Testing for change in mean of heteroskedastic time series

In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perform also some Monte Carlo simulations to analyze the size distortion and the power of the proposed test. We conclude that for moderate sample size, the test has a good performance. We finally carry out an empirical application using the daily closing level of the S\&P 500 stock index, in order to illustrate the usefulness of the proposed test.Brownian bridge, changes in mean, functional central limit theorem, heteroskedasticity, time series

wrong estimation of the true number of shifts in structural break models: Theoretical and numerical evidence

The aim of the paper is to consider the problem of selecting the number of breaks in the mean of a time series. Indeed, we prove analytically and show by a Monte Carlo study that some model selection criteria will tend to choose a spuriously high number of structural breaks when the process is trend-stationary without changes. The important question suggested by our results is that of distinction between trend-stationary process and random walk when modelling real data series.Model selection

Estimation of the long memory parameter in non stationary models: A Simulation Study

In this paper we perform a Monte Carlo study based on three well-known semiparametric estimates for the long memory fractional parameter. We study the efficiency of Geweke and Porter-Hudak, Gaussian semiparametric and wavelet Ordinary Least-Square estimates in both stationary and non stationary models. We consider an adequate data tapers to compute non stationary estimates. The Monte Carlo simulation study is based on different sample size. We show that for d belonging to [1/4,1.25) the Haar estimate performs the others with respect to the mean squared error. The estimation methods are applied to energy data set for an empirical illustration.wavelets; long memory; tapering; non-stationarity; volatility.

A Measure of Variability in Comovement for Economic Variables : a Time-Varying Coherence Function Approach

In this paper, we test the instability of comovement, in time and frequency domain, for the GDP growth rate of the US and the UK. We use the frequency approach, which is based on evolutionary spectral analysis (Priestley, 1965-1996). The graphical analysis of the Time-Varying Coherence Function (TVCF) reports the existence of variability in correlation between the two series. Our goal is to estimate first the TVCF of the two series, then to test stability in both the cross-spectra density and in TVCF by detecting various breakpoints in each function.comovement ; spectral analysis ; time-varying coherence function ; structural change

The power of some standard tests of stationarity against changes in the unconditional variance

Abrupt changes in the unconditional variance of returns have been recently revealed in many empirical studies. In this paper, we show that traditional KPSS-based tests have a low power against nonstationarities stemming from changes in the unconditional variance. More precisely, we show that even under very strong abrupt changes in the unconditional variance, the asymptotic moments of the statistics of these tests remain unchanged. To overcome this problem, we use some CUSUM-based tests adapted for small samples. These tests do not compete with KPSS-based tests and can be considered as complementary. CUSUM-based tests confirm the presence of strong abrupt changes in the unconditional variance of stock returns, whereas KPSS-based tests do not. Consequently, traditional stationary models are not always appropriate to describe stock returns. Finally, we show how a model allowing abrupt changes in the unconditional variance is well appropriate for CAC 40 stock returns.KPSS test, panel stationarity test, unconditional variance, abrupt changes, stock returns, size-power curve.

A METHODOLOGY FOR DETECTING BREAKS IN THE MEAN AND COVARIANCE STRUCTURE OF TIME SERIES

Some structural break techniques defined in the time and frequency domains are presented to explore, at the same time, the empirical evidence of the mean and covariance instability by uncovering regime-shifts in some inflation series. To that effect, we pursue a methodology that combines two approaches; the first is defined in the time domain and is designed to detect mean-shifts, and the second is defined in the frequency domain and is adopted to study the instability problem of the covariance function of the series. The proposed methodology has a double interest since, besides the detection of regime-shifts occasioned in the covariance structure of the series, it allows taking into account the presence of mean-shifts in this series. Note that unlike the works existing in the literature which often adopt a single technique to study the break identification problem, our methodology combines two approaches, parametric and nonparametric, to examine this problem.Structural change, mean and variance shifts, parametric and nonparametric approaches.

A Measure of Variability in Comovement for Economic Variables : a Time-Varying Coherence Function Approach

In this paper, we test the instability of comovement, in time and frequency domain, for the GDP growth rate of the US and the UK. We use the frequency approach, which is based on evolutionary spectral analysis (Priestley, 1965-1996). The graphical analysis of the Time-Varying Coherence Function (TVCF) reports the existence of variability in correlation between the two series. Our goal is to estimate first the TVCF of the two series, then to test stability in both the cross-spectra density and in TVCF by detecting various breakpoints in each function.comovement ; spectral analysis ; time-varying coherence function ; structural change

A Measure of Variability in Comovement for Economic Variables: a Time-Varying Coherence Function Approach

In this paper, we suggest a different dynamic measure of comovement which is unlike previous studies allowing to test instability in comovement between two non stationary economic time series. We use the frequency approach, which is based on evolutionary spectral analysis, to estimate the Time-Varying Coherence Function (TVCF). Then we test stability in both cross-spectra and TVCF by detecting endogenously various break points in each function. Applying this new methodology to the GDP growth rate of the US and UK, we get an interesting result about period of business cycle convergence and divergence for these economies.Comovement, Spectral Analysis, Time Varying Coherence Function, Structural Change

Testing for change in mean of heteroskedastic time series

In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perform also some Monte Carlo simulations to analyze the size distortion and the power of the proposed test. We conclude that for moderate sample size, the test has a good performance. We finally carry out an empirical application using the daily closing level of the S\&P 500 stock index, in order to illustrate the usefulness of the proposed test

Analysing CPI inflation by the fractionally integrated ARFIMA-STVGARCH model

The aim of this paper is to study the dynamic evolution of inflation rate. The model is constructed by extending the ARFIMA-GARCH to ARFIMA with a time varying GARCH model where the transition from one regime to another is evolving smoothly over time. We show by Monte Carlo experiments that the constancy parameter tests perform well. We apply then this new model on eight countries from Europe, Japan and Canada and find that this model is appropriate for six among these countries.ARFIMA model, Generalised autoregressive conditional heteroscedasticity model, Inflation rate, Long memory process, Nonlinear time series, Time-varying parameter mode