Lynx Data Research Articles

Analysing biodiversity observation data collected in continuous time: Should we use discrete‐ or continuous‐time occupancy models?

Abstract Biodiversity monitoring is undergoing a revolution, with fauna observation data being increasingly gathered continuously over extended periods, through sensors like camera traps and acoustic recorders, or via opportunistic observations. These data are often analysed with discrete‐time ecological models, requiring the transformation of continuously collected data into arbitrarily chosen, non‐independent discrete‐time intervals. To overcome this issue, ecologists are increasingly turning to the existing continuous‐time models in the literature. Closer to the real detection process, they are lesser known than discrete‐time models, not always easily accessible and can be more complex. Focusing on occupancy models, a type of species distribution models, we asked ourselves: Should we dedicate time and effort to learning and using these continuous‐time models, or can we go on using discrete‐time models? We conducted a comparative simulation study using data generated within a continuous‐time framework. We assessed the performance of five static occupancy models with varying detection processes: discrete detection/non‐detection process, discrete count process, continuous‐time Poisson process and two types of modulated Poisson processes. Our goal was to assess their abilities to estimate occupancy probability with continuously collected data. We applied all models to empirical lynx data as an illustrative example. In scenarios with easily detectable animals, we found that all models accurately estimated occupancy. All models reached their limits with highly elusive animals. Variation in discretisation intervals had minimal impact on the discrete models' capacity to estimate occupancy accurately. Our study underscores that opting for continuous‐time models with an increased number of parameters, aiming to get closer to the sensor detection process, may not offer substantial advantages over simpler models when the sole aim is to accurately estimate occupancy. Model choice can thus be driven by practical considerations such as data availability or implementation time. However, occupancy models can encompass goals beyond estimating occupancy probability. Continuous‐time models, particularly those considering temporal variations in detection, can offer valuable insights into specific species behaviour and broader ecological inquiries. We hope that our findings offer valuable guidance for researchers and practitioners working with continuously collected data in wildlife monitoring and modelling.

Analysis of the Canadian Lynx Data Under Two Different Transformations

Analysis of the Canadian Lynx Data Under Two Different Transformations

Stability Analysis of Deep Belief Network: Based SD-AR Model for Nonlinear Time Series

As for nonlinear time series prediction, many different kinds of varying-coefficient models have been proposed and analysised in recent years. A kind of varying functional-coefficient autoregressive model, called the deep belief network-based state-dependent autoregressive (DBN-AR) model is considered in this paper. The stability conditions and existing conditions of limit cycle of the DBN-AR model are also studied. An especial designed parameter estimation method is used to identify the DBN-AR model. The DBN-AR model is used to predict the famous Canadian lynx data and Henon chaotic series, the prediction capability of the DBN-AR model is compared with other prediction models, the experimental results show that the DBN-AR model obtains better prediction accuracy.

Forecasting Implementation of Hybrid Time Series and Artificial Neural Network Models

This study implemented AR, SARIMA, and SETAR models and their hybrid with ANN using the Canadian lynx data. Implementing a SETAR-ANN has been shown to be successful in generating up to 10-step forecasts. The forecasting capability of AR-ANN and SARIMA-ANN applied to the same data are also investigated. The study shows that implementing hybridization does not guarantee better forecasting performance and accuracy, except for the case of SETAR-ANN. Despite results showing that the efficiency of the hybrid models may be worse than its components models, this study exhibits the promising predictive capability of time series, ANN, and its hybrid models.

Klasik Kanada Lynx Verileri İçin Önceden Bulunmuş Zaman Serisi Modellerinin K-Means Küme Yöntemi ve BDS Testi ile İncelenmesi

Canadian lynx data are widely used and modeled in the literature. Although many different models have been made so far, no model-based classification studies have been carried out in terms of residuals to investigate the similarities or differences between these models. This study reviewed previously obtained models for the Canadian lynx time series. The starting point of the current study is residuals, and some statistical data analysis tools are used for this. The residual series of the models are clustered with the K-means cluster method. Besides, a new model is proposed for this time series, and the model is included in the data analysis together with other models in the literature. In addition, chaos analysis was performed for all residual time series of the models.

English

Time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This paper proposes a new stepwise model determination method for artificial neural network (ANN) and a novel hybrid model combining autoregressive integrated moving average (ARIMA) model, ANN and discrete wavelet transformation (DWT). Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed method, ARIMA-DWT-ANN. Also, two real data sets, Lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and Lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ANN and ARIMA-DWT-ANN due to their robustness and high accuracy. Since the performance of hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.

