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Evaporation is a key element for water resource management, hydrological modelling, and irrigation system designing. Monthly evaporation (Ep) was projected by deploying three machine learning (ML) models included Extreme Gradient Boosting, ElasticNet Linear Regression, and Long Short-Term Memory; and two empirical techniques namely Stephens-Stewart and Thornthwaite. The aim of this study is to develop a reliable generalised model to predict evaporation throughout Malaysia. In this context, monthly meteorological statistics from two weather stations in Malaysia were utilised for training and testing the models on the basis of climatic aspects such as maximum temperature, mean temperature, minimum temperature, wind speed, relative humidity, and solar radiation for the period of 2000–2019. For every approach, multiple models were formulated by utilising various combinations of input parameters and other model factors. The performance of models was assessed by utilising standard statistical measures. The outcomes indicated that the three machine learning models formulated outclassed empirical models and could considerably enhance the precision of monthly Ep estimate even with the same combinations of inputs. In addition, the performance assessment showed that Long Short-Term Memory Neural Network (LSTM) offered the most precise monthly Ep estimations from all the studied models for both stations. The LSTM-10 model performance measures were (R2 = 0.970, MAE = 0.135, MSE = 0.027, RMSE = 0.166, RAE = 0.173, RSE = 0.029) for Alor Setar and (R2 = 0.986, MAE = 0.058, MSE = 0.005, RMSE = 0.074, RAE = 0.120, RSE = 0.013) for Kota Bharu.

This paper deals with the problem of joint determination of the delay parameter and autoregressive orders of the Self-Exciting Threshold Autoregressive (SETAR) models. More specifically, we propose...

Nonlinear time series model is a time series model applied to data that has the nonlinear pattern. One of the nonlinear time series models is Self-Exciting Threshold Autoregressive (SETAR). The SETAR model is a time series model that data modeling is done by dividing data into multiple regimes, whereas each regime following an autoregressive (AR) model. The division of the regime based on the score of the delay and threshold of the data itself. The number of SETAR model parameters not only resulted from the best model search process but also resulted in a SETAR model that is not yet optimum. Based on these findings, this study used Genetic Algorithm (GA) to produce the best and optimum SETAR model. In this research, using SETAR simulation data modeling and return data of Bank Rakyat Indonesia (BRI) were performed. The method used to model the data is Grid Search (GS) and Genetic Algorithm (GA). The result of analysis of SETAR simulation data shows that GA method gives better modeling result than GS method. The GA motive AIC value for the amount of 200 data is -3.976178 which is smaller than the AIC GS method of 1.361723. For the amount of data of 500 AIC values, GA method is also smaller than AIC GS method. In BRI stock return data, GA method also gives better modeling result compared to GS. It is marked by the GA AIC method value of -11147.66 less than -11146.26 which is the AIC method of GS. Thus, the result of analysis of SETAR model simulation data and BRI stock return shows that GA method gives better modeling result compared to GS method based on generated AIC value.

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step, through a simple model. In particular, the lack of consistency is shown for the estimation of the autoregressive parameter when the independence hypothesis is violated in the random coefficients. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results., Comment: 29 pages

For the first-order autoregressive model, we establish the asymptotic theory of the weighted least squares estimations whether the underlying autoregressive process is stationary, unit root, near integrated or even explosive under a weaker moment condition of innovations. The asymptotic limit of this estimator is always normal. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. An empirical likelihood confidence interval is proposed for interval estimations of the autoregressive coefficient. The results improve the corresponding ones of Chan et al. (Econ Theory 28:705–717, 2012). Some simulations are conducted to illustrate the proposed method.

