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The purpose of this study is to establish the complete assessment of flexible pavement maintenance activities carried out from Sungai Petani KM107.90 to Alor Setar KM51.40, Section N2,North South Expressway Northern Region. The assessment includes the visual inspection to determine the rating criteria for each defect found on the flexible pavement and the determination of proper rehabilitation work along Section N2 by referring to Inspection Manual for Pavement Maintenance Management System – PLUS Bhd and OPUS NMM NRO and Buku Panduan Pemeriksaan Penyelenggaraan Bulanan Lebuhraya-Lembaga Lebuhraya Malaysia (LLM). Quality Assurance and Quality Control (QA/QC) practice also been incorporated throughout the assessment as listed in Method Statement in Work Order and Standard Specification for Road Works JKR/SPJ/2008-S4 Fexible Pavement. It is including before, during and after rehabilitation work is implemented. From the visual inspection, cracking recorded the highest percentage of the defect found on north bound with 32%, while south bound recorded as 44%. Both are categorized in rating C condition which require repairs for user comfort which mill and pave method been chosen for repairing works after considering several factors; such as optimum time and cost. A good assessment at defected area will increase the life span of the pavement and minimize the overall maintenance cost.

This paper considers the uniform strong consistency of the error cumulative distribution function (CDF) estimator. Under appropriate assumptions, the classical Glivenko-Cantelli Theorem is obtained for the residual based empirical error CDF in the nonlinear autoregressive time series.

In time series modeling consistent criteria like Bayesian Information Criterion (BIC) outperform in terms of predictability loss-efficient criteria like Akaike Information Criterion (AIC) when data are generated by a finite-order autoregressive process, and the reverse is true when data are generated by an infinite-order autoregressive process. Since in practice we don’t know the data-generating process, it is useful to have an adaptive criterion that behaves as either a consistent or just as a loss-efficient criterion, whichever performs better. Here we derive such a criterion. Moreover, our criterion is adaptive to effective sample sizes and not sensitive to maximum a priori determined order limits.

This paper considers the stochastic systems described by the autoregressive output error autoregressive (AR-OEAR) models. The AR-OEAR model is a special output error model which has an extra autoregressive term of the output signal. Basing on the auxiliary model idea, the recursive method and the iterative principle, the auxiliary model based recursive and iterative least squares algorithms are proposed to estimate the parameters of the autoregressive output error autoregressive system which contains the autoregressive output error system model and the autoregressive noise model, respectively. The simulation results indicate that the proposed algorithms can work well.

We present a solution to problems where the response variable is a count, a rate or binary using a generalised linear space–time autoregressive model with space–time autoregressive disturbances (GLSTARAR). The possibility to test the fixed effect specification against the random effect specification of the panel data model is extended to include space–time error autocorrelation or a space–time lagged dependent variable. Space-time generalised estimating equations are used to estimate the spatio-temporal parameters in the model. We also present a measure of goodness of fit, and show the pseudo-best linear unbiased predictor for prediction purposes. Additionally, we propose a joint space–time modelling of mean and dispersion to give a solution when the variance is not constant. In the application, we use social, economic, geographic and state presence variables for 32 Colombian departments in order to analyse the relationship between the number of armed actions (AAs) per 1000 km2 committed by the guerrillas...

Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.

Summary In the hydrology studies, it is well known that the river flows are affected by various factors, and therefore the dynamics in their associated time series are complicated and have nonlinear behaviors. In an empirical study, we investigate the capability of five classes of nonlinear time series models, namely Threshold Autoregressive (TAR), Smooth Transition Autoregressive (STAR), Exponential Autoregressive (EXPAR), Bilinear Model (BL) and Markov Switching Autoregressive (MSAR) to capture the dynamics in the Colorado river discharge time series. Least Squares (LS) and Maximum Likelihood (ML) methods are employed to estimate parameters of the models. For model comparison three criteria, namely loglikelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are calculated. The results show that a self-exciting TAR (SETAR) model performs better than other four competing models. To forecast future river discharge values an iterative method is applied and forecasting confidence intervals are constructed. The out-of-sample 1-day to 5-day ahead forecasting performances of the models based on ten forecast accuracy measures are evaluated. Comparing verification metrics of all models, SETAR model presents the best forecasting performance.