Weighted MLP-ARIMA series hybrid model for time series forecasting

With the increasing importance of forecasting with the utmost degree of accuracy, utilizing hybrid frameworks become a must for obtaining more accurate and more reliable forecasting results. Series hybrid methodology is one of the most widely-used hybrid approaches that has encountered a great amount of popularity in the literature of time series forecasting and has been applied successfully in a wide variety of domains. In such hybrid methods is assumed that there is an additive relationship among different components of time series. Thus, based on this assumption, various individual models can apply separately on decomposed components, and the final forecast can be obtained. However, developed series hybrid models in the literature are constructed based on the decomposing time series into linear and nonlinear parts and generating linear-nonlinear modeling order for decomposed parts. Another assumption considered in the traditional series model is assigning equal weights to each model used for modeling linear and nonlinear components. Thus, contrary to traditional series hybrid models, to improve the performance of series hybrid models, these two basic assumptions have been violated in this paper. This study aims to propose a novel weighted MLP-ARIMA model filling the gap of series hybrid models by changing the order of sequence modeling and assigning weight for each component. Firstly, the modeling order is changed to nonlinear-linear, and then Multi-Layer Perceptron Neural Network (MLPNN) -Auto-Regressive Integrated Moving Average(ARIMA) models are employed to model and process nonlinear and linear components respectively. Secondly, each model's weights are computed by the Ordinary Least Square (OLS) weighting algorithm. Thus, in this paper, a novel improved weighted MLP-ARIMA series hybrid model is proposed for time series forecasting. The real-world benchmark data sets, including Wolf's sunspot data, the Canadian lynx data, and the British pound/US dollar exchange rate data, are elected to verify the effectiveness of the proposed weighted MLP-ARIMA series hybrid model. The simulation results revealed that the weighted MLP-ARIMA model could obtain superior performance compared to ARIMA-MLP, MLP-ARIMA, as well as the ARIMA and MLPNN individual models. The proposed hybrid model can be an effective alternative to improve forecasting accuracy obtained by traditional series hybrid methods.

R-Squared-Bootstrapping for Gegenbauer-Type Long Memory

The autocorrelation of long memory processes decays much slower than that of short memory processes, e.g. autoregressive processes. Fractional integration and Gegenbauer are basic models that show long memory behavior. Many tests for long memory of the fractional integration type (at f = 0) have been developed based on test statistics (e.g. the R/S-type statistics) or parameter estimators (e.g. the GPH estimator). But, so far, no work has shown reasonable power on testing for cyclic long memory. The authors investigate a parametric bootstrap procedure with an R-squared statistic as an assessment of cyclic long memory behavior. According to simulation results, the R-squared-bootstrapping method performs excellently in detecting Gegenbauer-type processes (e.g. with long memory behavior associated with frequencies $$f\in (0,0.5]$$ ) while at the same time controlling observed significance levels. The R-squared-bootstrapping test is also applied to the Lynx data and the result suggests the presence of long range dependence.

Improvement of time forecasting models using a novel hybridization of bootstrap and double bootstrap artificial neural networks

Hybrid models such as the Artificial Neural Network-Autoregressive Integrated Moving Average (ANN–ARIMA) model are widely used in forecasting. However, inaccuracies and inefficiency remain in evidence. To yield the ANN–ARIMA with a higher degree of accuracy, efficiency and precision, the bootstrap and the double bootstrap methods are commonly used as alternative methods through the reconstruction of an ANN–ARIMA standard error. Unfortunately, these methods have not been applied in time series-based forecasting models. The aims of this study are twofold. First, is to propose the hybridization of bootstrap model and that of double bootstrap mode called Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (B-ANN–ARIMA) and Double Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (DB-ANN–ARIMA), respectively. Second, is to investigate the performance of these proposed models by comparing them with ARIMA, ANN and ANN–ARIMA. Our investigation is based on three well-known real datasets, i.e., Wolf’s sunspot data, Canadian lynx data and, Malaysia ringgit/United States dollar exchange rate data. Statistical analysis on SSE, MSE, RMSE, MAE, MAPE and VAF is then conducted to verify that the proposed models are better than previous ARIMA, ANN and ANN–ARIMA models. The empirical results show that, compared with ARIMA, ANNs and ANN–ARIMA models, the proposed models generate smaller values of SSE, MSE, RMSE, MAE, MAPE and VAF for both training and testing datasets. In other words, the proposed models are better than those that we compare with. Their forecasting values are closer to the actual values. Thus, we conclude that the proposed models can be used to generate better forecasting values with higher degree of accuracy, efficiency and, precision in forecasting time series results becomes a priority.

