Wavelet Polynomial Autoregression for Monthly Bigeye Tuna Catches Forecasting

In this paper, we use a functional autoregressive (FAR) model combined with multi-scale stationary wavelet decomposition technique for one-month-ahead monthly sardine catches forecasting in northern area of Chile (18 o 21***S *** 24 o S ).The monthly sardine catches data were collected from the database of the National Marine Fisheries Service for the period between 1 January 1973 and 30 December 2007. The proposed forecasting strategy is to decompose the raw sardine catches data set into trend component and residual component by using multi-scale stationary wavelet transform. In wavelet domain, the trend component and residual component are predicted by use a linear autoregressive model and FAR model; respectively. Hence, proposed forecaster is the co-addition of two predicted components. We find that the proposed forecasting method achieves a 99% of the explained variance with a reduced parsimonious and high accuracy. Besides, is showed that the wavelet-autoregressive forecaster is more accurate and performs better than both multilayer perceptron neural network model and FAR model.

This study compares the efficiency of a non-linear model called artificial neural network with linear autoregressive and random walk models in the one-step-ahead prediction of daily Indian rupee/US dollar exchange rate. We find that neural network and linear autoregressive models outperform random walk model in in-sample and out-of-sample forecasts. The in-sample forecasting of neural network is found to be better than that of linear autoregressive model. As far as out-of-sample forecasting is concerned, the results are mixed and we do not find a "winner" model between neural network and linear autoregressive model. However, neural network is able to improve upon the linear autoregressive model in terms of sign predictions. In addition to this, we also find that the number of input nodes has greater impact on neural network's performance than the number of hidden nodes.

We analyzed the variability of sea surface height anomaly (SSHA), and its relationship with Bigeye tuna catch in the eastern Indian Ocean (EIO) off of Java Island (Indonesia). Both time series of SSHA and Bigeye tuna HR show dominant signals corresponding to the annual and inter-annual variability. During the southeast monsoon the wind blows along southern coast of Java and produces coastal upwelling. This causes sea level to drop due to an offshore Ekman transport, and thermocline becomes shallower. During El Niño and Indian Ocean Dipole (IOD) positive phase, upwelling is more intense and a large cold eddy forms in the EIO off Java. Generally, Bigeye tuna HR tends to increase during upwelling seasons and becomes even higher during El Niño and the positive phase of the IOD. The increased Bigeye tuna HR during the southeast monsoon, El Niño and the IOD positive phase can be attributed to the shallower thermocline depth and the enhancement of biological productivity due to development of eddies and strong upwelling in the EIO. The spatial distribution of SSHA indicates that Bigeye tuna catches are abundant in the frontal regions between cold and warm eddies.

BackgroundReliable evaluations of state-level policies are essential for identifying effective policies and informing policymakers’ decisions. State-level policy evaluations commonly use a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. More guidance is needed about which set of statistical models perform best when estimating how state-level policies affect outcomes.MethodsMotivated by applied state-level opioid policy evaluations, we implemented an extensive simulation study to compare the statistical performance of multiple variations of the two-way fixed effect models traditionally used for DID under a range of simulation conditions. We also explored the performance of autoregressive (AR) and GEE models. We simulated policy effects on annual state-level opioid mortality rates and assessed statistical performance using various metrics, including directional bias, magnitude bias, and root mean squared error. We also reported Type I error rates and the rate of correctly rejecting the null hypothesis (e.g., power), given the prevalence of frequentist null hypothesis significance testing in the applied literature.ResultsMost linear models resulted in minimal bias. However, non-linear models and population-weighted versions of classic linear two-way fixed effect and linear GEE models yielded considerable bias (60 to 160%). Further, root mean square error was minimized by linear AR models when we examined crude mortality rates and by negative binomial models when we examined raw death counts. In the context of frequentist hypothesis testing, many models yielded high Type I error rates and very low rates of correctly rejecting the null hypothesis (< 10%), raising concerns of spurious conclusions about policy effectiveness in the opioid literature. When considering performance across models, the linear AR models were optimal in terms of directional bias, root mean squared error, Type I error, and correct rejection rates.ConclusionsThe findings highlight notable limitations of commonly used statistical models for DID designs, which are widely used in opioid policy studies and in state policy evaluations more broadly. In contrast, the optimal model we identified--the AR model--is rarely used in state policy evaluation. We urge applied researchers to move beyond the classic DID paradigm and adopt use of AR models.

Even in sustained vowels, the durations of successive glottal cycles are not identical. They fluctuate quasi-randomly around an average. This phenomenon is known as jitter. Correlation analysis has shown that perturbations of neighboring glottal cycles are interdependent, i.e. they are not purely random. The non-random component of jitter can be modeled by means of a linear autoregressive time series model which absorbs correlations between fluctuations of adjacent cycles and leaves a purely random component. The problem is that nonlinear relations may be missed by correlation analysis or linear autoregressive modeling. Nonlinear relations could be the signature of chaotic vibratory patterns which some authors expect for some pathological conditions of the vocal folds. We therefore decided to search inside whitened jitter time series (i.e. time series from which any linear correlations had been removed) for nonlinear or other anomalous dependencies between neighboring cycles. The results showed the following. Of the 265 time series, 231 appeared to have been correctly represented by linear autoregressive models. For 29 series out of the 34 remaining, deviations from pure randomness could be traced to isolated anomalous glottal cycles which statistical time series models had not taken into account. Finally, five signals, produced by three speakers, were detected which displayed relations between neighboring cycles which could not be traced either to linear correlations or to isolated glitches.

