Search Results (19)

This study proposes an extension of Seasonal Autoregressive Integrated Moving Average models with exogenous regressors (SARIMAX) by incorporating skew-normal and zero-inflated skew-normal error structures to better accommodate asymmetry and excess zeros in time series data. The proposed framework demonstrates improved flexibility and robustness compared to traditional Gaussian-based models. Simulation experiments reveal that the skewness parameter significantly affect forecasting accuracy, with reductions in mean absolute error (MAE) and root mean square error (RMSE) observed across both positively and negatively skewed scenarios. Notably, in negative-skew contexts, the model achieved an MAE of 0.40 and RMSE of 0.49, outperforming its symmetric-error counterparts. The inclusion of zero-inflation probabilities further enhances model performance in sparse datasets, yielding superior values in goodness-of-fit criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). To illustrate the practical value of the methodology, a real-world case study is presented involving the modeling of optical density (OD₆₀₀) data from Escherichia coli during stationary-phase growth. A SARIMAX(1,1,1) model with skew-normal errors was fitted to 200 time-stamped absorbance measurements, revealing significant positive skewness in the residuals. Bootstrap-derived confidence intervals confirmed the significance of the estimated skewness parameter ($\alpha =14.033$ with 95% CI [12.07, 15.99]). The model outperformed the classical ARIMA benchmark in capturing the asymmetry of the stochastic structure, underscoring its relevance for biological, environmental, and industrial applications in which non-Gaussian features are prevalent. Full article

The goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an additional self-normalization factor, which enables effective control the Type I error. We theoretically investigate the asymptotic properties of the monitoring method under the null hypothesis as well as the alternative hypothesis. Since the asymptotic distribution under the null hypothesis is quite complicated, we apply the multivariate stationary bootstrap method to estimate the critical value of the sequential test. Numerical simulations and a real-world application demonstrate the usefulness of the proposed method. Full article

This study examines the bias in weighted least absolute deviation ($\mathrm{W}{L}_1$) estimation within the context of stationary first-order bifurcating autoregressive (BAR(1)) models, which are frequently employed to analyze binary tree-like data, including applications in cell lineage studies. Initial findings indicate that $\mathrm{W}{L}_1$ estimators can demonstrate substantial and problematic biases, especially when small to moderate sample sizes. The autoregressive parameter and the correlation between model errors influence the volume and direction of the bias. To address this issue, we propose two bootstrap-based bias-corrected estimators for the $\mathrm{W}{L}_1$ estimator. We conduct extensive simulations to assess the performance of these bias-corrected estimators. Our empirical findings demonstrate that these estimators effectively reduce the bias inherent in $\mathrm{W}{L}_1$ estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range. Full article

A key summary statistic in a stationary functional time series is the long-run covariance function that measures serial dependence. It can be consistently estimated via a kernel sandwich estimator, which is the core of dynamic functional principal component regression for forecasting functional time series. To measure the uncertainty of the long-run covariance estimation, we consider sieve and functional autoregressive (FAR) bootstrap methods to generate pseudo-functional time series and study variability associated with the long-run covariance. The sieve bootstrap method is nonparametric (i.e., model-free), while the FAR bootstrap method is semi-parametric. The sieve bootstrap method relies on functional principal component analysis to decompose a functional time series into a set of estimated functional principal components and their associated scores. The scores can be bootstrapped via a vector autoregressive representation. The bootstrapped functional time series are obtained by multiplying the bootstrapped scores by the estimated functional principal components. The FAR bootstrap method relies on the FAR of order 1 to model the conditional mean of a functional time series, while residual functions can be bootstrapped via independent and identically distributed resampling. Through a series of Monte Carlo simulations, we evaluate and compare the finite-sample accuracy between the sieve and FAR bootstrap methods for quantifying the estimation uncertainty of the long-run covariance of a stationary functional time series. Full article

