Long Run And Cyclical Dynamics In The Us Stock Market

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases

Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500

Published in International Economic Review, https://doi.org/10.1111/iere.12132</p

Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model

Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form

The specification of Smooth Transition Regression models consists of a sequence of tests, which are typically based on the assumption of i.i.d. errors. In this paper we examine the impact of conditional heteroskedasticity and investigate the performance of several heteroskedasticity robust versions. Simulation evidence indicates that conventional tests can frequently result in finding spurious nonlinearity. Conversely, when the true process is nonlinear in mean the tests appear to have low size adjusted power and can lead to the selection of misspecified models. The above deficiencies also hold for tests based on Heteroskedasticity Consistent Covariance Matrix Estimators but not for the Fixed Design Wild Bootstrap. We highlight the importance of robust inference through empirical applications.

Bootstraping financial time series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.Publicad

A time series analysis of U.K. construction and real estate indices

This study assess the nonlinear behavior of U.K. Construction and Real Estate indices. Standard unit root tests show that both time series are I(1) processes. However, the empirical results show that the returns series for both indices deviate from the null hypothesis of white noise. Moreover, we have found evidence of nonlinearity but strong evidence against chaos for the returns series. Further tests show that the source of nonlinearity is rather different. Hence, the Construction index returns series displays weak nonlinear forecastability, typical of nonlinear deterministic processes, whereas the Real Estate index could be characterized as a stationary process about a nonlinear deterministic trend

Mean and variance causality between the Cyprus Stock Exchange and major equity markets

This paper examines the issue of mean and variance causality across four equities markets using daily data for the period 1996-2002. We apply the testing procedure developed by Cheung and Ng (1996) in order to test for mean and variance spillovers. The main findings are: (i) In contrast to the findings of previous studies, EGARCH-M processes characterize each stock returns series in all markets; (ii) There is substantial evidence of causality in both mean and variance with the causality in mean largely being driven by the causality in variance; and (iii) The results indicate the stock markets of Athens, London and New York are the major exporters of causality and the stock market of Cyprus is an importer of causality.Causality, cross-correlation function, EGARCH-M, equity market,