Information criteria for nonlinear time series models

AbstractIn this paper the performance of different information criteria for simultaneous model class and lag order selection is evaluated using simulation studies. We focus on the ability of the criteria to distinguish linear and nonlinear models. In the simulation studies, we consider three different versions of the commonly known criteria AIC, SIC and AICc. In addition, we also assess the performance of WIC and evaluate the impact of the error term variance estimator. Our results confirm the findings of different authors that AIC and AICc favor nonlinear over linear models, whereas weighted versions of WIC and all versions of SIC are able to successfully distinguish linear and nonlinear models. However, the discrimination between different nonlinear model classes is more difficult. Nevertheless, the lag order selection is reliable. In general, information criteria involving the unbiased error term variance estimator overfit less and should be preferred to using the usual ML estimator of the error term variance.

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Parametric bootstrap estimators for hybrid inference in forest inventories

Forestry An International Journal of Forest Research ◽

10.1093/forestry/cpx048 ◽

2017 ◽

Vol 91 (3) ◽

pp. 354-365 ◽

Cited By ~ 7

Author(s):

Mathieu Fortin ◽

Rubén Manso ◽

Robert Schneider

Keyword(s):

Multiple Imputation ◽

Nonlinear Models ◽

Parametric Bootstrap ◽

Simulation Studies ◽

Variance Estimator ◽

Resampling Methods ◽

Forest Inventories ◽

Point Estimator ◽

Complex Models ◽

High Level

Abstract In forestry, the variable of interest is not always directly available from forest inventories. Consequently, practitioners have to rely on models to obtain predictions of this variable of interest. This context leads to hybrid inference, which is based on both the probability design and the model. Unfortunately, the current analytical hybrid estimators for the variance of the point estimator are mainly based on linear or nonlinear models and their use is limited when the model reaches a high level of complexity. An alternative consists of using a variance estimator based on resampling methods (Rubin, D. B. (1987). Multiple imputation for nonresponse surveys. John Wiley & Sons, Hoboken, New Jersey, USA). However, it turns out that a parametric bootstrap (BS) estimator of the variance can be biased in contexts of hybrid inference. In this study, we designed and tested a corrected BS estimator for the variance of the point estimator, which can easily be implemented as long as all of the stochastic components of the model can be properly simulated. Like previous estimators, this corrected variance estimator also makes it possible to distinguish the contribution of the sampling and the model to the variance of the point estimator. The results of three simulation studies of increasing complexity showed no evidence of bias for this corrected variance estimator, which clearly outperformed the BS variance estimator used in previous studies. Since the implementation of this corrected variance estimator is not much more complicated, we recommend its use in contexts of hybrid inference based on complex models.

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Fast nonlinear Froude–Krylov force calculation for prismatic floating platforms: a wave energy conversion application case

Journal of Ocean Engineering and Marine Energy ◽

10.1007/s40722-021-00212-z ◽

2021 ◽

Author(s):

Giuseppe Giorgi ◽

Sergej Sirigu ◽

Mauro Bonfanti ◽

Giovanni Bracco ◽

Giuliana Mattiazzo

Keyword(s):

Real Time ◽

Wave Energy ◽

Linear Models ◽

Nonlinear Models ◽

Internal Degree ◽

Parameters Optimization ◽

Energy Field ◽

Floating Platforms ◽

Force Calculation ◽

The Impact

AbstractComputationally fast and accurate mathematical models are essential for effective design, optimization, and control of wave energy converters. However, the energy-maximising control strategy, essential for reaching economic viability, inevitably leads to the violation of linearising assumptions, so the common linear models become unreliable and potentially unrealistic. Partially nonlinear models based on the computation of Froude–Krylov forces with respect to the instantaneous wetted surface are promising and popular alternatives, but they are still too slow when floaters of arbitrary complexity are considered; in fact, mesh-based spatial discretisation, required by such geometries, becomes the computational bottle-neck, leading to simulations 2 orders of magnitude slower than real-time, unaffordable for extensive iterative optimizations. This paper proposes an alternative analytical approach for the subset of prismatic floating platforms, common in the wave energy field, ensuring computations 2 orders of magnitude faster than real-time, hence 4 orders of magnitude faster than state-of-the-art mesh-based approaches. The nonlinear Froude–Krylov model is used to investigate the nonlinear hydrodynamics of the floater of a pitching wave energy converter, extracting energy either from pitch or from an inertially coupled internal degree of freedom, especially highlighting the impact of state constraints, controlled/uncontrolled conditions, and impact on control parameters’ optimization, sensitivity and effectiveness.

