Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Residual-based Inference for Common Nonlinear Features

This paper investigates common nonlinear features in multivariate nonlinear autore-gressive models via testing the estimated residuals. A Wald-type test is proposed and itis asymptotically Chi-squared distributed. Simulation studies are given to examine thefinite-sample properties of the proposed test.

Common Features in Vector Nonlinear Time Series Models

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.

Three principles of competitive nonlinear pricing

We make three contributions to the theory of contracting under asymmetric information. First, we establish a competitive analog to the revelation principIe which we call the implementation principIe. This principIe provides a complete characterization of all incentive compatible, indirect contracting mechanisms in terms of contract catalogs (or menus), and allows us to conclude that in competi tive contracting situations, firms in choosing their contracting strategies can restrict attention, without loss of generality, to contract catalogs. Second, we establish a competi tive taxation principIe. This principIe, a refinement of the implementation principIe, provides a complete characterization of all implementable nonlinear pricing schedules in terms of product-price catalogs and allows us to reduce any game played over nonlinear pricing schedules to a strategically equivalent game played over product-price catalogs. Third, using the competitive taxation principIe and a recent result due to Reny (1999) on the existence of Nash equilibria in discontinuous games, we demonstrate the existence of a N ash equilibrium for the mixed extension of the nonlinear pricing game.

Moral hazard and nonlinear pricing in a general equilibrium model

The paper analyzes a two period general equilibrium model with individual risk and moral hazard. Each household faces two individual states of nature in the second period. These states solely differ in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period households choose a non-observable action. Higher leveis of action give higher probability of the good state of nature to occur, but lower leveIs of utility. Households have access to an insurance market that allows transfer of income across states of oature. I consider two models of financiaI markets, the price-taking behavior model and the nonlínear pricing modelo In the price-taking behavior model suppliers of insurance have a belief about each household's actíon and take asset prices as given. A variation of standard arguments shows the existence of a rational expectations equilibrium. For a generic set of economies every equilibrium is constraíned sub-optímal: there are commodity prices and a reallocation of financiaI assets satisfying the first period budget constraint such that, at each household's optimal choice given those prices and asset reallocation, markets clear and every household's welfare improves. In the nonlinear pricing model suppliers of insurance behave strategically offering nonlinear pricing contracts to the households. I provide sufficient conditions for the existence of equilibrium and investigate the optimality properties of the modeI. If there is a single commodity then every equilibrium is constrained optimaI. Ir there is more than one commodity, then for a generic set of economies every equilibrium is constrained sub-optimaI.

Existence of nash equilibrium in competitive nonlinear pricing games with adverse selection

We show that for a large class of competitive nonlinear pricing games with adverse selection, the property of better-reply security is naturally satisfied - thus, resolving via a result due to Reny (1999) the issue of existence of Nash equilibrium for a large class of competitive nonlinear pricing games.

Nonlinear pricing beyond the demand profile approach

Wilson [16] introduced a general methodology to deal with monopolistic pricing in situations where customers have private information on their tastes (‘types’). It is based on the demand profile of customers: For each nonlinear tariff by the monopolist the demand at a given level of product (or quality) is the measure of customers’ types whose marginal utility is at least the marginal tariff (‘price’). When the customers’ marginal utility has a natural ordering (i.e., the Spence and Mirrlees Condition), such demand profile is very easy to perform. In this paper we will present a particular model with one-dimensional type where the Spence and Mirrlees condition (SMC) fails and the demand profile approach results in a suboptimal solution for the monopolist. Moreover, we will suggest a generalization of the demand profile procedure that improves the monopolist’s profit when the SMC does not hold.

Forecast comparison with nonlinear methods for brazilian industrial production

Este trabalho avalia as previsões de três métodos não lineares — Markov Switching Autoregressive Model, Logistic Smooth Transition Autoregressive Model e Autometrics com Dummy Saturation — para a produção industrial mensal brasileira e testa se elas são mais precisas que aquelas de preditores naive, como o modelo autorregressivo de ordem p e o mecanismo de double differencing. Os resultados mostram que a saturação com dummies de degrau e o Logistic Smooth Transition Autoregressive Model podem ser superiores ao mecanismo de double differencing, mas o modelo linear autoregressivo é mais preciso que todos os outros métodos analisados.