Air-quality forecasting is difficult because air quality time series are heterogeneous, consisting of one-dimension series data and multi-dimension panel data. Therefore, a hybrid forecasting model with both linear and nonlinear models may be appropriate to represent the complex behavior of a heterogeneous time series data set. In this paper, a new hybrid-Garch (Generalized Autoregressive Conditional Heteroskedasticity) methodology is proposed in order to integrate the individual forecasting models of the ARIMA (Autoregressive Integrated Moving Average) and SVM(Support Vector Machine). The hybrid-Garch approach for time series prediction is tested by 10-day hourly PM 2.5 concentrations data including linear and non-linear, in Shenzhen, China. Empirical results from six station data sets indicate that: 1) the PM 2.5 concentrations of Shenzhen experiences a regular fluctuation during the 24 h of the whole day with the peak value in working hours due to factory and vehicle emissions. 2) Spatial difference of PM 2.5 concentrations is not noticeable because of the geographical and meteorological conditions. 3) The proposed hybrid model generates a more reliable and accurate forecast capability. 4) The proposed hybrid model analyses the time series data with possibly conditional heteroscedasticity characteristics and estimates the variance for the volatility of the PM 2.5 concentrations.

This paper introduces an economically important new idea for detrending macroeconomic time series and examines the Spanish business cycle pattern with respect to potential asymmetries. To address difficulties in the trend and cycle decomposition, a nonparametric trend estimation approach is introduced and exemplary applied to the Spanish GDP data for the period 1850 to 2015. The application of an iterative plug-in (IPI) algorithm for endogenous bandwidth selection solves the problem of choosing an adequate smoothing parameter for nonparametric regression. The algorithm identifies continuously Moving Trends (MT) with a time length of 34 years. After we estimate the trend nonparametrically, we fit several time series models to the residuals for further analysis. Although asymmetry during expansion and recession phases is indicated, it is not unambiguous.

This paper develops empirical tests for the purchasing power parity (PPP) hypothesis for China, Japan and South Korea by using the quantile unit root and quantile cointegrating regression method. Unlike the conventional unit root and cointegration methods, we test for the validity of the PPP hypothesis at both the quantile interval and the single quantile level. While conventional nonlinear models could also capture the regime switching behaviour, the quantile approach enables us to avoid choosing the appropriate form of nonlinearity, and therefore, avoid the misspecification risk. When conventional methods are used, the PPP hypothesis is not strongly supported for all three countries. However, when the quantile-based approach is used, the PPP hypothesis holds for China at some quantile levels when producer price index (PPI) is used as price variable, and it also holds for Japan over the lower and upper quantile levels. Interestingly, the PPP hypothesis for South Korea holds over all quantile levels when the consumer price index (CPI) is used as the price variable.

The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.

In this paper, we use the local influence method to study a vector autoregressive model under Student′s t-distributions. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature diagnostics for the vector autoregressive model under three usual perturbation schemes for identifying possible influential observations. The effectiveness of the proposed diagnostics is examined by a simulation study, followed by our data analysis using the model to fit the weekly log returns of Chevron stock and the Standard & Poor's 500 Index as an application.

In most researches in the area of profile monitoring, it is assumed that observations are independent of each other. Whereas, this assumption is usually violated in practice and observations are autocorrelated. The control charts are the most important tools of the statistical process control which are used to monitor the processes over time. The control charts usually signal the out-of-control status of the process with a time delay. Whereas knowing real-time of the change (change point), one can achieve great savings on time and expenses. In this paper, the estimation of the change point in the simple linear profiles with AR (1) autocorrelation structure within each profile is considered. In the proposed method, by acquiring the joint probability density function of the autocorrelated observations, the maximum likelihood estimation method is applied to estimate the step change point. Here, we specifically focus on Phase II and compare the performance of the proposed estimator with the existing estimators in the literature through simulation studies. In addition, the application of the proposed estimator in comparison with the two estimators is illustrated through a real case. The results show the better performance of the proposed estimator.

The radiation data is important for solar data analysis which is significantly for modeling, designing on energy conversion system development and outputting it as a variable that is needed by other related scientific researches.Obtaining the complete data for solar intensity is a tough job when the technical problem is raised either from the sensor’s devices or faulty data transmission. Next, missing values occur accordingly.As a solution, missing value estimation has been introduced to substitute the absent values with imputed values.This article is highlighted to propose cubic Bezier interpolation as potential techniques to generate replacement values. Afterwards, compare the performance capability of few submitted interpolation techniques dealing with difference amount of simulated missing data. Based on our knowledge, curiosity works for replaceable values by applying Bezier interpolation on solar radiation data is limited. The cubic Bezier interpolation performs very well on both areas but the most effective condition is at the lower missing values and higher absent values that come from Alor Setar and Penang cities, respectively, which offer the lowest RMSE value and the r² value nearest to 1

