First-order Autoregressive Error Research Articles

Non-linear regression models in the management of accumulated production of parchment coffee in Peru

Parchment coffee results from washing the coffee cherry, and its production has achieved a significant increase in the coffee-growing regions of Peru. Knowing the production pattern of this grain is essential to help coffee producers make decisions in the economic and social sector. As growth curves generally have sigmoidal behavior, which is well fit by non-linear models, this study aimed to model the cumulative production pattern of parchment coffee as a function of time (in months) in the year 2022, comparing the fit of the non-linear Logistic, Gompertz and von Bertalanffy models. The cumulative national production, and production of the departments of Huánuco and San Martín, in Peru, were analyzed. Data used to fit the models were obtained from the Ministry of Development and Irrigation (MIDAGRI) of Peru. To check the assumptions of normality, homoscedasticity, and independence of residuals, the Shapiro-Wilk, Breusch-Pagan, and Durbin-Watson tests were used, respectively. The model parameters were estimated using the least squares method using the Gauss-Newton algorithm in the R software. The goodness-of-fit of the models was tested using goodness-of-fit measures such as Coefficient of Determination (R2), Residual Standard Deviation (RSD), Akaike Information Criterion (AIC), and nonlinearity measures. Based on the models’ goodness-of-fit measures, the Gompertz model with a first-order autoregressive error term (AR1) fit best to national production data, and the Logistic model was the most suitable for describing the production of the departments of Huánuco, and San Martín.

Night-time population consistently explains the transmission dynamics of coronavirus disease 2019 in three megacities in Japan.

Mobility data are crucial for understanding the dynamics of coronavirus disease 2019 (COVID-19), but the consistency of the usefulness of these data over time has been questioned. The present study aimed to reveal the relationship between the transmissibility of COVID-19 in Tokyo, Osaka, and Aichi prefectures and the daily night-time population in metropolitan areas belonging to each prefecture. In Japan, the de facto population estimated from GPS-based location data from mobile phone users is regularly monitored by Ministry of Health, Labor, and Welfare and other health departments. Combined with this data, we conducted a time series linear regression analysis to explore the relationship between daily reported case counts of COVID-19 in Tokyo, Osaka, and Aichi, and night-time de facto population in downtown areas estimated from mobile phone location data, from February 2020 to May 2022. As an approximation of the effective reproduction number, the weekly ratio of cases was used. Models using night-time population with lags ranging from 7 to 14 days were tested. In time-varying regression analysis, the night-time population level and the daily change in night-time population level were included as explanatory variables. In the fixed-effect regression analysis, the inclusion of either the night-time population level or daily change, or both, as explanatory variables was tested, and autocorrelation was adjusted by introducing first-order autoregressive error of residuals. In both regression analyses, the lag of night-time population used in best fit models was determined using the information criterion. In the time-varying regression analysis, night-time population level tended to show positive to neutral effects on COVID-19 transmission, whereas the daily change of night-time population showed neutral to negative effects. The fixed-effect regression analysis revealed that for Tokyo and Osaka, regression models with 8-day-lagged night-time population level and daily change were the best fit, whereas in Aichi, the model using only the 9-day-lagged night-time population level was the best fit using the widely applicable information criterion. For all regions, the best-fit model suggested a positive relationship between night-time population and transmissibility, which was maintained over time. Our results revealed that, regardless of the period of interest, a positive relationship between night-time population levels and COVID-19 dynamics was observed. The introduction of vaccinations and major outbreaks of Omicron BA. Two subvariants in Japan did not dramatically change the relationship between night-time population and COVID-19 dynamics in three megacities in Japan. Monitoring the night-time population continues to be crucial for understanding and forecasting the short-term future of COVID-19 incidence.

Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors

Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors

Nonlinear models to describe the growth of Jatropha plant (Jatropha curcas L.)

Brazil stands out in the renewable energy sector due to the growing demand for clean energy sources, mainly with biodiesel production, which uses vegetable oils and animal fats as raw material. With this, research has been developed with oilseed plants for this purpose and, among these plants, Jatropha has stood out for its productivity and ability to grow in regions with water scarcity. Thus, it is necessary to study the growth of this plant over time to assist management techniques and detection of factors that affect the plant development. Therefore, modeling this type of growth can subsidize knowledge and application of effi cient techniques for agricultural practices. The objective of this study was to fi t and compare the nonlinear Logistic and Gompertz models with four parameters in the description of growth in height of the Jatropha plant according to days after the phenological cycle in the second year of the plant development, totaling 25 observations. The models were fi t using the statistical software R, considering the fi rst order autoregressive error structure for the CNPAE-169 and CNPAE-259 accessions. All models fi t well to the data from the three accessions under study, but the Logistic model stood out for the CNPAE-169 and CNPAE-102 accessions and the Gompertz model for the CNPAE-259 accession. The CNPAE-102 accession stood out from the others, presenting greater height in the study period.

Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure

The determination of leverage observations have been frequently investigated through ordinary least squares and some biased estimators proposed under the multicollinearity problem in the linear regression models. Recently, the identification of leverage and influential observations have been also popular on the general linear regression models with correlated error structure. This paper proposes a new projection matrix and a new quasiprojection matrix to determination of leverage observations for principal component regression and r-k class estimators, respectively, in general linear regression model with first-order autoregressive error structure. Some useful properties of these matrices are presented. Leverage observations obtained by generalized least squares and ridge regression estimators available in the literature have been compared with proposed principal component regression and r-k class estimators over a simulation study and a numerical example. In the literature, the first leverage is considered separately due to the first-order autoregressive error structure. Therefore, the behaviours of first leverages obtained by principal component regression and r-k class estimators has been also investigated according to the autocorrelation coefficient and biasing parameter through applications. The results showed that the leverage of the first observation obtained by principal component regression and r-k estimators is smaller than that obtained by generalized least squares and ridge regression estimators. In addition, as the autocorrelation coefficient goes to -1, the leverage of the first transformed observation decreases for PCR and r-k class estimators, while its increases while the autocorrelation coefficient goes to 1.

Study on the growth curve of the internal cavity of ‘Dwarf green’ coconut fruits

The aim of the work was to evaluate the adjustment of the logistic and gompertz model with structure of first-order autoregressive errors in the study on the ‘Dwarf green’ coconut fruit growth based on longitudinal and cross-sectional internal cavity diameter data (DLCI and DTCI). Model adjustments showed positive residual autocorrelation, according to the Durbin-Watson test and for both variables, DLCI and DTCI, the residue was modeled according to first-order autoregressive process (AR1). The analysis was performed using the least squares method in the PROC MODEL of the SAS software and results indicated that for both characteristics under study, the logistic model was the most appropriate in describing fruit growth and, according to the model, fully developed ‘Dwarf green’ coconut fruits have longitudinal and cross-sections internal cavity diameter of approximately 7.39 cm and 7.60 cm, respectively.

Trans-dimensional geoacoustic inversion and uncertainty quantification for SBCEX17 data

This paper presents an efficient and general approach to Bayesian inversion and uncertainty quantification for seabed geoacoustic profile estimation. The model-selection problem of estimating an appropriate seabed parameterization is addressed with trans-dimensional (trans-D) inversion via reversible-jump Markov-chain Monte Carlo, which samples probabilistically over the number of layers. An efficient proposal density for parameter perturbations is based on using a linearized approximation to the posterior probability density, applied in principal-component (PC) space where the (rotated) parameters are uncorrelated. The acceptance rate of perturbations and birth/death steps is improved by parallel tempering, based on a series of interacting Markov chains with successively tempered (relaxed) likelihoods. The PC proposals are adapted individually to the tempering of each Markov chain. The data-error model is based on the assumption of multivariate Gaussian errors with correlations represented by an autoregressive process. The parameters of zeroth- and first-order autoregressive error processes are sampled trans-dimensionally to avoid over- or under-parameterizing the error model. The approach is illustrated for three data sets from the 2017 Seabed Characterization Experiment (SBCEX17), including broadband seabed reflection coefficients; dispersion of water-borne acoustic modes, resolved by warping analysis; and ship noise recorded at a bottom-mounted horizontal array of hydrophones.

Trans-dimensional geoacoustic inversion on the New England Mud Patch using modal dispersion data

This paper presents trans-dimensional geoacoustic inversion of two low-frequency broadband signals recorded during the Seabed Characterization Experiment (SBCEX). The considered sources are a chirp emitted by a towed J15 source and an underwater impulse created by a combustive sound source (CSS). Corresponding received signals are recorded on single hydrophones, and the two source/receiver configurations are reciprocal, on the same track. Input data for inversion are modal time-frequency dispersion curves, estimated using warping. Inversion is then performed within a Bayesian framework. A trans-dimensional inverse algorithm is used to estimate the model parametrization (i.e., number of seabed layers), and the mode covariance matrices are estimated as a first-order autoregressive error process. Inversion results on the two reciprocal tracks are consistent with the modal information available in each dataset. Results are also consistent with what is known about the area.