This paper investigates the properties of the change in persistence detection for observations with infinite variance. The innovations are assumed to be in the domain of attraction of a stable law with index $\kappa \in (0,2]$. We provide a new test statistic and show that its asymptotic distribution under the null hypothesis of non-stationary $I\left(1\right)$ series is a functional of a stable process. When the change point in persistence is not known, the consistency is always given under the alternative, either from stationary $I\left(0\right)$ to non-stationary $I\left(1\right)$ or vice versa. The proposed tests can be used to identify the direction of change and do not over-reject against constant $I\left(0\right)$ series, even in relatively small samples. Furthermore, we also consider the change point estimator which is consistent and the asymptotic behavior of the test statistic in the case of near-integrated time series. A block bootstrap method is suggested to determine critical values because the null asymptotic distribution contains the unknown tail index, which results in critical values depending on it. The simulation study demonstrates that the block bootstrap-based test is robust against change in persistence for heavy-tailed series with infinite variance. Finally, we apply our methods to the two series of the US inflation rate and USD/CNY exchange rate, and find significant evidence for persistence changes, respectively, from $I\left(0\right)$ to $I\left(1\right)$ and from $I\left(1\right)$ to $I\left(0\right)$. Full article

In this study, we present a thorough comparison of the performance of four different bootstrap methods for assessing the significance of causal analysis in time series data. For this purpose, multivariate simulated data are generated by a linear feedback system. The methods investigated are uncorrelated Phase Randomization Bootstrap (uPRB), which generates surrogate data with no cross-correlation between variables by randomizing the phase in the frequency domain; Time Shift Bootstrap (TSB), which generates surrogate data by randomizing the phase in the time domain; Stationary Bootstrap (SB), which calculates standard errors and constructs confidence regions for weakly dependent stationary observations; and AR-Sieve Bootstrap (ARSB), a resampling method based on AutoRegressive (AR) models that approximates the underlying data-generating process. The uPRB method accurately identifies variable interactions but fails to detect self-feedback in some variables. The TSB method, despite performing worse than uPRB, is unable to detect feedback between certain variables. The SB method gives consistent causality results, although its ability to detect self-feedback decreases, as the mean block width increases. The ARSB method shows superior performance, accurately detecting both self-feedback and causality across all variables. Regarding the analysis of the Impulse Response Function (IRF), only the ARSB method succeeds in detecting both self-feedback and causality in all variables, aligning well with the connectivity diagram. Other methods, however, show considerable variations in detection performance, with some detecting false positives and others only detecting self-feedback. Full article

It is likely that changing monsoon patterns and changes in other climatic parameters will have an impact on forests. Tree growth and biomass may respond differently across the different forest recovery contexts after the disturbance regimes. It is essential to understand the response of different tree species in order to comprehend their ability to adapt to climate change. An enhanced understanding of how tree species dynamics change with a substantial shift in climate attributes is crucial to develop adaptive forest management strategies. Advances in the statistical application of tree ring data results in more reliable dating with the high accuracy and precision of any of the paleo-records and robust and long-term reconstructions of key indices such as temperature and precipitation. In this study, we analyzed how different species inhabiting together respond to changes in climatic variables using dendroclimatic analysis. We assessed the growth performance of Abies pindrow, Pinus wallichiana, and Tsuga dumosa in the temperate region of Nepal. The climate sensitivity of the species was analyzed using bootstrap correlation analysis and the climate-growth relationship over time was assessed using the moving correlation function. Tree ring growth of Abies pindrow is stimulated by higher June temperatures and higher March precipitation. This positive relationship is consistent and stationary over time. However, in the other two species, both response function and moving correlation analysis showed that the relationship between climate and growth is inconsistent and changes over time. Full article

The problem of testing the equality of generating processes of two multivariate time series is addressed in this work. To this end, we construct two tests based on a distance measure between stochastic processes. The metric is defined in terms of the quantile cross-spectral densities of both processes. A proper estimate of this dissimilarity is the cornerstone of the proposed tests. Both techniques are based on the bootstrap. Specifically, extensions of the moving block bootstrap and the stationary bootstrap are used for their construction. The approaches are assessed in a broad range of scenarios under the null and the alternative hypotheses. The results from the analyses show that the procedure based on the stationary bootstrap exhibits the best overall performance in terms of both size and power. The proposed techniques are used to answer the question regarding whether or not the dotcom bubble crash of the 2000s permanently impacted global market behavior. Full article

Researchers have utilized Other Test Method (OTM) 33A to quantify methane emissions from natural gas infrastructure. Historically, errors have been reported based on a population of measurements compared to known controlled releases of methane. These errors have been reported as 2σ errors of ±70%. However, little research has been performed on the minimum attainable uncertainty of any one measurement. We present two methods of uncertainty estimation. The first was the measurement uncertainty of the state-of-the-art equipment, which was determined to be ±3.8% of the estimate. This was determined from bootstrapped measurements compared to controlled releases. The second approach of uncertainty estimation was a modified Hollinger and Richardson (H&R) method which was developed for quantifying the uncertainty of eddy covariance measurements. Using a modified version of this method applied to OTM 33A measurements, it was determined that uncertainty of any given measurement was ±17%. Combining measurement uncertainty with that of stochasticity produced a total minimum uncertainty of 17.4%. Due to the current nature of stationary single-sensor measurements and the stochasticity of atmospheric data, such uncertainties will always be present. This is critical in understanding the transport of methane emissions and indirect measurements obtained from the natural gas industry. Full article