Integer-valued time series analysis offers various applications in biomedical, financial, and environmental research. However, existing works usually assume no or constant over-dispersion. In this paper, we propose a new model for time series of counts, the autoregressive conditional negative binomial model that has a time-varying conditional autoregressive mean function and heteroskedasticity. The location and scale parameters of the negative binomial distribution are flexible in the proposed set-up, inducing dynamic over-dispersion. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize deviance information criterion for model comparison. We conduct simulations to investigate the estimation performance of this sampling scheme for the proposed negative binomial model. To demonstrate the proposed approach in modelling time-varying over-dispersion, we consider two types of criminal incidents recorded by New South Wales (NSW) Police Force in Australia. We also fit the autoregressive conditional Poisson model to these two datasets. Our results demonstrate that the proposed negative binomial model is preferable to the Poisson model.

This note is concerned with the limiting properties of the least squares estimation for the random coefficient autoregressive model. In contrast with existing results, ours is applicable to a wide range of models under more general assumptions.

Despite significant research advances achieved during the last decades, seemingly inconsistent forecasting results related to stochastic, chaotic, and black-box approaches have been reported. Herein, we attempt to address the entropy/complexity resulting from hydrological and climatological conditions. Accordingly, mutual information function, correlation dimension, averaged false nearest neighbor with E1 and E2 quantities, and complexity analysis that uses sample entropy coupled with iterative amplitude adjusted Fourier transform were employed as nonlinear deterministic identification tools. We investigated forecasting of daily streamflow for three climatologically different Swedish rivers, Helge, Ljusnan, and Kalix Rivers using self-exciting threshold autoregressive (SETAR), k-nearest neighbor (k-nn), and artificial neural networks (ANN). The results suggest that the streamflow in these rivers during the 1957–2012 period exhibited dynamics from low to high complexity. Specifically, (1) lower complexity lead to higher predictability at all lead-times and the models’ worst performances were obtained for the most complex streamflow (Ljusnan River), (2) ANN was the best model for 1-day ahead forecasting independent of complexity, (3) SETAR was the best model for 7-day ahead forecasting by means of performance indices, especially for less complexity, (4) the largest error propagation was obtained with the k-nn and ANN and thus these models should be carefully used beyond 2-day forecasting, and (5) higher number input variables except for the dominant variables made insignificant impact on forecasting performances for ANN and k-nn models.

To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts, the NWP model is run multiple times, each time with variations in the mathematical representations of the model and/or initial or boundary conditions. To correct for possible biases and dispersion errors in the ensemble, statistical postprocessing models are frequently employed. These statistical models yield full predictive probability distributions for a weather quantity of interest and thus allow for a more accurate representation of forecast uncertainty. This article proposes to combine the state-of-the-art Ensemble Model Output Statistics (EMOS) with an ensemble that is adjusted by an autoregressive process fitted to the respective error series by a spread-adjusted linear pool in the case of temperature forecasts. The basic ensemble modification technique we introduce may be used to simply adjust the ensemble itself as well as to obtain a full predictive distribution for the weather quantity. As demonstrated for temperature forecasts from the European Centre for Medium-Range Weather Forecasts ensemble, the proposed procedure gives rise to improved results over the basic (local) EMOS method.

Bootstrap-based unit root tests are a viable alternative to asymptotic distribution-based procedures and, in some cases, are preferable because of the serious size distortions associated with the latter tests under certain situations. While several bootstrap-based unit root tests exist for autoregressive moving average processes with homoskedastic errors, only one such test is available when the innovations are conditionally heteroskedastic. The details for the exact implementation of this procedure are currently available only for the first order autoregressive processes. Monte-Carlo results are also published only for this limited case. In this paper we demonstrate how this procedure can be extended to higher order autoregressive processes through a transformed series used in augmented Dickey–Fuller unit root tests. We also investigate the finite sample properties for higher order processes through a Monte-Carlo study. Results show that the proposed tests have reasonable power and size properties.

