arXiv subjects

J. Eduardo Vera-Valdés

Publications and source records attributed to J. Eduardo Vera-Valdés.

7 recordsLinked to original sources

arXiv2026

Cointegration by Parts: Locating Cointegration in Time

Tests for cointegration are typically applied to a single window spanning the entire sample, assuming that the long-run relationship holds throughout. When it holds over only a part of the sample, such tests lose power, because the stationary episode is diluted by periods without cointegration. We propose three statistics for testing whether two or more series cointegrate only over a part of the sample, each an infimum of the Engle-Granger statistic over recursive, backward-expanding, or doubly-flexible windows. We derive their limiting distributions and establish which alternatives each is consistent against. Only the doubly-flexible statistic has power against both break directions. Inspired by the seminal work of James G. MacKinnon, critical values are obtained by simulation and summarized through response surface regressions. We apply the tests to global mean sea level and global mean surface temperature anomalies. All three reject the null of no cointegration at the 5% level, locating it in a sub-period of the 1880--2019 record that coincides with documented discontinuities in sea surface temperature data collection.

stat.ME↗

arXiv2026

The kinematics of global warming: Semiparametric analysis of warming level, rate, and acceleration

Three features of the global warming process are of central scientific interest: its level, its warming rate, and changes in that warming rate. We develop a semiparametric kinematic state-space framework for estimating the latent kinematic path of global warming from noisy monthly temperature observations. The framework estimates the warming level, warming rate, and warming acceleration jointly, while incorporating covariates, serial dependence, and time-varying error variance directly in the model. Applying the framework to five major global temperature records, and comparing it with nonparametric kernel and parametric benchmark estimators, we show that the inferred recent warming dynamics depend strongly on the object being estimated. The current underlying warming level is estimated precisely and is robust across datasets and methods, with estimates close to $1.4\,^{\circ}\mathrm{C}$ above pre-industrial levels. Estimates of the current warming rate are consistently positive and elevated, but differ materially across estimator classes: flexible local estimators imply substantially higher current rates than long-window parametric specifications, which instead summarize average post-break or restricted-curvature behaviour. Our preferred state-space specification estimates the current warming rate at approximately $0.47\,^{\circ}\mathrm{C}$ per decade. Evidence on acceleration is necessarily more uncertain, because acceleration is a local second derivative. Nevertheless, the estimated kinematic paths show positive acceleration in the recent period, and the endpoint acceleration estimates are positive across datasets and methods.

stat.AP↗

arXiv2024

Breaching 1.5°C: Give me the odds

Climate change communication is crucial to raising awareness and motivating action. In the context of breaching the limits set out by the Paris Agreement, we argue that climate scientists should move away from point estimates and towards reporting probabilities. Reporting probabilities will provide policymakers with a range of possible outcomes and will allow them to make informed timely decisions. To achieve this goal, we propose a method to calculate the probability of breaching the limits set out by the Paris Agreement. The method can be summarized as predicting future temperatures under different scenarios and calculating the number of possible outcomes that breach the limits as a proportion of the total number of outcomes. The probabilities can be computed for different time horizons and can be updated as new data become available. As an illustration, we performed a simulation study to investigate the probability of breaching the limits in a statistical model. Our results show that the probability of breaching the 1.5°C limit is already greater than zero for 2024. Moreover, the probability of breaching the limit is greater than 99% by 2042 if no action is taken to reduce greenhouse gas emissions. Our methodology is simple to implement and can easily be extended to more complex models of the climate system. We encourage climate model developers to include the probabilities of breaching the limits in their reports.

stat.AP↗

arXiv2024

Robust estimation of carbon dioxide airborne fraction under measurement errors

This paper discusses the effect of measurement errors in the estimation of the carbon dioxide (CO$_2$) airborne fraction. We are the first to present regression-based estimates and standard errors that are robust to measurement errors for the extended model, the preferred specification to estimate the CO$_2$ airborne fraction. To achieve this goal, we add to the literature in three ways: $i)$ We generalise the Deming regression to handle multiple variables. $ii)$ We introduce a bootstrap approach to construct confidence intervals for Deming regression in both univariate and multivariate scenarios. $iii)$ Propose to estimate the airborne fraction using instrumental variables (IV), taking advantage of the variation of additional measurements, to obtain consistent estimates that are robust to measurement errors. IV estimates for the airborne fraction are 44.8%($\pm$ 1.4%; 1$σ$) for the simple specification, and 47.3%($\pm$ 1.1%; 1$σ$) for the extended specification. We show that these estimates are not statistically different from the ordinary least squares (OLS) estimates, while being robust to measurement errors without relying on additional assumptions. In contrast, OLS estimates are shown to fall outside the confidence interval of the Deming regression estimates.

