Nonlinear Time Series Models Research Articles

Testing for the buffered autoregressive processes

This paper investigates a quasi-likelihood ratio (LR) test for the thresh- olds in buffered autoregressive processes. Under the null hypothesis of no threshold, the LR test statistic converges to a function of a centered Gaussian process. Un- der local alternatives, this LR test has nontrivial asymptotic power. A bootstrap method is proposed to obtain the critical value for the LR test. Simulation studies and an example are given to assess the performance of the test. The proof here is not standard and can be used in other non-linear time series models.

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Linking changes in eastern Bering Sea jellyfish populations to environmental factors via nonlinear time series models

Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520, USA Indiana University School of Medicine, Department of Biostatistics, Indianapolis, Indiana 46202, USA College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, USA Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington 98115, USA Joint Institute for the Study of the Atmosphere and Ocean, University of Washington, Seattle, Washington 98115, USA Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, USA

Mathematical and Quantitative Methods: Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series

Timo Terasvirta of Aarhus University reviews, “Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series” by Andrew C. Harvey. The Econlit abstract of this book begins: “Presents a theory for a class of nonlinear time series models that can deal with dynamic distributions, with an emphasis on models in which the conditional distribution of an observation may be heavy-tailed and the location and/or scale changes over time. Discusses statistical distributions and asymptotic theory; location; scale; location/scale models for nonnegative variables; dynamic kernel density estimation and time-varying quantiles; multivariate models, correlation, and association; and further directions in dynamic models. Harvey is Professor of Econometrics at the University of Cambridge and Fellow of Corpus Christi College, the Econometric Society, and the British Academy.”

Assessing DSGE Model Nonlinearities

We develop a new class of nonlinear time-series models to identify nonlinearities in the data and to evaluate nonlinear DSGE models. U.S. output growth and the federal funds rate display nonlinear conditional mean dynamics, while inflation and nominal wage growth feature conditional heteroskedasticity. We estimate a DSGE model with asymmetric wage/price adjustment costs and use predictive checks to assess its ability to account for nonlinearities. While it is able to match the nonlinear inflation and wage dynamics, thanks to the estimated downward wage/price rigidities, these do not spill over to output growth or the interest rate.

Forecasting Stock Prices With Linear And Nonlinear Settings: A Comparison

This paper is devoted to the application and comparison of linear (VAR) and nonlinear Multiple Adaptive Regression Splines (MARS) forecasting models, in estimating, evaluating, and selecting among linear and non-linear forecasting models for economic and financial time series. We argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. Nonlinear models reduce nonlinearity and Gaussianity in the residuals of the linear models. Linear models, however, demonstrate better forecasts than nonlinear. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models

This article introduces an automatic test for the correct specification of a vector autoregression (VAR) model. The proposed test statistic is a Portmanteau statistic with an automatic selection of the order of the residual serial correlation tested. The test presents several attractive characteristics: simplicity, robustness, and high power in finite samples. The test is simple to implement since the researcher does not need to specify the order of the autocorrelation tested and the proposed critical values are simple to approximate, without resorting to bootstrap procedures. In addition, the test is robust to the presence of conditional heteroscedasticity of unknown form and accounts for estimation uncertainty without requiring the computation of large-dimensional inverses of near-to-singularity covariance matrices. The basic methodology is extended to general nonlinear multivariate time series models. Simulations show that the proposed test presents higher power than the existing ones for models commonly employed in empirical macroeconomics and empirical finance. Finally, the test is applied to the classical bivariate VAR model for GNP (gross national product) and unemployment of Blanchard and Quah (1989) and Evans (1989). Online supplementary material includes proofs and additional details.