This article provides out-of-sample forecasts of linear and nonlinear models of US and four Census subregions’ housing prices. The forecasts include the traditional point forecasts, but also include interval and density forecasts, of the housing price distributions. The nonlinear smooth-transition autoregressive model outperforms the linear autoregressive model in point forecasts at longer horizons, but the linear autoregressive and nonlinear smooth-transition autoregressive models perform equally at short horizons. In addition, we generally do not find major differences in performance for the interval and density forecasts between the linear and nonlinear models. Finally, in a dynamic 25-step ex-ante and interval forecasting design, we, once again, do not find major differences between the linear and nonlinear models. In sum, we conclude that when forecasting regional housing prices in the United States, generally the additional costs associated with nonlinear forecasts outweigh the benefits for forecasts only a few months into the future.

In this paper, the aim is to apply a functional autoregressive (FAR) model combined with wavelet smoothing analysis for monthly bigeye tuna catches forecasting in the equatorial Indian ocean. The raw monthly tuna catches data is smoothed by using discrete stationary wavelet transform and then appropriate is used as inputs to the FAR model. We find that the proposed forecasting strategy achieves $97\%$ of the explained variance with reduced parsimony and high accuracy.

An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.

This article introduces autoregressive (AR) linear models to psychology students and researchers through a step-by-step approach using SPSS and R. Despite their relevance, AR models remain underutilized in behavioral sciences, possibly due to conceptual challenges and difficulties interpreting autocorrelation and seasonality. Our aim is to simplify their implementation by presenting time series models as special cases of linear regression, using accessible language and practical examples. The article illustrates AR estimation using real data, incorporating lagged values as predictors of the dependent variable. Residual diagnostics, a frequently overlooked aspect in applied research, receive special attention, including figures and statistical tests. As Kmenta (1971) demonstrated, serially correlated residuals can lead to artificially low p values for the parameter estimates, potentially resulting in explanatory variables being deemed significant when they truly are not. To promote understanding, we offer intuitive visualizations and clear decision rules for model building, lag selection, and seasonality detection. We compare polynomial and AR models using the confounding test. The data set and annotated R and SPSS scripts are included to support replication and help readers learn basic syntax. We also discuss conceptual and practical limitations of moving average, integration (I), and exponential smoothing models, emphasizing the practical advantages of AR-only models in psychological contexts. Throughout, we stress the importance of aligning statistical models with theoretical assumptions and the temporal structure of data. By combining step-by-step explanations, visual guidance, and real-data applications, this tutorial provides a practical foundation for incorporating AR models into applied psychological research. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

A nonlinear approach to modelling the residential electricity consumption in Ethiopia

We introduce a new class of nonlinear autoregressive models from their representation as linear autoregressive models with time-varying coefficients. The parameter updating scheme is subsequently based on the score of the predictive likelihood function at each point in time. We study in detail the information theoretic optimality properties of this updating scheme and establish the asymptotic theory for the maximum likelihood estimator of the static parameters of the model. We compare the dynamic properties of the new model with those of well-known nonlinear dynamic models such as the threshold and smooth transition autoregressive models. Finally, we study the model’s performance in a Monte Carlo study and in an empirical out-of-sample forecasting analysis for U.S. macroeconomic time series.

Optimal filtering of complex turbulent systems with memory depth through consistency constraints

L'obiettivo del lavoro e la ricerca di nessi causativi tra sequenze di dati idrologici (piezometrie e precipitazioni) mediante modelli lineari di tipo autoregressivo e a media mobile (ARMA). Tali dati derivano da un pozzo e da una stazione meteorologica situati nella Provincia di Cremona, e sono relativi al periodo Gennaio 1951-Dicembre 1998.Nel modello proposto, la sequenza pluviometrica e l'ingresso di un sistema dinamico lineare a tempo discreto, mentre la sequenza piezometrica e la sua uscita: il valore corrente di piezometria e cosi determinato dalla combinazione lineare di piezometrie e pluviometrie passate.Dopo una fase preliminare di analisi statistica delle sequenze (nei domini di tempo e frequenza), il modello ARMA e stato utilizzato dapprima per ricostruire le sequenze piezometriche disponibili e identificare i parametri della combinazione lineare, e poi per operare la previsione delle piezometrie: calcolando il residuo di previsione (tramite il confronto di piezometria predetta e misurata), e caratterizzandolo statisticamente si e valutata la capacita predittiva del modello.I risultati hanno mostrato che il predittore costruito presenta un errore quadratico di predizione relativamente piccolo. Nonostante cio, dall'analisi del residuo emerge che il predittore costruito non riesce a descrivere in maniera accurata tutte le proprieta del processo piezometrico. Questo puo essere dovuto al fatto che la grandezza impiegata come ingresso del sistema dinamico (precipitazione) non e l'unica voce che concorre al bilancio idrogeologico.

Robust quantile regression is a collection of statistical procedures based on regression, autoregression and conditional quantiles and on regression and autoregression rank scores . These procedures can replace the classical estimation and testing procedures in the linear regression and autoregression models, based on least squares, in situations when we cannot guarantee that our observations follow the normal distribution. The character of these methods is nonparametric (i.e. they do not assume any specific probability distribution of the observations), and robust (with respect to outliers in the dependent variables). Moreover, the procedures based on the regression rank scores do not depend on an eventual nuisance regression, because the regression rank scores are invariant to the regression parameters, similarly as the ordinary ranks are invariant to the shift in location. Regression quantiles and regression rank scores are dual in the linear programming sense, but their relation also extends the duality of the quantiles (order statistics) and ranks from the location to the linear regression (autoregression) models.