A Hybridized Forecasting Method Based on Weight Adjustment of Neural Network Using Generalized Type-2 Fuzzy Set

This paper proposes a hybridized forecasting method on weight adjustment of neural networks with back-propagation learning using general type-2 fuzzy sets. Initialization of weights and their adjustment in neural network are important areas of research as it increases the computation speed to get the optimized result. Higher order fuzzy logic systems are able to deal with the high levels of uncertainties present in the majority of real-world problems. Here, the concept of interval-based zSlices has been used to obtain the general type-2 fuzzy weights for the neural network architecture. We implement this proposed methodology on benchmark Mackey–Glass time series data (for $$\tau =17$$ ) and present a comparison of the results obtained with our approach and those of the existing approaches. The method is also applied on enrollment data of University of Alabama, closing price index of Shenzhen stock exchange, closing price index of Shanghai stock exchange, Canadian lynx data, and the results are presented.

Incorporating natural and human factors in habitat modelling and spatial prioritisation for the <i>Lynx lynx martinoi</i>

Abstract. Countries in south-eastern Europe are cooperating to conserve a sub-endemic lynx species, Lynx lynx martinoi. Yet, the planning of species conservation should go hand-in-hand with the planning and management of (new) protected areas. Lynx lynx martinoi has a small, fragmented distribution with a small total population size and an endangered population. This study combines species distribution modelling with spatial prioritisation techniques to identify conservation areas for Lynx lynx martinoi. The aim was to determine locations of high probability of occurrence for the lynx, to potentially increase current protected areas by 20 % in Albania, the former Yugoslav Republic of Macedonia, Montenegro, and Kosovo. The species distribution modelling used generalised linear models with lynx occurrence and pseudo-absence data. Two models were developed and fitted using the lynx data: one based on natural factors, and the second based on factors associated with human disturbance. The Zonation conservation planning software was then used to undertake spatial prioritisations of the landscape using the first model composed of natural factors as a biological feature, and (inverted) a second model composed of anthropological factors such as a cost layer. The first model included environmental factors as elevation, terrain ruggedness index, woodland and shrub land, and food factor as chamois prey (occurrences) and had a prediction accuracy of 82 %. Second model included anthropological factors as agricultural land and had a prediction accuracy of 65 %. Prioritised areas for extending protected areas for lynx conservation were found primarily in the Albania–Macedonia–Kosovo and Montenegro–Albania–Kosovo cross-border areas. We show how natural and human factors can be incorporated into spatially prioritising conservation areas on a landscape level. Our results show the importance of expanding the existing protected areas in cross-border areas of core lynx habitat. The priority of these cross-border areas highlight the importance international cooperation can play in designing and implementing a coherent and long-term conservation plan including a species conservation plan to securing the future of the lynx.

Error modeling approach to improve time series forecasters

In time series forecasting exercises it has been usual to suppose that the error series generated by the forecasters have a white noise behavior. However, it is possible that such supposition is violated in practice due to model misspecification or disturbances of the phenomenon not captured by the predictive models. It may lead to statistically biased and/or inefficient predictors. The present paper introduces an approach to correct predetermined forecasters by recursively modeling their remaining residuals. Two formalisms are used to illustrate the recursive approach: the well-known (linear) autoregressive integrated moving average (ARIMA) and the (non-linear) Artificial Neural Network (ANN). These models are recursively adjusted to the remaining residuals of a given forecaster until a white noise behavior is achieved. Applications involving ARIMA and ANN forecasters for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, Nasdaq Index, Wolf׳s Sunspot, and Canadian Lynx data series indicate the usefulness of the proposed framework.

Time Series Forecasting using Least Square Support Vector Machine for Canadian Lynx Data

Time series analysis and forecasting is an active research area over the last few decades. There are various kinds of forecasting models have been developed and researchers have relied on statistical techniques to predict the future. This paper discusses the application of Least Square Support Vector Machine (LSSVM) models for Canadian Lynx forecasting. The objective of this paper is to examine the flexibility of LSSVM in time series forecasting by comparing it with other models in previous research such as Artificial Neural Networks (ANN), Auto-Regressive Integrated Moving Average (ARIMA), Feed-Forward Neural Networks (FNN), Self-Exciting Threshold Auto-Regression (SETAR), Zhang’s model, Aladang’s hybrid model and Support Vector Regression (SVR) model. The experiment results show that the LSSVM model outperforms the other models based on the criteria of Mean Absolute Error (MAE) and Mean Square Error (MSE). It also indicates that LSSVM provides a promising alternative technique in time series forecasting.

Exploiting the interpretability and forecasting ability of the RBF-AR model for nonlinear time series

In this paper, we explore the radial basis function network-based state-dependent autoregressive (RBF-AR) model by modelling and forecasting an ecological time series: the famous Canadian lynx data. The interpretability of the state-dependent coefficients of the RBF-AR model is studied. It is found that the RBF-AR model can account for the phenomena of phase and density dependencies in the Canadian lynx cycle. The post-sample forecasting performance of one-step and two-step ahead predictors of the RBF-AR model is compared with that of other competitive time-series models including various parametric and non-parametric models. The results show the usefulness of the RBF-AR model in this ecological time-series modelling.

