Estimating Brazilian Monthly GDP: a State-Space Approach

This paper has several original contributions. The first is to employ a superior interpolation method that enables to estimate, nowcast and forecast monthly Brazilian GDP for 1980-2012 in an integrated way; see Bernanke, Gertler and Watson (1997, Brookings Papers on Economic Activity). Second, along the spirit of Mariano and Murasawa (2003, Journal of Applied Econometrics), we propose and test a myriad of interpolation models and interpolation auxiliary series- all coincident with GDP from a business-cycle dating point of view. Based on these results, we finally choose the most appropriate monthly indicator for Brazilian GDP. Third, this monthly GDP estimate is compared to an economic activity indicator widely used by practitioners in Brazil - the Brazilian Economic Activity Index - (IBC-Br). We found that the our monthly GDP tracks economic activity better than IBC-Br. This happens by construction, since our state-space approach imposes the restriction (discipline) that our monthly estimate must add up to the quarterly observed series in any given quarter, which may not hold regarding IBC-Br. Moreover, our method has the advantage to be easily implemented: it only requires conditioning on two observed series for estimation, while estimating IBC-Br requires the availability of hundreds of monthly series. Third, in a nowcasting and forecasting exercise, we illustrate the advantages of our integrated approach. Finally, we compare the chronology of recessions of our monthly estimate with those done elsewhere.

Estimating brazilian monthly GDP: a state-space approach

This paper has several original contributions. The rst is to employ a superior interpolation method that enables to estimate, nowcast and forecast monthly Brazilian GDP for 1980-2012 in an integrated way; see Bernanke, Gertler and Watson (1997, Brookings Papers on Economic Activity). Second, along the spirit of Mariano and Murasawa (2003, Journal of Applied Econometrics), we propose and test a myriad of interpolation models and interpolation auxiliary series all coincident with GDP from a business-cycle dating point of view. Based on these results, we nally choose the most appropriate monthly indicator for Brazilian GDP. Third, this monthly GDP estimate is compared to an economic activity indicator widely used by practitioners in Brazil - the Brazilian Economic Activity Index - (IBC-Br). We found that the our monthly GDP tracks economic activity better than IBC-Br. This happens by construction, since our state-space approach imposes the restriction (discipline) that our monthly estimate must add up to the quarterly observed series in any given quarter, which may not hold regarding IBC-Br. Moreover, our method has the advantage to be easily implemented: it only requires conditioning on two observed series for estimation, while estimating IBC-Br requires the availability of hundreds of monthly series. Third, in a nowcasting and forecasting exercise, we illustrate the advantages of our integrated approach. Finally, we compare the chronology of recessions of our monthly estimate with those done elsewhere.

Estimating Brazilian monthly GDP: a state-space approach

This paper has several original contributions. The rst is to employ a superior interpolation method that enables to estimate, nowcast and forecast monthly Brazilian GDP for 1980-2012 in an integrated way; see Bernanke, Gertler and Watson (1997, Brookings Papers on Economic Activity). Second, along the spirit of Mariano and Murasawa (2003, Journal of Applied Econometrics), we propose and test a myriad of interpolation models and interpolation auxiliary series all coincident with GDP from a business-cycle dating point of view. Based on these results, we nally choose the most appropriate monthly indicator for Brazilian GDP. Third, this monthly GDP estimate is compared to an economic activity indicator widely used by practitioners in Brazil- the Brazilian Economic Activity Index - (IBC-Br). We found that the our monthly GDP tracks economic activity better than IBC-Br. This happens by construction, since our state-space approach imposes the restriction (discipline) that our monthly estimate must add up to the quarterly observed series in any given quarter, whichmay not hold regarding IBC-Br. Moreover, our method has the advantage to be easily implemented: it only requires conditioning on two observed series for estimation, while estimating IBC-Br requires the availability of hundreds of monthly series. Third, in a nowcasting and forecasting exercise, we illustrate the advantages of our integrated approach. Finally, we compare the chronology of recessions of our monthly estimate with those done elsewhere.

Estimating Brazilian monthly GDP: a state-space approach

The first contribution of this paper is to employ a superior interpolation method that enables to estimate, nowcast and forecast monthly Brazilian GDP for 1980-2012 in an integrated way; see Bernanke, Gertler and Watson (1997, Brookings Papers on Economic Activity). The second contribution, along the spirit of Mariano and Murasawa (2003, Journal of Applied Econometrics), is to propose and test a myriad of inter-polation models and interpolation auxiliary series all coincident with GDP from a business-cycle dating point of view. Based on these results, we finally choose the most appropriate monthly indicator for Brazilian GDP. Third, this monthly GDP estimate is compared to an economic activity indicator widely used by practitioners in Brazil - the Brazilian Economic Activity Index - (IBC-Br). We found that our monthly GDP tracks economic activity better than IBC-Br. This happens by construction, since our state-space approach imposes the restriction (discipline) that our monthly estimate must add up to the quarterly observed series in any given quarter, which may not hold regarding IBC-Br. Moreover, our method has the advantage to be easily implemented: it only requires conditioning on two observed series for estimation, while estimating IBC-Br requires the availability of hundreds of monthly series. The third contribution is to illustrate, in a nowcasting and forecasting exercise, the advantages of our integrated approach. Finally, we compare the chronology of recessions of our monthly estimate with those done elsewhere.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

An enriched radial point interpolation method based on weak-form and strong-form

In this article, an enriched radial point interpolation method (e-RPIM) is developed for computational mechanics. The conventional radial basis function (RBF) interpolation is novelly augmented by the suitable basis functions to reflect the natural properties of deformation. The performance of the enriched meshless RBF shape functions is first investigated using the surface fitting. The surface fitting results have proven that, compared with the conventional RBF, the enriched RBF interpolation has a much better accuracy to fit a complex surface than the conventional RBF interpolation. It has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF interpolation, but also can accurately reflect the deformation properties of problems. The system of equations for two-dimensional solids is then derived based on the enriched RBF shape function and both of the meshless strong-form and weak-form. A numerical example of a bar is presented to study the effectiveness and efficiency of e-RPIM. As an important application, the newly developed e-RPIM, which is augmented by selected trigonometric basis functions, is applied to crack problems. It has been demonstrated that the present e-RPIM is very accurate and stable for fracture mechanics problems.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.