Linear autoregressive (LAR) models poorly predict asset prices in nonlinear, regime-switching markets. In this article, the authors use SETAR, a threshold model that accounts for nonlinearities, to test for the existence of regime-switching in global equity markets. A comparison of SETAR’s predictive power against that of LAR models suggests that SETAR yields more accurate long forecasts, in both emerging and developed stock markets. The authors discuss extensions of threshold models into portfolio management, corporate valuation, and the long-term forecasting of financial indicators.

We propose a gradient radial basis function based varying-coefficient autoregressive (GRBF-AR) model for modeling and predicting time series that exhibit nonlinearity and homogeneous nonstationarity. This GRBF-AR model is a synthesis of the gradient RBF and the functional-coefficient autoregressive (FAR) model. The gradient RBFs, which react to the gradient of the series, are used to construct varying coefficients of the FAR model. The Mackey-Glass chaotic time series are used to evaluate the performance of the proposed method. It is shown that the GRBF-AR model not only achieves much more parsimonious structure but also much better prediction performance than that of GRBF network.

In this article, a new chaotic functional-coefficient nonlinear autoregressive time series model is formulated. Asymptotic stability of the equilibria of the skeleton is studied. Complex dynamics of the proposed model are investigated by means of the bifurcations, time series diagrams, and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon are also discussed via simulation. Two chaotic indicators, namely, the fractal dimension and the Lyapunov exponent methods are investigated for the model.

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model.

This work proposes a method to find the set of the most influential lags and the rule structure of a Takagi---Sugeno---Kang (TSK) fuzzy model for time series applications. The proposed method resembles the techniques that prioritize lags, evaluating the proximity of nearby samples in the input space using the closeness of the corresponding target values. Clusters of samples are generated, and the consistency of the mapping between the predicted variable and the set of candidate past values is evaluated. A TSK model is established, and possible redundancies in the rule base are avoided. The proposed method is evaluated using simulated and real data. Several simulation experiments were conducted for five synthetic nonlinear autoregressive processes, two nonlinear vector autoregressive processes and eight benchmark time series. The results show a competitive performance in the mean square error and a promising ability to find a proper set of lags for a given autoregressive process.

Purpose – The purpose of this study is to ascertain whether nonlinearities could be present in electricity loads observed in subtropical environments, where none or little heating is required, and whether threshold autoregressive (TAR)-type regime switching models could be advantageous in the modeling of those loads. Design/methodology/approach – The actual observed load of a Brazilian regional electricity distributor from January 2013 to August 2012 was modeled using a popularly employed ARMA model for reference, and smooth and non-smooth TAR transition (non-linear) models were used as non-linear regime switching models. Findings – Evidence of nonlinearities were found in the load series, and evidence was also found on the intrinsic resistance of this type of models to structural breaks in the data. Additionally, to reacting well to asymmetries in the data, these models avoid the use of exogenous variables. Altogether, this could prove to be a definite advantage of the use of such model alternatives. Research limitations/implications – However, even if the present work may have been limited by the observation frequency of the available data, it appears TAR models appear to be a viable alternative to forecasting short-term electricity loads. Nonetheless, additional research is required to achieve a higher accuracy of forecast data. Practical implications – If such models can be successfully used, it will be a great advantage for electricity generators, as the computational effort involved in the use of such models is not significantly larger than regular linear ones. Originality/value – To our knowledge, this type of research has not yet been made with subtropical/tropical electricity load data.

This article focuses on exponential autoregressive time series models. A key feature of these models is that the observations have marginal exponential distributions. The models are described, and estimation of the model parameters and prediction are discussed. A review of other related models is also included. Keywords: exponential; Weibull; gamma; Laplace distributions; autoregressive; moving average models; conditional least squares estimation; prediction

This article proposes a novel stochastic volatility (SV) model that draws from the existing literature on autoregressive SV models, aggregation of autoregressive processes, and Bayesian nonparametric modeling to create a SV model that can capture long-range dependence. The volatility process is assumed to be the aggregate of autoregressive processes, where the distribution of the autoregressive coefficients is modeled using a flexible Bayesian approach. The model provides insight into the dynamic properties of the volatility. An efficient algorithm is defined which uses recently proposed adaptive Monte Carlo methods. The proposed model is applied to the daily returns of stocks.

