1,720,969 research outputs found
Entropy-Based Tests for Complex Dependence in Economic and Financial Time Series with the R Package tseriesEntropy
Full text linkTesting for complex serial dependence in economic and financial time series is a crucial task that bears many practical implications. However, the linear paradigm remains pervasive among practitioners as the autocorrelation function, because, despite its known shortcomings, it is still one of the most used tools in time series analysis. We propose a solution to the problem, by introducing the R package tseriesEntropy, dedicated to testing for serial/cross dependence and nonlinear serial dependence in time series, based on the entropy metric S-rho. The package implements tests for both continuous and categorical data. The nonparametric tests, based on S-rho, rely on minimal assumptions and have also been shown to be powerful for small sample sizes. The measure can be used as a nonlinear auto/cross-dependence function, both as an exploratory tool, or as a diagnostic measure, if computed on the residuals from a fitted model. Different null hypotheses of either independence or linear dependence can be tested by means of resampling methods, backed up by a sound theoretical background. We showcase our methods on a panel of commodity price time series. The results hint at the presence of a complex dependence in the conditional mean, together with conditional heteroskedasticity, and indicate the need for an appropriate nonlinear specification
On the Ergodicity of First-Order Threshold Autoregressive Moving-Average Processes
No full textWe introduce a certain Markovian representation for the threshold autoregressive moving-average (TARMA) process with which we solve the long-standing problem regarding the irreducibility condition of a first-order TARMA model. Under some mild regularity conditions, we obtain a complete classification of the parameter space of an invertible first-order TARMA model into parametric regions over which the model is either transient or recurrent, and the recurrence region is further subdivided into regions of null recurrence or positive recurrence, or even geometric recurrence. We derive a set of necessary and sufficient conditions for the ergodicity of invertible first-order TARMA processes
Testing for Threshold Regulation in Presence of Measurement Error
No full textRegulation is an important feature of dynamic phenomena, and is commonly tested within the threshold autoregressive setting, with the null hypothesis being a global nonstationary process. Nonetheless, this setting is debatable, because data are often corrupted by measurement errors. Thus, it is more appropriate to consider a threshold autoregressive moving-average model as the general hypothesis. We implement this new setting with the integrated moving-average model of order one as the null hypothesis. We derive a Lagrange multiplier test that has an asymptotically similar null distribution, and provide the first rigorous proof of tightness in the context of testing for threshold nonlinearity against difference stationarity, which is of independent interest. Simulation studies show that the proposed approach enjoys less bias and higher power in detecting threshold regulation than existing tests, especially when there are measurement errors. We apply the new approach to time series of real exchange rates of a panel of European countries
A role for circular code properties in translation
Full text linkCircular codes represent a form of coding allowing detection/correction of frame-shift errors. Building on recent theoretical advances on circular codes, we provide evidence that protein coding sequences exhibit in-frame circular code marks, that are absent in introns and are intimately linked to the keto-amino transformation of codon bases. These properties strongly correlate with translation speed, codon influence and protein synthesis levels. Strikingly, circular code marks are absent at the beginning of coding sequences, but stably occur 40 codons after the initiator codon, hinting at the translation elongation process. Finally, we use the lens of circular codes to show that codon influence on translation correlates with the strong-weak dichotomy of the first two bases of the codon. The results can lead to defining new universal tools for sequence indicators and sequence optimization for bioinformatics and biotechnological applications, and can shed light on the molecular mechanisms behind the decoding process
The validity of bootstrap testing for threshold autoregression
Full text linkWe consider bootstrap-based testing for threshold effects in non-linear threshold autoregressive (TAR) models. It is well-known that classic tests based on asymptotic theory tend to be biased in case of small, or even moderate sample sizes, especially when the estimated parameters indicate non-stationarity, or in presence of heteroskedasticity, as often witnessed in the analysis of financial or climate data. To address the issue we propose a supremum Lagrange Multiplier test statistic (sLM), where the null hypothesis specifies a linear autoregressive (AR) model against the alternative of a TAR model. We consider both the classical recursive residual i.i.d. bootstrap (sLMi) and a wild bootstrap (sLMw), applied to the sLM statistic, and establish their validity under the null hypothesis. The framework is new, and requires the proof of non-standard results for bootstrap analysis in time series models; this includes a uniform bootstrap law of large numbers and a bootstrap functional central limit theorem. The Monte Carlo evidence shows that the bootstrap tests have correct empirical size even for small samples; the wild bootstrap version (sLMw) is also robust against the presence of heteroskedasticity. Moreover, there is no loss of empirical power when compared to the asymptotic test and the size of the tests is not affected if the order of the tested model is selected through AIC. Finally, we use our results to analyse the time series of the Greenland ice sheet mass balance. We find a significant threshold effect and an appropriate specification that manages to reproduce the main nonlinear features of the series, such as the asymmetric seasonal cycle, the main periodicities and the multimodality of the probability density function
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