Forecast comparison with nonlinear methods for Brazilian industrial production

This work assesses the forecasts of three nonlinear methods | Markov Switching Autoregressive Model, Logistic Smooth Transition Auto-regressive Model, and Auto-metrics with Dummy Saturation | for the Brazilian monthly industrial production and tests if they are more accurate than those of naive predictors such as the autoregressive model of order p and the double di erencing device. The results show that the step dummy saturation and the logistic smooth transition autoregressive can be superior to the double di erencing device, but the linear autoregressive model is more accurate than all the other methods analyzed.

Egg production curve fitting using nonlinear models for selected and nonselected lines of White Leghorn hens

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparison of different nonlinear functions to describe Nelore cattle growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Controlador preditivo não linear aplicado ao controle de golfadas em processos de produção de petróleo

Slugging is a well-known slugging phenomenon in multiphase flow, which may cause problems such as vibration in pipeline and high liquid level in the separator. It can be classified according to the place of its occurrence. The most severe, known as slugging in the riser, occurs in the vertical pipe which feeds the platform. Also known as severe slugging, it is capable of causing severe pressure fluctuations in the flow of the process, excessive vibration, flooding in separator tanks, limited production, nonscheduled stop of production, among other negative aspects that motivated the production of this work . A feasible solution to deal with this problem would be to design an effective method for the removal or reduction of the system, a controller. According to the literature, a conventional PID controller did not produce good results due to the high degree of nonlinearity of the process, fueling the development of advanced control techniques. Among these, the model predictive controller (MPC), where the control action results from the solution of an optimization problem, it is robust, can incorporate physical and /or security constraints. The objective of this work is to apply a non-conventional non-linear model predictive control technique to severe slugging, where the amount of liquid mass in the riser is controlled by the production valve and, indirectly, the oscillation of flow and pressure is suppressed, while looking for environmental and economic benefits. The proposed strategy is based on the use of the model linear approximations and repeatedly solving of a quadratic optimization problem, providing solutions that improve at each iteration. In the event where the convergence of this algorithm is satisfied, the predicted values of the process variables are the same as to those obtained by the original nonlinear model, ensuring that the constraints are satisfied for them along the prediction horizon. A mathematical model recently published in the literature, capable of representing characteristics of severe slugging in a real oil well, is used both for simulation and for the project of the proposed controller, whose performance is compared to a linear MPC

Investigation of the two-photon absorption cross-section in perylene tetracarboxylic derivatives: Nonlinear spectra and molecular structure

We investigated the 2PA absorption spectrum of a family of perylene tetracarboxylic derivatives ( PTCDs): bis( benzimidazo) perylene ( AzoPTCD), bis( benzimidazo) thioperylene ( Monothio BZP), n-pentylimidobenzimidazoperylene ( PazoPTCD), and bis( n-butylimido) perylene ( BuPTCD). These compounds present extremely high two-photon absorption, which makes them attractive for applications in photonics devices. The two-photon absorption cross-section spectra of perylene derivatives obtained via Z-scan technique were fitted by means of a sum-over-states ( SOS) model, which described with accuracy the different regions of the 2PA cross-section spectra. Frontier molecular orbital calculations show that all molecules present similar features, indicating that nonlinear optical properties in PTCDs are mainly determined by the central portion of the molecule, with minimal effect from the lateral side groups. In general, our results pointed out that the differences in the 2PA cross-sections among the compounds are mainly due to the nonlinearity resonance enhancement.

About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

This work summarizes the HdHr group of Hermitian integration algorithms for dynamic structural analysis applications. It proposes a procedure for their use when nonlinear terms are present in the equilibrium equation. The simple pendulum problem is solved as a first example and the numerical results are discussed. Directions to be pursued in future research are also mentioned. Copyright (C) 2009 H.M. Bottura and A. C. Rigitano.