Extreme value modeling for extreme rainfall is one of the most important processes in the field of hydrology. For the improvement of extreme value modeling and its physical meaning, large-scale climate modes have been widely used as covariates of distribution parameters, as they can physically account for climate variability. This study proposes a novel procedure for extreme value modeling of rainfall based on the significant relationship between the long-term trend of the annual maximum (AM) daily rainfall and large-scale climate indices. This procedure is characterized by two main steps: (a) identifying significant seasonal climate indices (SCIs), which impact the long-term trend of AM daily rainfall using statistical approaches, such as ensemble empirical mode decomposition, and (b) selecting an appropriate generalized extreme value (GEV) distribution among the stationary GEV and nonstationary GEV (NS-GEV) using time and SCIs as covariates by comparing their model fit and uncertainty. Our findings showed significant relationships between the long-term trend of AM daily rainfall over South Korea and SCIs (i.e., the Atlantic Meridional Mode, Atlantic Multidecadal Oscillation in the fall season, and North Atlantic Oscillation in the summer season). In addition, we proposed a model selection procedure considering both the Akaike information criterion and residual bootstrap method to select an appropriate GEV distribution among a total of 59 GEV candidates. As a result, the NS-GEV with SCI covariates generally showed the best performance over South Korea. We expect that this study can contribute to estimating more reliable extreme rainfall quantiles using climate covariates. Full article

This study aims to overcome the problem of dimensionality, accurate estimation, and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) uncertainty intervals in high frequency data. A Bayesian bootstrapping and backtest density forecasts, which are based on a weighted threshold and quantile of a continuously ranked probability score, are developed. Developed backtesting procedures revealed that an estimated Seasonal autoregressive integrated moving average-generalized autoregressive score-generalized extreme value distribution (SARIMA–GAS–GEVD) with a skewed student-t distribution had the best prediction performance in forecasting and bootstrapping VaR and ES. Extension of this non-stationary distribution in literature is quite complicated since it requires specifications not only on how the usual Bayesian parameters change over time but also those with bulk distribution components. This implies that the combination of a stochastic econometric model with extreme value theory (EVT) procedures provides a robust basis necessary for the statistical backtesting and bootstrapping density predictions for VaR and ES. Full article

In this paper, we address the classical problem of testing for stationarity in the prices of energy-related commodities. A panel of fourteen time series of monthly prices is analyzed for the 1980–2020 period. Nine of the series are classical nonrenewable, GHG-emissions-intensive resources (coal, crude oil, natural gas), whereas the remaining, low-emission group includes both uranium and four commodities employed in biofuels (rapeseed, palm, and soybean oils, and ethanol). A nonparametric, bootstrap-based stationarity testing framework is employed. The main advantage of this procedure is its asymptotically model-free nature, being less sensitive than parametric tests to the risks of misspecification and detection of spurious unit roots, although it has the potential limitation of typically requiring larger samples than mainstream tools. Results suggest that most of the series analyzed may be trend stationary. The only exception would be crude oil, where different conclusions are obtained depending on whether a seasonal correction is applied or not. Full article

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust. Full article

Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed bootstrap). In these contexts, four new bandwidth parameter selectors are proposed based on closed bootstrap expressions of the MISE of the kernel density estimator (case 1) and two approximations of the kernel hazard rate estimation (case 2). These expressions turn out to be very useful since Monte Carlo approximation is no longer needed. Finally, these smoothing parameter selectors are empirically compared with the already existing ones via a simulation study. Full article

Almost sure bootstrap consistency of the blockwise bootstrap for the Average Value at Risk of single risks is established for strictly stationary $\beta$ -mixing observations. Moreover, almost sure bootstrap consistency of a multiplier bootstrap for the Average Value at Risk of collective risks is established for independent observations. The main results rely on a new functional delta-method for the almost sure bootstrap of uniformly quasi-Hadamard differentiable statistical functionals, to be presented here. The latter seems to be interesting in its own right. Full article