Working Papers
- “Estimation of Time Series Models Using Generalized Spectral Distribution Function”, 2021 (Job Market Paper, Latest draft! )
- Abstract: Univariate processes with non-fundamental representations have been employed to characterize nonlinear dynamics driven from predictable future innovations, which are of promising applications in Macroeconomics and Finance. In this paper, I propose a novel estimation technique of general linear time series which are possibly non-invertible and non-causal relying on the dependence structure of residuals. The generalized spectral cumulative function is considered to capture the general dependence of non-Gaussian residuals. The loss function is constructed by means of an L2 distance between the dependence measure in the unrestricted case and the one conjectured in the restricted case under the iid assumption. The information at all quantiles is used to achieve model identification. This method yields consistent estimates of the model parameters without imposing stringent conditions on the higher-order moments of innovations. Due to the non-differentiability of the original loss function, the asymptotic distribution of the estimates is approached by using a smoothed cumulative distribution function to approximate the indicator function. The efficiency improvement can be achieved by properly choosing the scaling parameter for residuals. Finite sample properties are studied through Monte Carlo simulations. An empirical application of this approach is provided by fitting the daily trading volume of Microsoft stock by autoregressive models with non-causal representation. Another empirical application on financial series will be included to illustrate the ability of non-causal process in modeling local explosive behaviours. The flexibility of the cumulative distribution function permits the proposed method to be extended to a more general dependence structure where innovations are conditional mean or quantile independent.
- “QAR-based Noncausality Testing”, 2021
- Abstract: Quantile autoregression (QAR) model has been a prevailing tool for carrying out the distributional study of response variables for time series. In this paper, we show that linear non-Gaussian non-causal processes can display “nonlinear” behaviors such as asymmetric dynamics and clustering volatility. Besides, we demonstrate that non-causal autoregression admits at least one nonlinear quantile representation conditional on past observations. On the contrary, the causal model produces constant QAR estimates at any quantile. We propose novel testing strategies for non-causality in the non-Gaussian processes within the QAR framework. Tests are constructed either by verifying the constancy of the slope coefficients or by applying a misspecification test of the linear QAR model over different quantiles of the process. Some simulations are included to illustrate the testing strategies. In the Monte Carlo experiment, we compare different specification tests for dynamic quantiles with the Kolmogorov-Smirnov constancy test in terms of the power of detecting non-causality in finite samples. The extension of the approach based on the specification test to AR processes driven by innovations with heteroskedasticity is studied through simulations. In the end, the methodology is applied to two empirical time series in stock markets to investigate the presence of speculative bubbles. The performance of QAR estimates of non-causal processes at extreme quantiles is also explored with some simulations.
- “Directional Predictability Tests”, joint with Carlos Velasco, 2022
- Abstract: This paper proposes new tests of predictability for non-Gaussian sequences that may display general nonlinear dependence in higher order properties. We test the null of martingale difference against parametric alternatives which can introduce linear or nonlinear dependence as generated by ARMA and all-pass restricted ARMA models, respectively. We also develop tests to check for linear predictability under the white noise null hypothesis parameterized by an all-pass model driven by martingale difference innovations and tests of non-linear predictability on ARMA residuals. Our Lagrange Multiplier tests are developed from a loss function based on pairwise dependence measures that identify the predictability of levels. We provide asymptotic and finite sample analysis of the properties of the new tests and investigate the predictability of different series of financial returns.
Working in progress
- Testing Change-points in the General ARMA Processes, 2023