A Parametric Bootstrap Test for Cycles

The paper proposes a simple test for the hypothesis of strong cycles and as a by-product a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi)Gaussian process G(t), t ? [0; 1]. Because the covariance structure of G(t) is a complicated function of t and model dependent, to obtain the critical values (if possible) of maxt?[0;1] G(t) may be difficult. For this reason we propose a bootstrap scheme in the frequency domain to circumvent the problem of obtaining (asymptotically) valid critical values. The proposed bootstrap can be regarded as an alternative procedure to existing bootstrap methods in the time domain such as the residual-based bootstrap. Finally, we illustrate the performance of the bootstrap test by a small Monte Carlo experiment and an empirical example.Cyclical data, strong and weak dependence, spectral density functions, Whittle estimator, bootstrap algorithms

Consistent estimation of the memory parameterfor nonlinear time series

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogramand local Whittle estimators, has been exhaustively examined and their properties are well established.However, except for some specific cases, little is known about the estimation of the memory parameter fornonlinear processes. The purpose of this paper is to provide general conditions under which the localWhittle estimator of the memory parameter of a stationary process is consistent and to examine its rate ofconvergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinearmodels, among others, signal plus noise processes, nonlinear transforms of a Gaussian process ?tandEGARCH models. Special cases where the estimator satisfies the central limit theorem are discussed. Thefinite sample performance of the estimator is investigated in a small Monte-Carlo study.Long memory, semiparametric estimation, local Whittle estimator.

Estimation and testing of persistence in nonlinear and cyclical time series.

Throughout this thesis, we are concerned with filling some of the gaps in the literature concerning parametric and semiparametric Whittle estimation of long-run and/or cyclical persistence in economic time series. In Chapter 2, we consider local Whittle estimation, and without relying on the assumption of a linear model, we establish sufficient conditions for consistency and provide expansions and rate of convergence for the estimator. In Chapter 3, we apply the results of Chapter 2 to examine the local Whittle estimator for the signal plus noise model and some special cases of it: structural model, nonlinear transformations of a Gaussian process, and long memory stochastic volatility model. Under these specifications, we establish the asymptotic properties of the estimator, and raise several issues concerning its rate of convergence and finite sample bias. In Chapter 4, we employ Monte-Carlo simulations to investigate the finite sample properties of the local Whittle estimator under the linear and nonlinear specifications of Chapters 2 and 3. Furthermore, we apply local Whittle estimation to expected and realized inflation rates, nominal and real interest rates, and transformations of foreign exchange rate returns, in order to assess their long-run persistence and address several issues that have appeared in the empirical literature. Finally, Chapter 5 presents two testing procedures, based on the parametric Whittle method, for the null hypothesis of no persistent component in the data. We derive the asymptotic properties of our test statistics, and moreover introduce and validate a bootstrap scheme for calculating their critical values. A Monte-Carlo study of the finite sample performance of our testing procedures, and an empirical application on the growth rate of industrial production and unemployment rate are also included

Testing Mean Stability of Heteroskedastic Time Series

Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of independent variates with changing variance and a stationary conditionally heteroskedastic (GARCH) process, such processes may be hard to distinguish in applied work using basic time series diagnostic tools. We develop and study some practical and easily implemented statistical procedures to test the mean and variance stability of uncorrelated and serially dependent time series. Application of the new methods to analyze the volatility properties of stock market returns leads to some unexpected surprising findings concerning the advantages of modeling time varying changes in unconditional variance

Robust Tests for White Noise and Cross-Correlation

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung-Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and non-stationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung-Box test for non-i.i.d. data a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation

The behaviour of SMEs’ capital structure determinants in different macroeconomic states

The recent global financial crisis has triggered questions in the scientific area of capital structure dynamic determination regarding how “quickly” companies tend to adjust their capital structure to their long-term targets, in different macroeconomic states. We broaden the scope of the debate by focusing on SMEs and by discussing the relative importance of firm-specific and macroeconomic variables, when macroeconomic conditions change. Based on a partial adjustment model, we find that short-term and long-term debt ratios follow different patterns regarding their adjustment speeds; the adjustment speed for long-term debt slows down during the crisis, while the respective of the short-term debt is not affected. We also find clear differentiations of the effects and the contribution of the firm-specific and the macroeconomic variables between short-term debt and long-term debt ratios, when macroeconomic states change. We thus conclude that the nature and maturity of borrowing affect the persistence and endurance of the relationship between determinants and borrowing, across different macroeconomic states

Reexamining the Long-Run Properties of the Real Interest Rate

In the empirical literature, stationary and nonstationary behavior has been reported for the U.S. real interest rate over dierent time periods. We examine its long-run properties, through estimation of the order of integration, and interpret the results in light of the Taylor rule for monetary policy. When concentrating on the post-October 1987 period, our analysis suggests that the business cycle component of the real interest rate dominates its trend. Under such a setup, we argue on the basis of a theoretical example and a simulation study that, in nite samples, the estimator of the order of integration recovers information on the strength of the cycle, rather than the trend. For that reason, we extract the cyclical part of the real interest rate, and obtain considerably lower estimates of the order of integration. We therefore conjecture that in the post-October 1987 period, the estimates of the order of integration for the real interest rate are uninformative, and that its degree of long-run dependence has been overestimated

Consistent estimation of the memory parameter for nonlinear time series

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties well established. However, except for some specific cases, little is known about the estimation of the memory parameter for nonlinear processes. The purpose of this paper is to provide the general conditions under which the local Whittle estimator of the memory parameter of a stationary process is consistent and to examine its rate of convergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinear models, among others, signal plus noise processes, nonlinear transforms of a Gaussian process ξt and exponential generalized autoregressive, conditionally heteroscedastic (EGARCH) models. Special cases where the estimator satisfies the central limit theorem are discussed. The finite-sample performance of the estimator is investigated in a small Monte Carlo study