Increased flexibility for modeling telemetry and nest‐survival data using the multistate framework

ABSTRACTAlthough telemetry is one of the most common tools used in the study of wildlife, advances in the analysis of telemetry data have lagged compared to progress in the development of telemetry devices. We demonstrate how standard known‐fate telemetry and related nest‐survival data analysis models are special cases of the more general multistate framework. We present a short theoretical development, and 2 case examples regarding the American black duck and the mallard. We also present a more complex lynx data analysis. Although not necessary in all situations, the multistate framework provides additional flexibility to analyze telemetry data, which may help analysts and biologists better deal with the vagaries of real‐world data collection. © 2014 The Wildlife Society.

An ARIMA‐ANN Hybrid Model for Time Series Forecasting

Autoregressive integrated moving average (ARIMA) model has been successfully applied as a popular linear model for economic time series forecasting. In addition, during the recent years, artificial neural networks (ANNs) have been used to capture the complex economic relationships with a variety of patterns as they serve as a powerful and flexible computational tool. However, most of these studies have been characterized by mixed results in terms of the effectiveness of the ANNs model compared with the ARIMA model. In this paper, we propose a hybrid model, which is distinctive in integrating the advantages of ARIMA and ANNs in modeling the linear and nonlinear behaviors in the data set. The hybrid model was tested on three sets of actual data, namely, the Wolf's sunspot data, the Canadian lynx data and the IBM stock price data. Our computational experience indicates the effectiveness of the new combinatorial model in obtaining more accurate forecasting as compared to existing models. Copyright © 2013 John Wiley & Sons, Ltd.

Stability analysis of RBF network-based state-dependent autoregressive model for nonlinear time series

Varying-coefficient models have attracted great attention in nonlinear time series analysis recently. In this paper, we consider a semi-parametric functional-coefficient autoregressive model, called the radial basis function network-based state-dependent autoregressive (RBF-AR) model. The stability conditions and existing conditions of limit cycle of the RBF-AR model are discussed. An efficient structured parameter estimation method and the modified multi-fold cross-validation criterion are applied to identify the RBF-AR model. Application of the RBF-AR model to the famous Canadian lynx data is presented. The forecasting capability of the RBF-AR model is compared to those of other competing time series models, which shows that the RBF-AR model is as good as or better than other models for the postsample forecasts.

Time Series Forecasting Using a Hybrid RBF Neural Network and AR Model Based On Binomial Smoothing

ANNARIMA that combines both autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models. This paper provides a hybrid methodology that combines both radial basis function (RBF) neural network and auto regression (AR) model based on binomial smoothing (BS) technique which is efficient in data processing, which is called BSRBFAR. This method is examined by using the data of Canadian Lynx data. Empirical results indicate that the over-fitting problem can be eased using RBF neural network based on binomial smoothing which is called BS-RBF, and the hybrid model—BS-RBFAR can be an effective way to improve forecasting accuracy achieved by BSRBF used separately. Keywords—binomial smoothing (BS), hybrid, Canadian Lynx data, forecasting accuracy.

A New Hybrid Methodology for Nonlinear Time Series Forecasting

Artificial neural networks (ANNs) are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. This is the reason that hybrid methodologies combining linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. Despite of all advantages of the traditional methodologies for combining ARIMA and ANNs, they have some assumptions that will degenerate their performance if the opposite situation occurs. In this paper, a new methodology is proposed in order to combine the ANNs with ARIMA in order to overcome the limitations of traditional hybrid methodologies and yield more general and more accurate hybrid models. Empirical results with Canadian Lynx data set indicate that the proposed methodology can be a more effective way in order to combine linear and nonlinear models together than traditional hybrid methodologies. Therefore, it can be applied as an appropriate alternative methodology for hybridization in time series forecasting field, especially when higher forecasting accuracy is needed.

Forecasting nonlinear time series with a hybrid methodology

In recent years, artificial neural networks (ANNs) have been used for forecasting in time series in the literature. Although it is possible to model both linear and nonlinear structures in time series by using ANNs, they are not able to handle both structures equally well. Therefore, the hybrid methodology combining ARIMA and ANN models have been used in the literature. In this study, a new hybrid approach combining Elman’s Recurrent Neural Networks (ERNN) and ARIMA models is proposed. The proposed hybrid approach is applied to Canadian Lynx data and it is found that the proposed approach has the best forecasting accuracy.