This paper develops a unified framework for fixed and random effects estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroskedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both a random effects and a fixed effects spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroskedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman-test of the spatial random against the spatial fixed effects model.

Many nonlinear time series models have been proposed in the last decades. Among them, the models with regime switchings provide a class of versatile and interpretable models which have received a particular attention in the literature. In this paper, we consider a large family of such models which generalize the well known Markov-switching AutoRegressive (MS-AR) by allowing non-homogeneous switching and encompass Threshold AutoRegressive (TAR) models. We prove various theoretical results related to the stability of these models and the asymptotic properties of the Maximum Likelihood Estimates (MLE). The ability of the model to catch complex nonlinearities is then illustrated on various time series.

The time series can be modeled by stochastic processes which are intended to explain the manner of economic phenomena evolution. Depending on the type of time series, several categories of stochastic processes as models for time series are used: autoregressive processes, moving average processes and composite models based on them.In general, each model has its own advantages and disadvantages, the aim of this study is to distinguish and to identify the most important features of each to determine which model provides the best predictions.In the empirical analysis we considered time series consists of data taken from the monthly reports of the National Bank of Romania for the inflation rate, between January 1997 - August 2013.

VAR (Vector Auto-regressive) model is a kind of commonly used econometric-model. It is used to estimate the dynamic relationship of the endogenous variables without any prior constraints. Since VAR is one of the most easily operated models to deal with the analysis and prediction of multiple related economic indicators, more and more attention has been paid by economists in two decades. However, with the increasing of data size, the individual computer has encountered its processing bottleneck. Meanwhile, the advantages of the distributed computing cluster have begun to show obvious strength, such as Hadoop, Spark, and so on. Due to the lack of VAR related model on Spark, MLlib, we developed approaches of VAR and SVAR (Structural Vector Auto-regression) model in Spark and Hadoop cluster. Meanwhile, SGD (Stochastic Gradient Descent) algorithm has been applied after the data processing. To verify the approaches, different sizes of data are used for model testing in different platform, including R and Spark cluster. According to the comparison of the response time of different data size in both platform, the experiment results have shown that the developed methods are simple and efficient in big data environment.

Prediction bands for time series are usually generated point-wise by bootstrap methods. Such bands only convey the prediction uncertainty for each horizon separately. The joint distribution is not taken into account. To represent the forecast uncertainty over the entire horizon, methods for constructing joint prediction bands for path forecasts from SETAR models are proposed. This class of nonlinear models is increasingly used in time series analysis and forecasting as it is useful for capturing nonlinear dynamics. Approaches based on statistical theory and explicit sequential and global optimization methods are both considered. Monte Carlo simulation is used to assess the performance of the proposed methods. The comparison is done with regard to the actual coverage of the constructed prediction bands for full path forecasts as well as with regard to the width of the bands. An empirical application demonstrates the relevance of the choice of bands for indicating the uncertainty of path forecasts in nonlinear models.

International audience; Bifurcating autoregressive processes, which can be seen as an adaptation of autoregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymptotic and asymptotic behaviour of the Nadaraya-Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by $\mathbb{T}_n$, up to the depth $n$. Estimators achieve the classical rate $|\mathbb {T}_n|^{-\beta /(2\beta +1)}$ in quadratic loss over Hölder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth and a moderate deviations principle. Our proofs rely on specific techniques used to study bifurcating Markov chains. Finally, we address the question of asymmetry and develop an asymptotic test for the equality of the two autoregressive functions.

