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on Econometric Time Series |
| By: | Kreye, Tom Jannik |
| Abstract: | In this paper, tests for fractional cointegration that allow for structural breaks in the long-run equilibrium are proposed. Traditional cointegration tests cannot handle shifts in fractional cointegration relationships, a limitation addressed here by allowing for a time-dependent memory parameter for the cointegration error. The tests are implemented by taking the extremum of a residual-based fractional cointegration test applied to different subsamples of the data. The subsampling procedures include sample splits, incremental samples, and rolling samples. A fairly general cointegration model is assumed, where the observed series and the cointegration error are fractionally integrated processes. Under the alternative hypothesis, the tests converge to the supremum of a chi-squared distribution. A Monte Carlo simulation is used to evaluate the finite sample performance of the tests. |
| Keywords: | Fractional Cointegration, Long Memory, Monte Carlo, Persistence Breaks, Structural Breaks, Subsample Analysis |
| JEL: | C12 C32 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-733 |
| By: | Jungbin Hwang (University of Connecticut); Yixiao Sun (University of California, San Diego) |
| Abstract: | This paper develops asymptotic F and t tests for nonlinear cointegrated re-gression, where regressors are asymptotically homogeneous transformations of I(1) processes. These transformations encompass a broad class of functions, includ-ing distribution-like functions, logarithmic functions, and asymptotically polynomial functions. Our asymptotic F and t test theory covers both the case with exogenous regressors and the case with endogenous regressors. For the exogenous case, we con-struct a novel set of basis functions for series long-run variance estimation, effectively accounting for parameter estimation uncertainty. For the endogenous case, we extend the transformed-augmented OLS approach developed for linear cointegrated settings. Monte Carlo simulations show that our asymptotic F and t tests outperform compet-ing tests, including the asymptotic chi-square test based on the fully modified OLS estimator and the non-standard fixed-b test based on the integrated modified OLS estimator. Furthermore, our theory extends to cases where the processes driving regressors are nonstationary, fractionally integrated processes. |
| Keywords: | F test and F distribution, nonlinear cointegrating regression, unit root, t test and t distribution, fractional integration |
| JEL: | C12 C13 C32 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:uct:uconnp:2025-01 |
| By: | Xiaoqian Wang; Rob J Hyndman |
| Abstract: | We consider the problem of constructing distribution-free prediction intervals for multi-step​ time series forecasting, with a focus on the temporal dependencies inherent in multi-step forecast​ errors. We establish that the optimal h-step-ahead forecast errors exhibit serial correlation​ up to lag (h-1) under a general non-stationary autoregressive data generating process. To​ leverage these properties, we propose the Autocorrelated Multi-step Conformal Prediction(AcMCP) method, which effectively incorporates autocorrelations in multi-step forecast errors, resulting in more statistically efficient prediction intervals. This method ensures theoretical​ long-run coverage guarantees for multi-step prediction intervals, though we note that increasedf​ orecasting horizons may exacerbate deviations from the target coverage, particularly in the​ context of limited sample sizes. Additionally, we extend several easy-to-implement conformal prediction methods, originally designed for single-step forecasting, to accommodate multi-step scenarios. Through empirical evaluations, including simulations and applications to data, we demonstrate that AcMCP achieves coverage that closely aligns with the target within local windows, while providing adaptive prediction intervals that effectively respond to varying conditions. |
| Keywords: | Conformal Prediction, Coverage Guarantee, Distribution-Free Inference, Exchangeability, Weighted Quantile Estimate |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2024-20 |
| By: | Gianluca Cubadda; Francesco Giancaterini; Stefano Grassi |
| Abstract: | This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive parallelization opportunities, significantly reducing estimation time and mitigating the risk of becoming trapped in local minima, a common issue in noncausal processes. Simulation studies demonstrate the strong ability of the algorithm to produce accurate estimates and correctly identify the process. In particular, we propose a novel identification methodology that leverages the Marginal Data Density and the Bayesian Information Criterion. Unlike previous studies, this methodology determines not only the causal and noncausal polynomial orders but also the error term distribution that best fits the data. Finally, Sequential Monte Carlo is applied to a bivariate process containing S$\&$P Europe 350 ESG Index and Brent crude oil prices. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.03945 |
| By: | Yangzhuoran Fin Yang; Rob J Hyndman; George Athanasopoulos; Anastasios Panagiotelis |
| Abstract: | We propose a novel forecast linear augmented projection (FLAP) method that can reduce the forecasterror variance of any multivariate forecast. The method first constructs new component series whichare linear combinations of the original series. Forecasts are then generated for both the original andcomponent series. Finally, the full vector of forecasts is projected onto a linear subspace where theconstraints implied by the combination weights hold. We show that the projection using the originalforecast error covariance matrix will result in improved forecasts. Notably, the new forecast errorvariance of each series is non-increasing with the number of components, and mild conditions are established for which it is strictly decreasing. It is also shown that the proposed method achieves maximum forecast error variance reduction among linear projection methods. We demonstrateour proposed method with an estimated covariance matrix using simulations and two empirical applications based on Australian tourism and FRED-MD data. In all cases,  forecasts are improved. Notably, using FLAP with Principal Component Analysis (PCA) to construct the new series leads tosubstantial forecast error variance reduction. |
| Keywords: | Forecasting; Hierarchical time series; Grouped time series; Linear forecast reconciliation; Integer programming |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2024-13 |
| By: | Pedro Isaac Chavez-Lopez (Bank of Mexico); Tae-Hwy Lee (Department of Economics, University of California Riverside) |