The aim of this paper is to evaluate the forecasting performance of SETAR models with an application to the Industrial Production Index (IPI) of four major European countries over a period which includes the last Great Recession. Both point and interval forecasts are considered at different horizons against those obtained from two linear models. We follow the approach suggested by Terasvirta et al. (2005) according to which a dynamic specification may improve the forecast performance of the nonlinear models with respect to the linear models. We re-specify the models every twelve months and we find that the advantages of this procedure are particularly evident in the forecast rounds immediately following the re-specification.

This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the remaining parameters are asymptotically normal. Our results include the asymptotic theory of the estimator for threshold AR models with autoregressive conditional heteroscedastic (ARCH) errors and threshold ARCH models as special cases, each of which is also new in literature. Two portmanteau-type statistics are also derived for checking the adequacy of fitted model when either the error is nonnormal or the threshold is unknown. Simulation studies are conducted to assess the performance of the score-based test and the estimator in finite sa...

A nonlinear stochastic self-exciting threshold autoregressive (SETAR) model and a chaotic k-nearest neighbour (k-nn) model, for the first time, were compared in one and multi-step ahead daily flow forecasting for nine rivers with low, medium, and high flows in the western United States. The embedding dimension and the number of nearest neighbours of the k-nn model and the parameters of the SETAR model were identified by a trial-and-error process and a least mean square error estimation method, respectively. Employing the recursive forecasting strategy for the first time in multi-step forecasting of SETAR and k-nn, the results indicated that SETAR is superior to k-nn by means of performance indices. SETAR models were found to be more efficient in forecasting flows in one and multi-step forecasting. SETAR is less sensitive to the propagated error variances than the k-nn model, particularly for larger lead times (i.e., 5 days). The k-nn model should carefully be used in multi-step ahead forecasting where peak flow forecasting is important by considering the risk of error propagation.

In regions where economies that are highly dependent on agricultural activities, estimation of evapotranspiration is vital for scheduling and managing the water resources. In this study, the estimation of the reference evapotranspiration (ET0) was performed for the west coast of Peninsular Malaysia, where oil palm is the major crop. Three stations, namely Station 48603 (Alor Setar), Station 48620 (Sitiawan) and Station 48650 (KLIA Sepang) were selected representing different regions along the west coast. Estimation of ET0 using the popular and conventional Penman-Monteith (PM) model is data intensive. On the contrary, simpler empirical models such as the temperature-based Hargreaves-Samani (HS), mass transfer-based Romanenko and radiation-based Makkink models are less accurate, unstable and are greatly affected by local climate conditions. In order to solve the problems of the PM and other simple empirical models, the SVM was used to mimic the simple empirical models. The results of this study revealed that the HS and Makkink models were favorable for ET0 estimation at the northern region, whereas for the central region, the Makkink model was not suitable. Simple averaging of the empirical models improved the estimations. However, the model was still deemed to be poor as the MARE ranged from 0.087 to 0.099, with the R2 still being possible to dip below 0.900. It was found that the SVM could greatly improve the ET0 estimation. Unlike the empirical models, the regional factor had minimal effect on the ET0 estimation; where the SVM-Mak model performed better than the SVM-HS and SVM-Rom models over the whole study area. The best performance was achieved by SVM-Mak model at Station 48620 (Sitiawan) where the MARE was only 0.020 when compared to the chosen standard PM model. It was found that the simple averaging of the SVM models could further boost the performance, but such an approach was non-rewarding. The SVM models were found to be better alternatives for the empirical models when using similar inputs. The study concluded that the SVM model which imitated the Makkink model was suitable for ET0 estimation along the west coast of Peninsular Malaysia.

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.

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.

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.

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.

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.

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVARS(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.