Fitting of self-exciting threshold autoregressive moving average nonlinear time-series model through genetic algorithm and development of out-of-sample forecasts

Self-exciting threshold autoregressive moving average (SETARMA) nonlinear time-series model is considered here. Sufficient conditions for invertibility and stationarity are derived. Parameter estimation algorithm is developed by employing real-coded genetic algorithm stochastic optimization procedure. A significant feature of the work done is that optimal out-of-sample forecasts up to three-step ahead and their forecast error variances are derived analytically. Relevant computer programs are written in statistical analysis system (SAS) and C. As an illustration, annual mackerel catch time-series data are considered. Forecast performance of the fitted model for hold-out data is evaluated by using Naive and Monte Carlo approaches. It is found that optimal out-of-sample forecast values are quite close to actual values and estimated variances are quite close to theoretical values. Superiority of the SETARMA model over the SETAR model for equal predictive ability through Diebold–Mariano test is also established.

Does restraining end effect matter in EMD-based modeling framework for time series prediction? Some experimental evidences

Following the “decomposition-and-ensemble” principle, the empirical mode decomposition (EMD)-based modeling framework has been widely used as a promising alternative for nonlinear and nonstationary time series modeling and prediction. The end effect, which occurs during the sifting process of EMD and is apt to distort the decomposed sub-series and hurt the modeling process followed, however, has been ignored in previous studies. Addressing the end effect issue, this study proposes to incorporate end condition methods into EMD-based decomposition and ensemble modeling framework for one- and multi-step ahead time series prediction. Four well-established end condition methods, Mirror method, Coughlin′s method, Slope-based method, and Rato′s method, are selected, and support vector regression (SVR) is employed as the modeling technique. For the purpose of justification and comparison, well-known NN3 competition data sets are used and four well-established prediction models are selected as benchmarks. The experimental results demonstrated that significant improvement can be achieved by the proposed EMD-based SVR models with end condition methods. The EMD–SBM–SVR model and EMD–Rato–SVR model, in particular, achieved the best prediction performances in terms of goodness of forecast measures and equality of accuracy of competing forecasts test.

Forecasting In One-Dimensional And Generalized Integrated Autoregressive Bilinear Time Series Models

In this paper, forecast of one-dimensional integrated autoregressive bilinear is compared with forecast of generalized integrated autoregressive bilinear model. We describe the method for estimation of these models and the forecast. It is also pointed out that for this class of non-linear time series models; it is possible to obtain optimal forecast. The estimation technique is illustrated with respect to a time series, and the optimal forecast of these time series are calculated. A comparison of these forecasts is made using the two models under study. The mean square error for forecast in generalized integrated autoregressive bilinear model is smaller than the mean square error for forecast in one-dimensional integrated autoregressive bilinear model. Though the two models are adequate for forecast when compared with the real series but forecast with generalized integrated autoregressive bilinear model is more adequate.Keywords: Optimal Forecast, Non-Linear Time Series Models, Bilinear Models, Estimation Technique, Mean Square Error.

A nonlinear, low data requirement model for producing spatially explicit fishery forecasts

AbstractSpatial variability can confound accurate estimates of catch per unit effort (CPUE), especially in highly migratory species. The incorporation of spatial structure into fishery stock assessment models should ultimately improve forecasts of stock biomass. Here, we describe a nonlinear time series model for producing spatially explicit forecasts of CPUE that does not require ancillary environmental or demographic data, or specification of a model functional form. We demonstrate this method using spatially resolved (1° × 1° cells) CPUE time series of North Pacific albacore in the California Current System. The spatial model is highly significant (P < 0.00001) and outperforms two spatial null models. We then create a spatial forecast map for years beyond the range of data. Such approaches can guide spatial management of resources and provide a complement to more data‐intensive, highly parameterized population dynamics and ecosystem models currently in use.

On nonergodicity for nonparametric autoregressive models

In this paper, we introduce a class of nonlinear time series models with random time delay under random environment, sufficient conditions for nonergodicity of these models are developed. The so-called Markovnization methods are used, that is, proper supplementary variables are added to a non-Markov process, then a new Markov process can be obtained.