| Abstract: | We propose a factor model for quantile regression using quantile-covariance(qcov), which will be called the Quantile-Covariance Three-Pass Regression Filter (Qcov3PRF). Inspired by the Three-Pass Regression Filter (3PRF, Kelly and Pruitt, 2015), our method selects the relevant factors from a large set of predictors to forecast the conditional quantile of a target variable. The measure qcov is implied by the first order condition from a univariate linear quantile regression. Our approach differs from the Partial Quantile Regression (PQR, Giglio et al., 2016) as Qcov3PRF successfully allows the estimation of more than one relevant factor using qcov. In particular, qcov permits us to run time series least squares regressions of each regressor on a set of transformations of the variables,  indexed for a specific quantile of the forecast target, known as proxies that only depend on the relevant factors. This is not possible to be executed using quantile regressions as regressing each predictor on the proxies refers to the conditional quantile of the predictor and not the quantile corresponding to the target. As a consequence of running a quantile regression of the target or proxy on each predictor, only one factor is recovered with PQR. By capturing the correct number of the relevant factors, the Qcov3PRF forecasts are consistent and asymptotically normal when both time and cross sectional dimensions become large. Our simulations show that Qcov3PRF exhibits good finite sample properties compared to alternative methods. Finally, three applications are presented: forecasting the Industrial Production Growth, forecasting the Real GDP growth, and forecasting the global temperature change index. |
| Keywords: | Quantile regression; factor models; quantile-covariance |
| JEL: | C1 C5 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:ucr:wpaper:202501 |
| By: | Nuwani K Palihawadana; Rob J Hyndman; Xiaoqian Wang |
| Abstract: | Forecasting often involves high-dimensional predictors which have nonlinear relationships with theoutcome of interest. Nonparametric additive index models can capture these relationships, while addressing the curse of dimensionality. This paper introduces a new algorithm, Sparse Multiple Index(SMI) Modelling, tailored for estimating high-dimensional nonparametric/semi-parametric additive index models, while limiting the number of parameters to estimate, by optimising predictor selectionand predictor grouping. The SMI Modelling algorithm uses an iterative approach based on mixed integer programming to solve an ℓ0-regularised nonlinear least squares optimisation problem withlinear constraints. We demonstrate the performance of the proposed algorithm through a simulationstudy, along with two empirical applications to forecast heat-related daily mortality and daily solarintensity. |
| Keywords: | Additive Index Models; Variable Selection; Dimension Reduction; Predictor Grouping; Mixed Integer Programming |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2024-16 |
| By: | S. A. Adedayo |
| Abstract: | Characterizing cause-effect relationships in complex systems could be critical to understanding these systems. For many, Granger causality (GC) remains a computational tool of choice to identify causal relations in time series data. Like other causal discovery tools, GC has limitations and has been criticized as a non-causal framework. Here, we addressed one of the recurring criticisms of GC by endowing it with proper causal interpretation. This was achieved by analyzing GC from Reichenbach's Common Cause Principles (RCCPs) and causal Bayesian networks (CBNs) lenses. We showed theoretically and graphically that this reformulation endowed GC with a proper causal interpretation under certain assumptions and achieved satisfactory results on simulation. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.02672 |
| By: | Xiaoqian Wang; Rob J Hyndman; Shanika Wickramasuriya |
| Abstract: | Forecast reconciliation ensures forecasts of time series in a hierarchy adhere to aggregation constraints, enabling aligned decision making. While forecast reconciliation can enhance overall accuracy in hierarchical or grouped structures, the most substantial improvements occur  in series with initially poor-performing base forecasts. Nevertheless, certain series may experience deteriorations in reconciled forecasts. In practical settings, series in a structure often exhibit poor base forecasts due to model  misspecification or low forecastability. To prevent their negative impact, we propose two categories of forecast reconciliation methods that incorporate time series selection based on  out-of-sample and in-sample information, respectively. These methods keep “poor†base forecasts unused in forming reconciled forecasts, while adjusting weights allocated to the remaining series accordingly when generating bottom-level reconciled forecasts. Additionally, our methods ameliorate disparities stemming from varied estimates of the base forecast error covariance matrix, alleviating challenges associated with estimator selection. Empirical evaluations through two simulation studies and applications using Australian labour force and domestic tourism data demonstrate improved forecast accuracy, particularly evident in higher aggregation levels, longer forecast horizons, and cases involving model misspecification. |
| Keywords: | Forecasting; Hierarchical Time Series; Grouped Time Series; Linear Forecast Reconciliation; Integer Programming |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2024-5 |
| By: | M. Hashem Pesaran; Yimeng Xie |
| Abstract: | In a recent paper Juodis and Reese (2022) (JR) show that the application of the CD test proposed by Pesaran (2004) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This paper considers the same problem but from a different perspective, and shows that the standard CD test remains valid if the latent factors are weak in the sense the strength is less than half. In the case where latent factors are strong, we propose a bias-corrected version, CD*, which is shown to be asymptotically standard normal under the null of error cross-sectional independence and have power against network type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD* test are investigated by Monte Carlo experiments and are shown to have the correct size for strong and weak factors as well as for Gaussian and non-Gaussian errors. In contrast, it is found that JR.s test tends to over-reject in the case of panels with non-Gaussian errors, and has low power against spatial network alternatives. In an empirical application, using the CD* test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the U.S., even after the effects of latent factors are filtered out. |
| Keywords: | latent factor models, strong and weak factors, error cross-sectional independence, spatial and network alternatives, size and power |
| JEL: | C18 C23 C55 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11470 |