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Forecasting Brazilian output and its turning points in the presence of breaks: a comparison of linear and nonlinear models

Estudos Econômicos (São Paulo) ◽

10.1590/s0101-41612006000100001 ◽

2006 ◽

Vol 36 (1) ◽

pp. 5-46 ◽

Cited By ~ 2

Author(s):

Brisne J. V. Céspedes ◽

Marcelle Chauvet ◽

Elcyon C. R. Lima

Keyword(s):

Business Cycle ◽

Structural Breaks ◽

Linear Models ◽

Nonlinear Models ◽

Markov Switching Models ◽

Real Gdp ◽

Switching Models ◽

Forecasting Performance ◽

Out Of Sample ◽

Linear And Nonlinear

This paper compares the forecasting performance of linear and nonlinear models under the presence of structural breaks for the Brazilian real GDP growth. The Markov switching models proposed by Hamilton (1989) and its generalized version by Lam (1990) are applied to quarterly GDP from 1975:1 to 2000:2 allowing for breaks at the Collor Plans. The probabilities of recessions are used to analyze the Brazilian business cycle. The in-sample and out-of-sample forecasting ability of growth rates of GDP of each model is compared with linear specifications and with a non-parametric rule. We find that the nonlinear models display a better forecasting performance than linear models. The specifications with the presence of structural breaks are important in obtaining a representation of the Brazilian business cycle and their inclusion improves considerably the models forecasting performance within and out-of-sample.

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A Survey of Some Recent Results on Nonlinear Fault Tolerant Control

Mathematical Problems in Engineering ◽

10.1155/2010/586169 ◽

2010 ◽

Vol 2010 ◽

pp. 1-25 ◽

Cited By ~ 34

Author(s):

Mouhacine Benosman

Keyword(s):

Control Theory ◽

Linear Models ◽

Fault Tolerant ◽

Nonlinear Models ◽

Fault Tolerant Control ◽

Operating Life ◽

Linear And Nonlinear ◽

The One

Fault tolerant control (FTC) is the branch of control theory, dealing with the control of systems that become faulty during their operating life. Following the systems classification, as linear and nonlinear models, FTC can be classified in two different groups, linear FTC (LFTC) dealing with linear models, and the one of interest to us in this paper, nonlinear FTC (NFTC), which deals with nonlinear models. We present in this paper a survey of some of the results obtained in these last years on NFTC.

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Nonlinearities In Stock Return Prediction: Evidence From South Africa

Journal of Applied Business Research (JABR) ◽

10.19030/jabr.v28i6.7341 ◽

2012 ◽

Vol 28 (6) ◽

pp. 1253 ◽

Cited By ~ 1

Author(s):

Kathleen Hodnett ◽

Heng-Hsing Hsieh ◽

Paul Van Rensburg

Keyword(s):

Cross Section ◽

Linear Models ◽

Nonlinear Models ◽

Learning Rule ◽

Equity Returns ◽

Neural Network Modeling ◽

Font Size ◽

Stock Selection ◽

Linear And Nonlinear ◽

The Cross

This research investigates the relationship between firm-specific style attributes and the cross-section of equity returns on the JSE Securities Exchange (JSE) over the period from 1 January 1997 to 31 December 2007. Both linear and nonlinear stock selection models are constructed based on the cross-section of equity returns with firm-specific attributes as model inputs. Both linear and nonlinear models identify book-value-to-price and cash flow-to-price as significant styles attributes that distinguish near-term future share returns on the JSE. The risk-adjusted performance of the nonlinear models is found to be comparable with that of linear models. In terms of artificial neural network modeling, the extended Kalman filter learning rule is found to outperform the traditional backpropagation approach. This finding is consistent with our prior findings on global stock selection.