On a constrained mixture vector autoregressive model

A mixture vector autoregressive model has recently been introduced to the literature. Although this model is a promising candidate for nonlinear multiple time series modeling, high dimensionality of the parameters and lack of method for computing the standard errors of estimates limit its application to real data. The contribution of this paper is threefold. First, a form of parameter constraints is introduced with an efficient EM algorithm for estimation. Second, an accurate method for computing standard errors is presented for the model with and without parameter constraints. Lastly, a hypothesis-testing approach based on likelihood ratio tests is proposed, which aids in the selection of unnecessary parameters and leads to the greater efficiency at the estimation. A case study employing U.S. Treasury constant maturity rates illustrates the applicability of the mixture vector autoregressive model with parameter constraints, and the importance of using a reliable method to compute standard errors.

Semiparametric estimation in triangular system equations with nonstationarity

A system of multivariate semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are assumed to be strictly exogenous. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary integrated time series. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is not consistent for the parametric component and a semiparametric instrumental variable (SIV) method is proposed instead. Under certain regularity conditions, the SIV estimator of the parametric component is shown to have a limiting normal distribution. The rate of convergence in the parametric component depends on the properties of the regressors. The conventional n rate may apply even when nonstationarity is involved in both sets of regressors.

Advertising Soft Drinks to Children: Are Voluntary Restrictions Effective?

ABSTRACTUsing nonlinear time series models, the authors explore the effects of an industry‐led initiative to have firms voluntarily restrict television advertising of carbonated soft drinks to children. They find that the market leader reduces its advertising to both adults and children and the second largest firm reduces advertising to adults. Advertising by a nonparticipating firm, however, increased for adults following the ban. The results emphasize the potential benefits and difficulty of coordinating cooperative behavior in this type of industry. Such policy strategies may be more effective directed at industries and not at individual firms.

Using the Reversible Jump MCMC Procedure for Identifying and Estimating Univariate TAR Models

One way that has been used for identifying and estimating threshold autoregressive (TAR) models for nonlinear time series follows the Markov chain Monte Carlo (MCMC) approach via the Gibbs sampler. This route has major computational difficulties, specifically, in getting convergence to the parameter distributions. In this article, a new procedure for identifying a TAR model and for estimating its parameters is developed by following the reversible jump MCMC procedure. It is found that the proposed procedure conveys a Markov chain with convergence properties.

Nonparametric Specification Testing in Nonlinear and Nonstationary Time Series Models: Theory and Practice

In this paper, we consider some specification testing problems in nonlinear time series models with nonstationarity. We propose using a nonparametric kernel test for specifying whether the regression is of a known parametric nonlinear form. The power of the proposed nonparametric test is systematically studied and an asymptotic distribution of the test statistic is shown to depend on the asymptotic behavior of the so called distance function under a sequence of general semiparametric local alternatives. The asymptotic theory developed in this paper differs from existing work on nonparametric specification testing in the stationary time series case. In order to implement the proposed test in practice, a computer-intensive bootstrap simulation procedure is introduced and asymptotic approximations for both the size and power functions are established. Furthermore, the bandwidth involved in the test is selected by maximizing the power while the size is controlled by a significance level. Meanwhile, both simulated and real data examples are provided to illustrate the proposed theory and methodology.

An efficient sampling scheme for dynamic generalized models

A multimove sampling scheme for the state parameters of non-Gaussian and nonlinear dynamic models for univariate time series is proposed. This procedure follows the Bayesian framework, within a Gibbs sampling algorithm with steps of the Metropolis---Hastings algorithm. This sampling scheme combines the conjugate updating approach for generalized dynamic linear models, with the backward sampling of the state parameters used in normal dynamic linear models. A quite extensive Monte Carlo study is conducted in order to compare the results obtained using our proposed method, conjugate updating backward sampling (CUBS), with those obtained using some algorithms previously proposed in the Bayesian literature. We compare the performance of CUBS with other sampling schemes using two real datasets. Then we apply our algorithm in a stochastic volatility model. CUBS significantly reduces the computing time needed to attain convergence of the chains, and is relatively simple to implement.

Fast Recursive Identification Algorithm for Nonlinear Time Series model based on improved Extreme Learning Machine

Fast Recursive Identification Algorithm for Nonlinear Time Series model based on improved Extreme Learning Machine

Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.