimate the outcome variable at the unit, as common macro‐level covariates are differenced away in the regression analysis. Using the real estate market data in Hong Kong, we applied Gibbs sampling to determine the posterior distribution of each model parameter. The result of our empirical analysis confirms that the adjustment of feature difference with an inclusion of the spatial error autocorrelation produces better out‐of‐sample prediction performance than other conventional spatial dependence models. In addition, our empirical analysis can identify components with more significant contributions.

Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

In statistical process monitoring, the usual assumption when designing monitoring schemes is that process parameters are known and have perfect measurements with independent and identically distributed observations. However, in real-life situation, these assumptions rarely hold. Hence, in this paper, the Phase II performance of the homogenously weighted moving average (HWMA) $\bar {X}$ monitoring scheme under the combined effect of autocorrelation and measurement errors is investigated when the unknown process parameters are estimated from an in-control Phase I dataset. Two models are considered, i.e. the first-order autoregressive model for within-sample autocorrelation and the linear covariate model for (constant and linearly increasing variance) measurement system error. Sampling strategies based on skipping some observations as well as mixing different subgroup samples and taking multiple measurements are implemented to reduce the negative effect of autocorrelation and measurement errors. Since the latter sampling strategies incur costs, as an alternative, increasing the slope coefficient of the linear covariate model compensate the negative effect of measurement errors. The new HWMA $\bar {X}$ scheme is shown to have some interesting detection abilities as compared to its competitors. A real-life example is used to illustrate the implementation of the proposed monitoring scheme.