Uwe Hassler

Long Memory in Inflation Rates: International Evidence

We examine monthly inflation rates of five industrial countries. The application of tests against stationarity as well as tests against a unit root yield contradictory results. Thus fractional integration allowing for long memory is a plausible model. We discuss and apply the periodogram regression to estimate the difference parameters. For all countries we find estimates significantly different from 1 as well as from 0. This is evidence in favor of long memory. Specification tests and maximum likelihood estimates support the fitted models. Finally, we relate our empirical results to the construction of the data.

Introduction to Modern Time Series Analysis

This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series. It attempts to bridge the gap between methods and realistic applications. This book contains the most important approaches to analyse time series which may be stationary or nonstationary. Modelling and forecasting univariate time series is the starting point. For multiple stationary time series Granger causality tests and vector autoregressive models are presented. For real applied work the modelling of nonstationary uni- or multivariate time series is most important. Therefore, unit root and cointegration analysis as well as vector error correction models play a central part. Modelling volatilities of financial time series with autoregressive conditional heteroskedastic models is also treated.

On the power of unit root tests against fractional alternatives

Abstract We investigate the probability of rejecting the I(1) hypothesis when unit root tests are applied to fractionally integrated time series. Especially the augmented Dickey-Fuller test performs poorly. Our analytical arguments are supported by Monte Carlo experiments.

Inference on the Cointegration Rank in Fractionally Integrated Processes

For univariate time series we suggest a new variant of efficient score tests against fractional alternatives. This test has three important merits. First, by means of simulations we observe that it is superior in terms of size and power in some situations of practical interest. Second, it is easily understood and implemented as a slight modification of the Dickey-Fuller test, although our score test has a limiting normal distribution. Third and most important, our test generalizes to multivariate cointegration tests just as the Dickey-Fuller test does. Thus it allows to determine the cointegration rank of fractionally integrated time series. It does so by solving a generalized eigenvalue problem of the type proposed by Johansen (1988). However, the limiting distribution of the corresponding trace statistic is X2 , where the degrees of freedom depend only on the cointegration rank under the null hypothesis. The usefulness of the asymptotic theory for finite samples is established in a Monte Carlo experiment.

Autoregressive Conditional Heteroscedasticity

All models discussed so far use the conditional expectation to describe the mean development of one or more time series. The optimal forecast, in the sense that the variance of the forecast errors will be minimised, is given by the conditional mean of the underlying model. Here, it is assumed that the residuals are not only uncorrelated but also homoscedastic, i.e. that the unexplained fluctuations have no dependencies in the second moments. However, BENOIT MANDELBROT (1963) already showed that financial market data have more outliers than would be compatible with the (usually assumed) normal distribution and that there are ‘volatility clusters’: small (large) shocks are again followed by small (large) shocks. This may lead to ‘leptokurtic distributions‘, which – as compared to a normal distribution – exhibit more mass at the centre and at the tails of the distribution. This results in ‘excess kurtosis’, i.e. the values of the kurtosis are above three.

Combining Significance of Correlated Statistics with Application to Panel Data

The inverse normal method, which is used to combine P‐values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol. 41, pp. 849–855), which is designed to allow for a certain correlation matrix of the transformed P‐values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross‐correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments.

LONG MEMORY TESTING IN THE TIME DOMAIN

An integration test against fractional alternatives is suggested for univariate time series. The new test is a completely regression based, lag augmented version of the LM test by Robinson (1991, Journal of Econometrics 47, 67-84). Our main contributions, however, are the following. First, we let the short memory component follow a general linear process. Second, the innovations driving this process are martingale dierences with eventual conditional heteroskedasticity that is accounted for by means of White’s standard errors. Third, we assume the number of lags to grow with the sample size, thus approximating the general linear process. Under these assumptions limiting normality of the test statistic is retained. The usefulness of the asymptotic results for finite samples is established in Monte Carlo experiments. In particular, we study several strategies of model selection.

Detecting Multiple Breaks in Long Memory: The Case of U.S. inflation

Multiple structural change tests by Bei and Perron (1998) are applied to the regression by Demetrescu, Kuzin and Hassler (2008) in order to detect breaks in the order of fractional integration. With this instrument we tackle time-varying inflation persistence as an important issue for monetary policy. We determine not only the location and significance of breaks in persistence, but also the number of breaks. Only one significant break in U.S. inflation persistence (measured by the long-memory parameter) is found to have taken place in 1973, while a second break in 1980 is not significant.

IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY

This paper focuses on the asymptotic behavior of the impulse response coef-ficients of fractionally integrated sequences, which, since their introduction byGranger and Joyeux (1980) and Hosking (1981), have been extended in manydirections and have become a useful modeling tool in geophysics, especially hy-drology and meteorology, econometrics, computer science, and many other areas.See Doukhan, Oppenheim, and Taqqu (2003), Robinson (2003), and Teyssiereand Kirman (2006) for recent overviews.Fractionally integrated processes are constructed by filtering a weakly depen-dent sequence with the filter

Testing For General Fractional Integration In The Time Domain

We propose a family of least-squares–based testing procedures that look to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series, and that are asymptotically equivalent to Lagrange multiplier tests. Our setting extends Robinson’s (1994) results to allow for short memory in a regression framework and generalizes the procedures in Agiakloglou and Newbold (1994), Tanaka (1999), and Breitung and Hassler (2002) by allowing for single or multiple fractional unit roots at any frequency in [0, π ]. Our testing procedure can be easily implemented in practical settings and is flexible enough to account for a broad family of long- and short-memory specifications, including ARMA and/or GARCH-type dynamics, among others. Furthermore, these tests have power against different types of alternative hypotheses and enable inference to be conducted under critical values drawn from a standard chi-square distribution, irrespective of the long-memory parameters.