This was a preliminary study conducted to examine the relationship between psychographic factors (i.e., personal value, risk attitude, and trust) and the purchase of life insurance among Alor Setar city folks. A non-probability convenience sampling technique was used to collect data from early February to mid-March 2015. A sample comprising 108 respondents were subjected to binary logistic regression analysis. The major finding of this study showed that risk attitude has a significant and negative relationship with the purchase of life insurance. Respondents in Alor Setar who are more likely to involve in risky behaviours or activities tend not to buy life insurance. Risk taking individuals do not behave like risk averse individuals who tend to seek protection by buying life insurance as a method to cover their personal risks. Meanwhile, personal value and trust were found to have no significant relationship with the purchase of life insurance among respondents in Alor Setar. It is recommended that a comprehensive study covering wider areas with larger sample sizes be included in future studies to obtain more reliable results that would enable the generalisation of findings. Keywords: Life insurance, Psychographic factors, Personal value, Risk attitude, Trust

Energy consumption in general is one of biggest challenges when it comes to wireless sensor networks (WSNs). Since the biggest amount of energy is used for communication, the most logical way to reduce the energy consumption is to reduce the number of packets transmitted between sensor and sink node. To address this issue, data reduction methods, which are predicting the measured values both at source and sink node, have been developed. Consequently, transmitting measurements is only required if the sensed value differs from the predicted one by a given threshold. The choice of data reduction strategy depends on the type of sensed phenomena. Especially when trying to predict data of nonlinear systems with a high entropy like electric engine or gearbox vibration, it becomes very difficult to build a model that describes and forecasts those values. In this paper, we use a Self-Exciting Threshold Autoregressive (SETAR) model as a Time Series Forecasting method in combination with nonlinear systems to overcome that problem. By applying this algorithm on real-world data using panStamp technology, we achieve a maximum energy saving of up to 73%.

Equivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.

International audience; The main objective of this paper is to establish the residual and the wild bootstrap procedures for periodically autoregressive models. We use the least squares estimators of model’s parameters and generate their bootstrap equivalents. We prove that the bootstrap procedures for causal periodic autoregressive time series with finite fourth moments are weakly consistent. Finally, we confirm our theoretical considerations by simulations.

This paper presents the results of relative risk estimation that applied to TB data in Kedah using the most common approach, Standardized Morbidity Ratio (SMR). Disease mapping has been recognized as one of the methods that can be used by government and public health in order to control diseases since it can give a clear picture of the risk areas. To get good disease mapping, relative risk estimation is an important issue that need to be considered. TB risk areas will be recognized through the map. From the result, Kulim shows the lowest risk areas of contracting TB while Kota Setar has the highest risk area.This paper presents the results of relative risk estimation that applied to TB data in Kedah using the most common approach, Standardized Morbidity Ratio (SMR). Disease mapping has been recognized as one of the methods that can be used by government and public health in order to control diseases since it can give a clear picture of the risk areas. To get good disease mapping, relative risk estimation is an important issue that need to be considered. TB risk areas will be recognized through the map. From the result, Kulim shows the lowest risk areas of contracting TB while Kota Setar has the highest risk area.

Nonnegative integer-valued time series arises in many applications. A time series model: first-order Integer-valued AutoRegressive (INAR(1)) is constructed by binomial thinning operator to model nonnegative integer-valued time series. INAR (1) depends on one period from the process before. The parameter of the model can be estimated by Conditional Least Squares (CLS). Specification of INAR(1) is following the specification of (AR(1)). Forecasting in INAR(1) uses median or Bayesian forecasting methodology. Median forecasting methodology obtains integer s, which is cumulative density function (CDF) until s, is more than or equal to 0.5. Bayesian forecasting methodology forecasts h-step-ahead of generating the parameter of the model and parameter of innovation term using Adaptive Rejection Metropolis Sampling within Gibbs sampling (ARMS), then finding the least integer s, where CDF until s is more than or equal to u . u is a value taken from the Uniform(0,1) distribution. INAR(1) is applied on pneumonia case...