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Modeling Flutter Using Deflection-Dependent Strain-Rate Damping

Volume 13: Sound, Vibration and Design ◽

10.1115/imece2010-40622 ◽

2010 ◽

Cited By ~ 1

Author(s):

Soroush Norouzi ◽

Siamak Arzanpour

Keyword(s):

Strain Rate ◽

Linear Models ◽

Nonlinear Models ◽

The Other ◽

Large Deflections ◽

Critical Importance ◽

Nonlinear Simulation ◽

The Past ◽

Dependent Strain ◽

Linear And Nonlinear

Flutter is a flow-induced unstable motion in structures that has drawn researchers’ attention in the past decades due to its presence in numerous applications including aviation. Linear and nonlinear models of flutter have been developed. Linear models are simple and accurate for predicting the critical velocity at which flutter occurs. However, they are not capable of describing the post-flutter behavior of structures. Nonlinear models, on the other hand, can properly demonstrate the unstable motion accompanied with the occurrence of flutter but they are highly complicated. In fact, numerical solution of these equations requires extensive computations. As a result, having a model that is both simple and valid for post-flutter simulations is of critical importance. Linear models lose their accuracy when large deflections take place in the structure. This is when the unconsidered tensions that oppose large deflections come into play and render the behavior of the structure nonlinear. Usually, a type of damping relative to strain-rate is assumed for modeling structures under flutter. This paper introduces a deflection-dependant strain-rate damping coefficient to the linear flutter model, so as the deflections grow the restraining forces increase to limit the motion. The new sets of equations are derived and simulations are conducted to ensure the capability of the model to capture the post-flutter behavior. Results are then compared with the results of nonlinear simulation to demonstrate the new model’s compliance with those of nonlinearly-modeled systems.

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The impact of energy consumption on economic growth: Evidence from linear and nonlinear models in Taiwan

Energy ◽

10.1016/j.energy.2006.01.017 ◽

2007 ◽

Vol 32 (12) ◽

pp. 2282-2294 ◽

Cited By ~ 106

Author(s):

Chien-Chiang Lee ◽

Chun-Ping Chang

Keyword(s):

Economic Growth ◽

Energy Consumption ◽

Nonlinear Models ◽

Linear And Nonlinear ◽

The Impact

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Linear and nonlinear QSAR models of acute intravenous toxicity to mice for organic chemicals

Biomeditsinskaya Khimiya ◽

10.18097/pbmc20125804357 ◽

2012 ◽

Vol 58 (4) ◽

pp. 357-371 ◽

Cited By ~ 1

Author(s):

O.A. Raevsky ◽

E.A. Liplavskaya ◽

A.V. Yarkov ◽

O.E. Raevskaya ◽

A.P. Worth

Keyword(s):

Functional Group ◽

Linear Models ◽

Nonlinear Models ◽

Statistical Characteristics ◽

Organic Chemicals ◽

Statistical Parameters ◽

Qsar Analysis ◽

Qsar Models ◽

Linear And Nonlinear ◽

Small Clusters

QSAR analysis of acute intravenous toxicity to mice for 68 monofunctional chemicals is presented. There compounds represents seven classes of organic chemicals: hydrocarbons (6 chemicals), alcohols (13), amides (22), amines (12), ethers (5), ketones (7), nitriles (3). Preliminary consideration of data for these chemicals showed that it is necessary to consider not only linear toxicity - descriptors relationships, but also nonlinear models. The linear and nonlinear QSAR models were considered for each from indicated classes of organic chemicals. Analogical models were constructed for whole subset of monofunctional chemicals. The statistical parameters and robustness of nonlinear models are essential better then statistics of linear models. Replacing a lipophilicity descriptor with molecular polarizability and H-bond ability in nonlinear models permits also to improve statistical characteristics. Clearly, if relationships between the intravenous toxicity of compounds bearing only a single functional group and lipophilicity are nonlinear, then similar relationships must be considered with compounds containing more than one functional group. To check up this idea whole set of small clusters containing structure relative compounds with few functional groups was examined from position of linear and nonlinear relationships between toxicity and lipophilicity. It was estimated in most causes advantages of nonlinear models.