stat.AP↗

arXiv2024

LongMemory.jl: Generating, Estimating, and Forecasting Long Memory Models in Julia

LongMemory.jl is a package for time series long memory modelling in Julia. The package provides functions to generate long memory, estimate model parameters, and forecast. Generating methods include fractional differencing, stochastic error duration, and cross-sectional aggregation. Estimators include the classic ones used to estimate the Hurst effect, those inspired by log-periodogram regression, and parametric ones. Forecasting is provided for all parametric estimators. Moreover, the package adds plotting capabilities to illustrate long memory dynamics and forecasting. This article presents the theoretical developments for long memory modelling, show examples using the data included with the package, and compares the properties of LongMemory.jl with current alternatives, including benchmarks. For some of the theoretical developments, LongMemory.jl provides the first publicly available implementation in any programming language. A notable feature of this package is that all functions are implemented in the same programming language, taking advantage of the ease of use and speed provided by Julia. Therefore, all code is accessible to the user. Multiple dispatch, a novel feature of the language, is used to speed computations and provide consistent calls to related methods. The package is related to the R packages LongMemoryTS and fracdiff.

cs.MS↗

arXiv2018

Nonfractional Memory: Filtering, Antipersistence, and Forecasting

The fractional difference operator remains to be the most popular mechanism to generate long memory due to the existence of efficient algorithms for their simulation and forecasting. Nonetheless, there is no theoretical argument linking the fractional difference operator with the presence of long memory in real data. In this regard, one of the most predominant theoretical explanations for the presence of long memory is cross-sectional aggregation of persistent micro units. Yet, the type of processes obtained by cross-sectional aggregation differs from the one due to fractional differencing. Thus, this paper develops fast algorithms to generate and forecast long memory by cross-sectional aggregation. Moreover, it is shown that the antipersistent phenomenon that arises for negative degrees of memory in the fractional difference literature is not present for cross-sectionally aggregated processes. Pointedly, while the autocorrelations for the fractional difference operator are negative for negative degrees of memory by construction, this restriction does not apply to the cross-sectional aggregated scheme. We show that this has implications for long memory tests in the frequency domain, which will be misspecified for cross-sectionally aggregated processes with negative degrees of memory. Finally, we assess the forecast performance of high-order $AR$ and $ARFIMA$ models when the long memory series are generated by cross-sectional aggregation. Our results are of interest to practitioners developing forecasts of long memory variables like inflation, volatility, and climate data, where aggregation may be the source of long memory.

math.ST↗

arXiv2017

On Long Memory Origins and Forecast Horizons

Most long memory forecasting studies assume that the memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator, and assess the performance of the autoregressive fractionally integrated moving average $(ARFIMA)$ model when forecasting series with long memory generated by nonfractional processes. We find that high-order autoregressive $(AR)$ models produce similar or superior forecast performance than $ARFIMA$ models at short horizons. Nonetheless, as the forecast horizon increases, the $ARFIMA$ models tend to dominate in forecast performance. Hence, $ARFIMA$ models are well suited for forecasts of long memory processes regardless of the long memory generating mechanism, particularly for medium and long forecast horizons. Additionally, we analyse the forecasting performance of the heterogeneous autoregressive ($HAR$) model which imposes restrictions on high-order $AR$ models. We find that the structure imposed by the $HAR$ model produces better long horizon forecasts than $AR$ models of the same order, at the price of inferior short horizon forecasts in some cases. Our results have implications for, among others, Climate Econometrics and Financial Econometrics models dealing with long memory series at different forecast horizons. We show in an example that while a short memory autoregressive moving average $(ARMA)$ model gives the best performance when forecasting the Realized Variance of the S\&P 500 up to a month ahead, the $ARFIMA$ model gives the best performance for longer forecast horizons.

econ.EM↗