Evaluating Influence of Neighboring Structures on Spatial Crash Frequency Modeling and Site-Ranking Performance

Many neighborhood weight matrices have been adopted for modeling crash spatial heterogeneity. However, there has been little evaluation of their influence on crash prediction modeling performance. This study investigated 17 spatial-proximity matrices for development of spatial crash prediction models and site ranking with county-level data in California. Of the group of matrices being evaluated, traffic exposure–weighted and population-weighted distance-based matrices were first proposed in the traffic safety field. Bayesian spatial analysis was conducted with a combination of a first-order autoregressive error process and time trend for crashes to address the serial correlation of crashes in successive years. Two diagnostic measures were used for assessment of goodness of fit and complexity of models, and seven evaluation criteria were employed to assess the benefits associated with better-fitting models in site ranking. The results showed that modeling performance improved with an increase in number of neighbors considered in the weight matrix. However, a larger number of neighbors also led to greater variability of modeling performance. Specifically, Queen-2 and Decay-50 models proved to be superior among the adjacency- and distance-based models, respectively. The significance of incorporating spatial correlations was highlighted by the consistently poor performance of the base model, which included only the heterogeneity random effect. Finally, model-fitting performance seems to be strongly correlated with site-ranking performance. The models with closer goodness of fit tend to yield more consistent ranking results.

Nowcasting Annual National Accounts with Quarterly Indicators: An Assessment of Widely Used Benchmarking Methods

Benchmarking methods can be used to extrapolate (or 'nowcast') low-frequency benchmarks on the basis of available high-frequency indicators. Quarterly national accounts are a typical example, where a number of monthly and quarterly indicators of economic activity are used to calculate preliminary annual estimates of GDP. Using both simulated and real-life national accounts data, this paper aims at assessing the prediction accuracy of three benchmarking methods widely used in the national accounts compilation: the proportional Denton method, the proportional Cholette-Dagum method with first-order autoregressive error, and the regression-based Chow-Lin method. The results show that the Cholette-Dagum method provides the most accurate extrapolations when the indicator and the annual benchmarks move along the same trend. However, the Denton and Chow-Lin methods could prevail in real-life cases when the quarterly indicator temporarily deviates from the target series.

Nowcasting Annual National Accounts with Quarterly Indicators: An Assessment of Widely Used Benchmarking Methods

Benchmarking methods can be used to extrapolate (or “nowcast”) low-frequency benchmarks on the basis of available high-frequency indicators. Quarterly national accounts are a typical example, where a number of monthly and quarterly indicators of economic activity are used to calculate preliminary annual estimates of GDP. Using both simulated and real-life national accounts data, this paper aims at assessing the prediction accuracy of three benchmarking methods widely used in the national accounts compilation: the proportional Denton method, the proportional Cholette-Dagum method with first-order autoregressive error, and the regression-based Chow-Lin method. The results show that the Cholette-Dagum method provides the most accurate extrapolations when the indicator and the annual benchmarks move along the same trend. However, the Denton and Chow-Lin methods could prevail in real-life cases when the quarterly indicator temporarily deviates from the target series.

Diagnostics of a Multiresponse Regression Model with Autocorrelated Errors

In this paper we study the diagnostics of a multiresponse regression model with a first-order autoregressive error sequence. The deletion technique is used to identify the outliers taking account of the dependence structure of the errors. Besides the usual measures, some scalar measures to gauge the impact of the ouliers on the regression are suggested.

Comparison of stem taper equations for eight major tree species in the Spanish Plateau

Aim of study: A stem taper function and a compatible merchantable volume system are compared to evaluate which provides a better description of the stem profile for the main species in central Spain.Area of study: This research was carried out in the region of Castile-Leon, located in Central Spain.Material and Methods: A total of 6,357 trees were selected for destructive sampling. All models were fitted using a first-order continuous autoregressive error structure to address the problem of autocorrelation.Main results: In terms of accuracy, the root mean square error (RMSE) in both models ranged from 0.75 to 2.72 depending on the species analyzed, presenting values similar to those reported in other studies. Small differences in the goodness-of-fit for both procedures were also found, and the Stud model provided better accuracy for 6 of the 8 species studied, with RMSE reductions of 0.5% to 8.6%. The RMSE obtained in the cross-validation phase was on average 1.22 times higher than what was obtained in the fitting phase.Research highlights: The non-linear extra sum of squares method indicated that the stem taper differs among the five softwood species and three hardwood species. In hardwoods, the first inflection point is lower than in softwoods (at around 5%) and the second inflection point is higher (at around 85%) than those of softwoods.Keywords: taper function; volume system; Central Spain; softwoods; hardwoods.