We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization., 33 pages, 5 figures

Recently, there has been a growing interest in studying the autoregressive conditional duration (ACD) models, originally introduced by (Engle, R. F., and J. R. Russell. 1998. “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data. Econometrica 66: 1127–1162). ACD models are useful for modeling the time between the events, especially, in financial context, the time between trading of stocks. In this paper, we propose a specific type of nonstationary ACD model, viz., time varying ACD model (tvACD), by allowing the parameters of the usual ACD model to vary as functions of time. Some probabilistic and inferential aspects of such models have been investigated. We also develop a local polynomial procedure for the estimation of the parameter functions of the proposed tvACD model. Asymptotic properties of the estimators have been investigated, including the asymptotic normality. The asymptotic distribution being dependent on the parameters of the original distribution, a weighted bootstrap estimator is suggested and its validity is established. Simulation study and empirical analysis using high frequency data (HFD) from National Stock Exchange (NSE, INDIA) illustrate the application of the proposed tvACD model.

We examine the conditions under which each individual series that is generated by a vector autoregressive model can be represented as an autoregressive model that is augmented with the lags of a few linear combinations of all the variables in the system. We call this multivariate index-augmented autoregression (MIAAR) modelling. We show that the parameters of the MIAAR can be estimated by a switching algorithm that increases the Gaussian likelihood at each iteration. Since maximum likelihood estimation may perform poorly when the number of parameters increases, we propose a regularized version of our algorithm for handling a medium–large number of time series. We illustrate the usefulness of the MIAAR modelling by both empirical applications and simulations.

The aim of this thesis is to analyze the performance of nonlinear threshold models in forecasting the exchange rate of Czech koruna against EUR. Data for this study were obtained from Statistical Data Warehouse of European Central Bank (ECB) website, from Czech National Bank (CNB) Board decisions minutes and from the press releases of Governing Council of ECB. The data set was split into two periods - from 1999 until November, 2013 when CNB started to use interventions and from November, 2013 until April, 2016. Models used in the thesis are Self-Exciting Threshold Auto Regressive (SETAR) models with one and two thresholds and two Threshold Auto Regres- sive (TAR) models with different threshold variables - meetings of CNB Board as dummy variable and average volatility over recent periods. The forecasting results indicate that SETAR models did not outperform Random Walk in any period. TAR models offered promising results in the period before interventions and surprisingly failed in the period during interventions. This study supports the general belief of exchange rates being difficult to forecast and that it holds in case of Czech koruna as well. JEL Classification F12, F21, F23 H25, H71, H87 Keywords forecasting, exchange rate, time series, nonlin- earity, SETAR, TAR Author's e-mail zaka.one@gmail.com...

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

This paper presents a general formulation for the univariate nonlinear autore- gressive model discussed by Glasbey (Journal of the Royal Statistical Society: Series C, 50(2001), 143-154) in the …rst order case, and provides a more thorough treat- ment of its theoretical properties and practical usefulness. The model belongs to the family of mixture autoregressive models but it diers from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the de…- nition of the model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in non- linear autoregressive models. Moreover, for a pth order model an explicit expression of the (p+ 1)-dimensional stationary distribution is known and given by a mixture of Gaussian distributions with constant mixing weights. Lower dimensional sta- tionary distributions have a similar form whereas the conditional distribution given the past observations is a Gaussian mixture with time varying mixing weights that depend on p lagged values of the series in a natural way. Due to the known sta- tionary distribution exact maximum likelihood estimation is feasible, and one can assess the applicability of the model in advance by using a nonparametric estimate of the density function. An empirical example with interest rate series illustrates the practical usefulness of the model. � The …rst and third authors thank the Academy of Finland and the OP-Pohjola Group Research

Autoregressive conditional heteroscedastic type and stochastic volatility SV models are designed to analyze and model the conditional variance volatility, but in some contexts the specification of the conditional mean is also important. In this paper we consider a combination model in which the conditional mean is modeled by an autoregressive AR model and conditional variance is modeled by an SV model. We call this model an ARp-SV model, consider some of its properties, discuss its likelihood, and estimate its parameters using simulated maximum likelihood. We also estimate the volatilities by a particle filter. Then these methods are applied to four financial time series. Copyright © 2014 John Wiley & Sons, Ltd.

The robust estimation for Poisson autoregressive models is studied. As a robust estimator, a minimum density power divergence estimator (MDPDE) is considered. It is shown that under regularity conditions, the MDPDE is strongly consistent and asymptotically normal. Simulation results are provided for illustration. A real data analysis is implemented for the polio incidence data.