This paper aims to model volatility of daily index returns for four Asian markets namely; Kuala Lumpur Composite Index of Malaysia, Jakarta Stock Exchange Composite Index of Indonesia, Straits Times Index of Singapore and the Stock Index of Korea over the period 03/01/2007 – 31/07/2013 excluding the public holidays. We utilized generalized autoregressive conditional heteroskedasticity models as these models are particularly suitable for high frequency financial time series such as the daily stock returns which has a time-varying variance. Unlike the linear structural models, these models are found very useful in explaining the most stylized facts about index returns such as leptokurtosis, volatility clustering and asymmetric or leverage effects. The key results of this study are as follows. Firstly, the conditional variance process is highly persistent in all markets. Secondly, the relationship between the expected risk and the expected return is positive as expected but the relationship is not statistically significant for all markets except Indonesia. For Indonesian market which is found to be more volatile than the other three markets, the estimated coefficient of risk premium appeared to be statistically significant indicating that increased risk leads to a rise in the returns. The risk-premium coefficients for other three markets are although positive but not statistically significant suggesting that increased risk does not necessarily produce higher return for those three markets. Finally, the asymmetric effects is exist in all cases signifying that negative shock produces higher impact on future volatility than the positive shock of the same magnitude.

We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.

Lake water level forecasting is very important for an accurate and reliable management of local and regional water resources. In the present study two nonlinear approaches, namely phase-space reconstruction and self-exciting threshold autoregressive model (SETAR) were compared for lake water level forecasting. The modeling approaches were applied to high-quality lake water level time series of the three largest lakes in Sweden; Vanern, Vattern, and Malaren. Phase-space reconstruction was applied by the k-nearest neighbor (k-NN) model. The k-NN model parameters were determined using autocorrelation, mutual information functions, and correlation integral. Jointly, these methods indicated chaotic behavior for all lake water levels. The correlation dimension found for the three lakes was 3.37, 3.97, and 4.44 for Vanern, Vattern, and Malaren, respectively. As a comparison, the best SETAR models were selected using the Akaike Information Criterion. The best SETAR models in this respect were (10,4), (5,8), and (7,9) for Vanern, Vattern, and Malaren, respectively. Both model approaches were evaluated with various performance criteria. Results showed that both modeling approaches are efficient in predicting lake water levels but the phase-space reconstruction (k-NN) is superior to the SETAR model.

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.

when multiple repeated observations are available, it would make a lot of sense to measure the outcome in the form of a time series; accounting trends, seasonal effects and

The article deals with the problem of testing a change in autoregressive matrices of the p-th order vector autoregressive process, VAR(p). The proposed test statistics are based on the likelihood ratio concept and are studied under the null hypothesis of no change in parameters. Their asymptotic behavior is derived under minimal moment assumptions in both cases where the time point of possible change is known a priori and is undefined. The Gumbel-type approximation of the test statistic is also developed, which previous papers on VAR(p) models do not cover.

In the study, we discussed the generalized autoregressive conditional heteroskedasticity model and enhanced it with wavelet transform to evaluate the daily returns for 1/4/2002-30/12/2011 period in Brent oil market. We proposed discrete wavelet transform generalized autoregressive conditional heteroskedasticity model to increase the forecasting performance of the generalized autoregressive conditional heteroskedasticity model. Our new approach can overcome the defect of generalized autoregressive conditional heteroskedasticity family models which can't describe the detail and partial features of times series and retain the advantages of them at the same time. Comparing with the generalized autoregressive conditional heteroskedasticity model, the new approach significantly improved forecast results and greatly reduces conditional variances.

Modeling Heart Rate Variability (HRV) data has become important for clinical applications and as a research tool. These data exhibit long memory and time-varying conditional variance (volatility). In HRV, volatility is traditionally estimated by recursive least squares combined with short memory AutoRegressive (AR) models. This work considers a parametric approach based on long memory Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with heteroscedastic errors. To model the heteroscedasticity nonlinear Generalized Autoregressive Conditionally Heteroscedastic (GARCH) and Exponential Generalized Autoregressive Conditionally Heteroscedastic (EGARCH) models are considered. The latter are necessary to model empirical characteristics of conditional volatility such as clustering and asymmetry in the response, usually called leverage in time series literature. The ARFIMA-EGARCH models are used to capture and remove long memory and characterize conditional volatility in 24 hour HRV recordings from the Noltisalis database. © 2016 IEEE.