Inference in non stationary asymmetric garch models

This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1,1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this framework: asymmetry and stationarity. The tests exploit the existence of a universal estimator of the asymptotic covariance matrix of the QMLE. By establishing the local asymptotic normality (LAN) property in this nonstationary framework, we can also study optimality issues

Virtual currency: a cointegration analysis between bitcoin prices and economic and financial data

The cryptocurrencies development around the world has been studied and published by the media, speculating on its continuity, applicability and security. The Bitcoin stands out as the virtual currency that has achieved the highest market value to date and for being in circulation for more than 5 years. This study intends to investigate the existence of a dynamic relationship between Bitcoin prices and economic and financial data whose relationship with physical currencies is known or it has been showed in previous studies. This data includes the Crude and Gold prices, the 6-month and 1-year U.S. Treasury Yields and the S&P 500 Index prices. The results of the study suggests that only the 6-month U.S. Treasury Yields presents a long-term relationship with the Bitcoin prices.A criação e crescimento de moedas virtuais pelo mundo têm sido alvo de vários estudos e notícias divulgadas pelos media, especulando-se quanto à sua continuidade, aplicabilidade e segurança. Dessas moedas, destaca-se a Bitcoin, a moeda virtual que apresentou até hoje o maior valor de mercado e que se tem mantido em circulação há mais de 5 anos. O presente estudo tem como objetivo investigar a existência de uma relação dinâmica entre os preços da Bitcoin e indicadores económico-financeiros cuja relação com as moedas físicas é conhecida ou foi demonstrada em estudos anteriores. Esses indicadores são os preços do petróleo e do ouro, as taxas de juro a 6 meses e a 1 ano das obrigações do Tesouro americanas e os valores de fecho do índice S&P 500. Os resultados deste estudo demonstram que apenas as taxas de juro a 6 meses de obrigações do Tesouro americanas apresentam uma relação de longo prazo com as cotações da Bitcoin

Limit Theory under Network Dependence and Nonstationarity

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity parametrization when modeling time series nonstationarity. Moreover, we present various non-asymptotic theory results for moderate deviation principles when considering the eigenvalues of covariance matrices as well as asymptotics for unit root moderate deviations in nonstationary autoregressive processes. Although not all applications from the literature are covered we also discuss some open problems in the time series and network econometrics literature.Comment: arXiv admin note: text overlap with arXiv:1705.08413 by other author

Three essays on predictive regression, low-frequency variation, and dynamic stochastic general equilibrium models

This dissertation investigates several important issues related to filtering, estimation, and inference in time series econometrics. The applied focus is on financial and macroeconomic models that include predictive regressions and dynamic stochastic general equilibrium models as prominent examples. Chapter 1 studies inference in predictive regression with a nearly integrated predictor. Conventional tests for predictive regressions exhibit substantial size distortions while existing valid inference procedures usually require multiple steps for their implementation. I propose a simple procedure using an augmented regression that requires only one step to test the coefficients in a predictive regression with a nearly integrated predictor. I prove that the usual $t$-test using conventional standard normal critical values is conservative. Furthermore, to address the situation where the predictive test is uninformative because of possible outlying events or regime changes, I propose a class of robust tests and study their asymptotic properties. In the empirical application, I find considerable evidence of the predictability of NYSE/AMEX returns using nearly integrated predictors, such as the log dividend-price ratio or the log earning-price ratio. Chapter 2 (joint with Alessandro Casini and Pierre Perron) establishes theoretical results about the low frequency contamination induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and hence deduces consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We show that for short memory nonstationarity data these estimates exhibit features akin to long memory due to low frequency contamination, to which, however, estimates based on nonparametric smoothing over time are robust. The theoretical findings are further confirmed by simulations. Since inconsistent long-run variance (LRV) estimation tends to be inflated when the data are nonstationary, HAR tests based on LRV can suffer from low frequency contamination, being more undersized with lower power than those based on HAC, whereas tests based on the recently introduced double kernel HAC estimator do not. The last chapter (joint with Zhongjun Qu) develops a new particle filter for dynamic stochastic general equilibrium (DSGE) models by mapping the state vector into two subvectors: a subvector whose components are observed and a subvector whose components are latent. By only sampling and propagating particles of the latent variables, we avoid the need to introduce measurement errors, a convenient but questionable practice. For implementation, we propose to approximate the observables' density conditional on the latent variables using series expansions. As an important feature, the new filter also allows us to study singular DSGE models using the composite likelihood, therefore providing a unified treatment of both singular and nonlinear DSGE models

Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour

This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices

Detection of non-constant long memory parameter

This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I(d_1) to I(d_2)

GMM Estimation of Autoregressive Roots Near Unity with Panel Data

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the moment condition under GLS detrending corresponds to taking the projected score on the Bhattacharya basis, linking the approach to recent work on projected score methods for models with infinite numbers of nuisance parameters (Waterman and Lindsay, 1998). Assuming that the localizing parameter takes a nonpositive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator has convergence rate n/{1/6}, slower than /n, when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data.Bias, boundary point asymptotics, GMM estimation, local to unity, moment conditions, nuisance parameters, panel data, pooled regression, projected score

Modelling and forecasting financial asset return and volatility spillovers: theory and applications

Hira Aftab studied the stochastic behaviour of financial asset returns and, the relationship between returns volatility and expected returns. She found evidence of asymmetric co-volatility spillovers, significant return shocks on volatility, Granger causality, and significant risk premia with reservations. These findings are useful for agents' asset allocation and diversification strategies

Three Essays in Macroeconomics and Empirical Finance

We measure macroeconomic uncertainty and study its link to asset returns via a consumption-based model employing recursive preferences. We introduce a stochastic volatility model with two asymptotic regimes and smooth transition. Smooth transition in regimes produces sizable equity premiums for even a small amount of consumption volatility if uncertainty unravels slowly. The relative risk aversion is estimated around two, the estimated elasticity of intertemporal substitution is greater than one, and the simulation suggests that our volatility channel matters in explaining asset returns. Next, we propose to use the Hodrick-Prescott filter to nonparametrically extract the conditional mean and volatility process of a time series. We find an optimal smoothing parameter for HP filter by minimizing the first order sample correlation of the residuals. The process extracted from our HP filter is therefore defined as the predictable component of the given time series, while the conventional HP filter decomposes a time series into trend and cyclical components. By simulations, we show that our HP filter performs better than the local linear estimator in terms of average mean squared error for both discrete and continuous time models. Finally, we develop a novel methodology to test for stock return predictability using multiple predictors. It has been reported that the conventional least squares approach has an unacceptable level of size distortions and over-reject the null hypothesis of no predictability. Previous literatures which tried to resolve the Endogeneity problem with a persistent predictor have failed to allow multiple covariates in the predictive regression. We propose to apply Heteroskedasticity and Endogeneity correction sequentially to tackle the issue. Our approach not only makes it possible to correctly test for the predictability of stock returns by multiple predictors but also reveals the marginal predictive power of each predictor. Using our new test, we find strong evidence for joint return predictability by dividend-price ratio, earnings-price ratio, short-term interest rates and term spread