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on Econometric Time Series |
| By: | Morten Ø. Nielsen (Queen's University and CREATES); Won-Ki Seo (Department of Economics, Queen's University); Dakyung Seong (University of California, Davis) |
| Abstract: | We propose a statistical testing procedure to determine the number of stochastic trends of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. Our test is based on a variance ratio statistic, adapted to a possibly infinite-dimensional setting. We derive the asymptotic null distribution and prove consistency of the test. Monte Carlo simulations show good performance of our test and provide some evidence that it outperforms the existing testing procedure. We apply our methodology to three empirical examples: age-specific US employment rates, Australian temperature curves, and Ontario electricity demand. |
| Keywords: | cointegration, functional data, nonstationary, stochastic trends, variance ratio |
| JEL: | C32 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1420&r=all |
| By: | Harvey, A.; Hurn, S.; Thiele, S. |
| Abstract: | Circular observations pose special problems for time series modeling. This article shows how the score-driven approach, developed primarily in econometrics, provides a natural solution to the difficulties and leads to a coherent and unified methodology for estimation, model selection and testing. The new methods are illustrated with hourly data on wind direction. |
| Keywords: | Autoregression, circular data, dynamic conditional score model, von Mises distribution, wind direction |
| JEL: | C22 |
| Date: | 2019–08–12 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1971&r=all |
| By: | Emanuele Russo; Neil Foster-McGregor; Bart Verpagen |
| Abstract: | In this paper we investigate whether long run time series of income per capita are better described by a trend-stationary model with few structural changes or by unit root processes in which permanent stochastic shocks are responsible for the observed growth discontinuities. To this purpose, we develop a methodology to test the null of a generic I(1) process versus a set of stationary alternatives with structural breaks. Differently from other tests in the literature, the number of structural breaks under the alternative hypothesis is treated as an unknown (up to some ex ante determined maximum). Critical values are obtained via Monte Carlo simulations and finite sample size and power properties of the test are reported. An application is provided for a group of advanced and developing countries in the Maddison dataset, also using bootstrapped critical values. As compared to previous findings in the literature, less evidence is found against the unit root hypothesis. Failures to reject the I(1) null are particularly strong for a set of developing countries considered. Finally, even less rejections are found when relaxing the assumption of Gaussian shocks. |
| Keywords: | Long-run growth; structural breaks; unit roots. |
| Date: | 2019–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2019/29&r=all |
| By: | James G. MacKinnon (Queen's University); Matthew D. Webb (Carleton University) |
| Abstract: | We discuss when and how to deal with possibly clustered errors in linear regression models. Specifically, we discuss situations in which a regression model may plausibly be treated as having error terms that are arbitrarily correlated within known clusters but uncorrelated across them. The methods we discuss include various covariance matrix estimators, possibly combined with various methods of obtaining critical values, several bootstrap procedures, and randomization inference. Special attention is given to models with few treated clusters and clusters that vary in size, where inference may be problematic. Two empirical examples and a simulation experiment illustrate the methods we discuss and the concerns we raise. |
| Keywords: | clustered data, cluster-robust variance estimator, CRVE, wild cluster bootstrap, robust inference |
| JEL: | C15 C21 C23 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1421&r=all |
| By: | Yicong Lin; Hanno Reuvers |
| Abstract: | This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares (FMGLS) estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers of stochastic trends to enter the cointegrating relations. Our fully modified estimator incorporates: (1) the direct estimation of the inverse autocovariance matrix of the multidimensional errors, and (2) second order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second order bias corrections are convenient byproducts of our approach and lead to standard asymptotic inference. The FMGLS framework also provides two new KPSS tests for the null of cointegration. A comprehensive simulation study shows good performance of the FMGLS estimator and the related tests. As a practical illustration, we test the Environmental Kuznets Curve (EKC) hypothesis for six early industrialized countries. The more efficient and more powerful FMGLS approach raises important questions concerning the standard model specification for EKC analysis. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.02552&r=all |
| By: | Bucci, Andrea |
| Abstract: | In the last few decades, a broad strand of literature in finance has implemented artificial neural networks as forecasting method. The major advantage of this approach is the possibility to approximate any linear and nonlinear behaviors without knowing the structure of the data generating process. This makes it suitable for forecasting time series which exhibit long memory and nonlinear dependencies, like conditional volatility. In this paper, I compare the predictive performance of feed-forward and recurrent neural networks (RNN), particularly focusing on the recently developed Long short-term memory (LSTM) network and NARX network, with traditional econometric approaches. The results show that recurrent neural networks are able to outperform all the traditional econometric methods. Additionally, capturing long-range dependence through Long short-term memory and NARX models seems to improve the forecasting accuracy also in a highly volatile framework. |
| Keywords: | Neural Networks; Realized Volatility; Forecast |
| JEL: | C22 C45 C53 G17 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95443&r=all |
| By: | Ta-Hsin Li |
| Abstract: | Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencies and quantile levels. It is a useful tool for quantile-frequency analysis (QFA) of nonlinear serial dependence. This paper introduces a number of spectral divergence metrics based on the quantile periodogram for diagnostic checks of financial time series models and model-based discriminant analysis. The parametric bootstrapping technique is employed to compute the $p$-values of the metrics. The usefulness of the proposed method is demonstrated empirically by a case study using the daily log returns of the S\&P 500 index over three periods of time together with their GARCH-type models. The results show that the QFA method is able to provide additional insights into the goodness of fit of these financial time series models that may have been missed by conventional tests. The results also show that the QFA method offers a more informative way of discriminant analysis for detecting regime changes in time series. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.02545&r=all |
| By: | Daiki Maki; Yasushi Ota |
| Abstract: | This study examines statistical performance of tests for time-varying properties under misspecified conditional mean and variance. When we test for time-varying properties of the conditional mean in the case in which data have no time-varying mean but have time-varying variance, asymptotic tests have size distortions. This is improved by the use of a bootstrap method. Similarly, when we test for time-varying properties of the conditional variance in the case in which data have time-varying mean but no time-varying variance, asymptotic tests have large size distortions. This is not improved even by the use of bootstrap methods. We show that tests for time-varying properties of the conditional mean by the bootstrap are robust regardless of the time-varying variance model, whereas tests for time-varying properties of the conditional variance do not perform well in the presence of misspecified time-varying mean. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.12107&r=all |
| By: | Daiki Maki; Yasushi Ota |
| Abstract: | This study compares statistical properties of ARCH tests that are robust to the presence of the misspecified conditional mean. The approaches employed in this study are based on two nonparametric regressions for the conditional mean. First is the ARCH test using Nadayara-Watson kernel regression. Second is the ARCH test using the polynomial approximation regression. The two approaches do not require specification of the conditional mean and can adapt to various nonlinear models, which are unknown a priori. Accordingly, they are robust to misspecified conditional mean models. Simulation results show that ARCH tests based on the polynomial approximation regression approach have better statistical properties than ARCH tests using Nadayara-Watson kernel regression approach for various nonlinear models. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.12752&r=all |