In this article, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. When the order of the model is 1, we derive an empirical likelihood ratio test statistic to test the stationary-ergodicity. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.

In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.

Improved implementations of previously suggested methods for constructing bootstrap prediction intervals for the self-exciting threshold autoregressive model are presented. The simulation results are compared with those reported by Li (2011). It is found that better estimates of actual coverage rates are obtained using the improved version of the methods.

This article investigates the asymptotic behavior of the error density function in nonlinear autoregressive stationary time series regression models. For any 1 ⩽ p < ∞, the kernel density estimator of residuals is shown to be consistent for the error estimator concerning the Lp-distance, which extends the result developed by Cheng and Sun (2008) in L2-norm. Moreover, the result developed in this article is extended the results of Horvath and Zitikis (2003) to nonlinear autoregressive models.

The paper considers testing parametric assumptions on the conditional mean and variance functions for nonlinear autoregressive models. To this end, we compare the kernel density estimate of the marginal density of the process with a convolution-type density estimate. It is shown that, interestingly, the latter estimate has a parametric $\left( {\sqrt n } \right)$ rate of convergence, thus substantially improving the classical kernel density estimates whose rates of convergence are much inferior. Our results are confirmed by a simulation study for threshold autoregressive processes and autoregressive conditional heteroskedastic processes.

A monitoring scheme is proposed to sequentially detect a structural change in random coefficient autoregressive time series of order p (RCA(p)) after a training period of size T. It extends structural change monitoring to RCA(p) time series. The asymptotic properties of our monitoring statistic are established under both the null of no change in parameters and the alternative of a change in coefficient. The finite sample properties are investigated by a simulation study.

Water resources and urban flood management require hydrologic and hydraulic modeling. However, incomplete precipitation data is often the issue during hydrological modeling exercise. In this study, gene expression programming (GEP) was utilised to correlate monthly precipitation data from a principal station with its neighbouring station located in Alor Setar, Kedah, Malaysia. GEP is an extension to genetic programming (GP), and can provide simple and efficient solution. The study illustrates the applications of GEP to determine the most suitable rainfall station to replace the principal rainfall station (station 6103047). This is to ensure that a reliable rainfall station can be made if the principal station malfunctioned. These were done by comparing principal station data with each individual neighbouring station. Result of the analysis reveals that the station 38 is the most compatible to the principal station where the value of R2 is 0.886.

This paper is concerned with the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation (SCAD) penalty for a partially linear model with time-series errors. By combining the profile semi-parametric least squares method and SCAD penalty technique, a new penalized estimation for the regression and autoregressive parameters in the model is proposed. We show that the asymptotic property of the resultant estimator is the same as if the order of autoregressive error structure and non-zero regression coefficients are known in advance, thus achieving the oracle property in the sense of Fan and Li (2001). In addition, based on a prewhitening technique, we construct a two-stage local linear estimator (TSLLE) for the non-parametric component. It is shown that the TSLLE is more asymtotically efficient than the one that ignores the autoregressive time-series error structure. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on electricity usage data is also illustrated. Copyright © 2014 Wiley Publishing Ltd

Nowadays, there exist various methods for modelling and forecasting foreign exchange (FX) rates including economical models, statistical methods and learning neural networks. Dealing with the problems of nonstationarity and nonlinearity has been a challenge. In this paper, we propose a combined neural model for effectively tackling the problems. The model is termed as neural gas mixture of autoregressive (NGMAR) models and it organizes the mixture of autoregressive models in the way of the neural gas. By taking the advantages of dynamic neighbourhood rankings of neural gas and the more appropriate similarity measure of the sum of autocorrelation coefficients, the model is able to effectively model and forecast nonstationary and nonlinear time series. The NGMAR has been tested on several benchmark data sets as well as a variety of FX rates. The experimental results show that the proposed method outperforms significantly other methods, in terms of normalized root mean squared error and correct trend prediction percentage. ?? 2014 Elsevier B.V. cited By (since 1996)0