Working Papers

• “Estimation of Time Series Using the Empirical Distribution of Residuals”, (nominated for the Best Paper Award in the “Econometrics” category in the Winter School 2021, Delhi School of Economics)
  • Abstract: This paper introduces a novel estimation technique for general linear time series models, which are potentially noninvertible and noncausal, by utilizing the empirical cumulative distribution function of residuals. The proposed method relies on the generalized spectral cumulative function to characterize the pairwise dependence of residuals at all lags. By exploiting the information in the joint distribution of residuals under the $iid$ assumption, model identification can be achieved. This method yields consistent estimates of the model parameters without imposing stringent conditions on the higher-order moments or any distributional assumptions on the innovations beyond non-Gaussianity. We investigate the asymptotic distribution of the estimates by employing a smoothed cumulative distribution function to approximate the indicator function, considering the non-differentiability of the original loss function. Efficiency improvements can be achieved by properly choosing the scaling parameter for residuals. Finite sample properties are explored through Monte Carlo simulations. An empirical application to illustrate this methodology is provided by fitting the daily trading volume of Microsoft stock by autoregressive models with noncausal representation.
• “Quantile Autoregression Based Noncausality Testing”,
  • Abstract: In this paper, we investigate the statistical properties of empirical conditional quantiles of non-causal processes. We show that the quantile autoregression (QAR) estimates for non-causal processes do not remain constant across different quantiles in contrast to their causal counterparts. Furthermore, we demonstrate that non-causal autoregressive processes admit nonlinear representations for conditional quantiles given past observations. Exploiting these properties, we propose three novel testing strategies of non-causality for non-Gaussian processes within the QAR framework. Some numerical experiments are included to examine the finite sample performance of the testing strategies, where we compare different specification tests for dynamic quantiles with the Kolmogorov-Smirnov constancy test. The new methodology is applied to some time series from financial markets to investigate the presence of speculative bubbles.

  Working in progress

• Testing for Bubbles in the Presence of Instabilities, joint with Josep Lluís Carrion-i-Silvestre
• The CUSUM Approach to Detect Change-Point in Time Series Models Under the General Heteroskedasticity

Publications —–

• “Directional Predictability Tests”, with Carlos Velasco, forthcoming in Econometric Reviews, 2024.