Partially linear models with first-order autoregressive symmetric errors

In this paper we discuss estimation and diagnostic procedures for partially linear models with first-order autoregressive [AR(1)] symmetric errors. The symmetric class includes all symmetric continuous distributions, particularly distributions with heavier and lighter tails than the normal ones, such as Student-t, power exponential and logistic, among others. Estimation is performed by maximum penalized likelihood and by using natural cubic splines. We derive the penalized score functions and the penalized Fisher information matrices for the parameters in the model. A reweighted iterative process based on the back-fitting algorithm is derived for the parameter estimation and the inference is based on the penalized Fisher information matrix. We discuss the effective degrees of freedom estimation and procedures for selecting the smoothing parameter. A small simulation study is performed for assessing the empirical distribution of the parameter estimates obtained from partially linear models with AR(1) errors. Residual analysis and derivation of conformal normal curvatures of local influence for some perturbation schemes are also given. Finally, a real data set is analyzed under partially linear models with AR(1) symmetric errors.

Estudio de Monte Carlo para comparar 8 pruebas de normalidad sobre residuos de mínimos cuadrados ordinarios en presencia de procesos autorregresivos de primer orden

The objective of this study is to assess the statistical power and size of 8 normality tests in presence of first-order autoregressive errors and different simple sizes. Using a Monte Carlo experiment, the following tests were compared: Cramér-von Mises, Anderson-Darling, Lilliefors, Pearson, Shapiro-Wilk, Shapiro-Francia, Jarque-Bera and D’Agostino-Pearson. Our results show 4 relevant findings: First, an asymmetrical effect of autocorrelation on the power and size of the tests. Second, the statistical size of all tests is affected by the autocorrelation. Third, none of the tests has greater power than the others. Fourth, the power of the normality test decreases as sample size decreases.

Fitting nonlinear autoregressive models to describe coffee seed germination

Cumulative germination of coffee has a longitudinal behavior mathematically characterized by a sigmoidal model. In the seed germination evaluation, the study of the germination curve may contribute to better understanding of this process. The aim of this study was to evaluate the goodness of fit of Logistic and Gompertz models, with independent and first-order autoregressive errors structure, AR (1), in the description of coffee (Coffea arabica L.) line Catuai vermelho IAC 99 germination, at five different potential germination. The data used were from an experiment conducted in 2011 at the Seed Analysis Laboratory of the Federal University of Lavras. The Logistic and Gompertz nonlinear models were appropriately adjusted to the percentage germination data. The Gompertz model with first-order autoregressive errors structure was the best to describe the germination process

Necessary and sufficient conditions in the problem of D-optimal weighing designs with autocorrelated errors

Necessary and sufficient conditions determining D-optimality of chemical balance weighing design with three objects are proved under first-order autoregressive errors with negative autocorrelation. D-optimality of the design constructed by Li and Yang (2005) is also shown.

Modified Maximum Likelihood Estimation in Autoregressive Processes with Generalized Exponential Innovations

We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.

Bayesian modeling of autoregressive partial linear models with scale mixture of normal errors

Normality and independence of error terms are typical assumptions for partial linear models. However, these assumptions may be unrealistic in many fields, such as economics, finance and biostatistics. In this paper, a Bayesian analysis for partial linear model with first-order autoregressive errors belonging to the class of the scale mixtures of normal distributions is studied in detail. The proposed model provides a useful generalization of the symmetrical linear regression model with independent errors, since the distribution of the error term covers both correlated and thick-tailed distributions, and has a convenient hierarchical representation allowing easy implementation of a Markov chain Monte Carlo scheme. In order to examine the robustness of the model against outlying and influential observations, a Bayesian case deletion influence diagnostics based on the Kullback–Leibler (K–L) divergence is presented. The proposed method is applied to monthly and daily returns of two Chilean companies.

Diagnostics for a Linear Model with First-Order Autoregressive Symmetrical Errors

In this article, we focus on some diagnostics for linear regression model with first-order autoregressive and symmetrical errors. The symmetrical class includes both light- and heavy-tailed univariate symmetrical distributions, which offers a more flexible framework for modeling. Maximum likelihood estimates are computed via the Fisher-score method. Score statistic and its adjustment are proposed for testing autocorrelation of the random errors. Local influence diagnostics are also derived for the model under some usual perturbation schemes. The performances of the test statistics are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our diagnostic methods.