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How well do linear and nonlinear time series models’ forecasts compete with international economic organizations?

Business & Economic Review ◽

10.22547/ber/12.3.2 ◽

2020 ◽

Vol 12 (3) ◽

pp. 23-70

Author(s):

Tayyab Raza Fraz ◽

Javed Iqbal ◽

Mudassir Uddin

Keyword(s):

International Economic ◽

Time Series ◽

Linear Models ◽

Nonlinear Models ◽

Nonlinear Time Series ◽

Time Series Models ◽

Macroeconomic Variables ◽

The Past ◽

Economic Organizations ◽

Linear And Nonlinear

This paper evaluates the forecasting performance of linear and non-linear time series models of some macroeconomic variables viz a viz the forecasts outlook of these variables generated by professionals in international economic organizations i.e. the International Monetary Fund (IMF) and the Organization of Economic Cooperation and Development (OECD). Many time series and econometrics models are used to forecast financial and macroeconomic variables. The accuracy of such forecasts depends crucially on careful handling of nonlinearity present in the time series. The debate of forecasting ability of linear vs nonlinear models is far from settled. These models use the past patterns of the economic time series to infer the parameters of the underlying stochastic process and use them to make forecasts. In doing so these models use only the information contained in the past data. However the economists working in professional international economic organizations not only look at the past trends but use the condition of local and global economy prevailing at the time and expected future path of economies as well as their professional expertise and judgment to arrive at forecasts of macroeconomic variables. However the specific underlying models and methodology used by the economists generating these forecast is usually not communicated to the public. In comparison to the forecasts of these organizations the time series models are well developed and accessible to researchers working anywhere around the globe. Thus it is an interesting task to compare the foresting ability of linear and nonlinear time series models. This paper aims at comparing the forecasts from these models to assess how well they compete with forecasts generated from the professional economists employed by international economic organizations. The nonlinear models employed in this study are quite well known namely the Self Exciting Threshold Autoregressive (SETAR) model and the Markov Switching Autoregressive (MSAR) model. The linear models employed are the AR and ARMA models. The paper have used annual data of three macroeconomic time series variables GDP growth, consumer price inflation and exchange rate of G7 countries i.e. Canada, France, Germany, Italy, Japan, United Kingdom (UK) and United States of America (USA) as well as an emerging south Asian economy namely Pakistan. Three forecast accuracy criteria i.e. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) are employed and the statistical significance of difference in forecasts is assessed using the Diebold-Mariono test. The results show that the forecasting ability of nonlinear Regime Switching models SETAR and MSAR is superior to the linear models. Further, although the point forecasts of linear and nonlinear models are not superior to that of economic organizations but in more than 60 percent of the cases considered the forecasting accuracy of two sets of forecast is not statistically significantly different.

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The influence of diurnal temperature range on the incidence of respiratory syncytial virus in Japan

Epidemiology and Infection ◽

10.1017/s0950268814001575 ◽

2014 ◽

Vol 143 (4) ◽

pp. 813-820 ◽

Cited By ~ 4

Author(s):

D. ONOZUKA

Keyword(s):

Respiratory Syncytial Virus ◽

Diurnal Temperature Range ◽

Linear Models ◽

Negative Binomial ◽

Nonlinear Models ◽

Quantitative Evidence ◽

Diurnal Temperature ◽

Temperature Range ◽

Syncytial Virus ◽

The Impact

SUMMARYThe incidence of respiratory syncytial virus (RSV) has been reported to exhibit seasonal variation. However, the impact of diurnal temperature range (DTR) on RSV has not been investigated. After acquiring data related to cases of RSV and weather parameters of DTR in Fukuoka, Japan, between 2006 and 2012, we used negative binomial generalized linear models and distributed lag nonlinear models to assess the possible relationship between DTR and RSV cases, adjusting for confounding factors. Our analysis revealed that the weekly number of RSV cases increased with a relative risk of 3·30 (95% confidence interval 1·65–6·60) for every 1°C increase in DTR. Our study provides quantitative evidence that the number of RSV cases increased significantly with increasing DTR. We suggest that preventive measures for limiting the spread of RSV should be considered during extended periods of high DTR.

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