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Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a series is (Formula presented.) for any δ lying in the usual stationary and invertible region of the parameter space. The second extension is the more substantive and addresses the well-known issue in the literature that long memory and level breaks can be mistaken for one another, with unmodeled level breaks rendering fractional integration tests highly unreliable. To deal with this inference problem, we extend the Lobato and Robinson approach to allow for the possibility of changes in level at unknown points in the series. We show that the resulting statistics have standard limiting null distributions, and that the tests based on these statistics attain the same asymptotic local power functions as infeasible tests based on the unobserved errors, and hence there is no loss in asymptotic local power from allowing for level breaks, even where none is present. We report results from a Monte Carlo study into the finite-sample behavior of our proposed tests, as well as several empirical examples.

This study investigates the impact of terrorist attacks and political violence on the number of tourist arrivals and overnight stays in Tunisia. The dataset employed consists of monthly data that covers the period from January 2000 to September 2016, which includes several political and terrorist attacks in Tunisia and the region. Empirically, we investigate the true data generating process (DGP) of these two proxies of tourism activity by accounting for four statistical properties that characterize these series: (1) seasonality, (2) unit roots, (3) breaks, and (4) long memory behavior. Our empirical findings show strong evidence of stationarity, five breaks in the tourist arrival time series and spurious long memory behavior. By estimating a 3-state Markov switching model consisting of the mean, trend, and variance, we find that the Tunisian Jasmine revolution and two recent terrorist attacks, one at the Bardo National Museum on March 18, 2015 and the other at the tourist resort at Port El Kantaoui, Sousse on June 26, 2015, played an important role in influencing the tourism activity of the country. Our empirical findings show also that local shocks have a more important impact than international shocks in influencing tourism activity. Interestingly, we find that the effects of terrorist shocks have a long duration compared to political violence shocks. Several security, marketing, and economic policies have been proposed and discussed in the paper. Dr. Charfeddine Lanouar is associate Professor of economics and econometrics at Qatar University. He holds a Ph.D in applied Econometrics in 2007 from University Paris II-Pantheon - Assas, France. His research area include nonlinear models (Switching and long memory processes), financial modeling and forecasting, energy economics, and fiscal and monetary policies. He has published several articles in these topics in internationally respected peer-reviewed journals including the journal of Energy Economics, Energy, Energy Policy, Economic Modeling, Emerging Market Review and Cleaner Energy Production etc. His research was funded by internal and external grants including the QFC and QNRF grants. Scopus

We examine the Croatian Kuna, the Czech Koruna, the Hungarian Forint, the Polish Złoty, the Romanian Leu, and the Swedish Krona whether their Euro exchange rates volatility exhibits true or spurious long memory. Recent research reveals long memory in foreign exchange rate volatility and we confirm this finding for these currency pairs by examining the long memory behavior of squared residuals by means of the V/S test. However, by using the ICSS approach we also find structural breaks in the unconditional variance. Literature suggests that structural breaks might lead to spurious long memory behavior. In a refined test strategy, we distinguish true from spurious long memory for the six exchange rates. Our findings suggest that Czech Koruna and Hungarian Forint only feature spurious long memory, while the rest of the series have both structural breaks and true long memory. Lastly, we demonstrate how to extend existing models to jointly model both properties yielding superior fit and better Value-at-Risk forecasts. The results of our work help to avoid misspecification and provide a better understanding of the properties of the foreign exchange rate volatility.

Lobato and Robinson (1998) develop semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First we show that it can be generalised to allow for testing of the null hypothesis that a series is I(ẟ) for any ẟ lying in the usual stationary and invertible region of the parameter space. The second extension is the more substantive and addresses the well known issue in the literature that long memory and level breaks can be mistaken for one another, with unmodelled level breaks rendering fractional integration tests highly unreliable. To deal with this inference problem we extend the Lobato and Robinson (1998) approach to allow for the possibility of changes in level at unknown points in the series. We show that the resulting statistics have standard limiting null distributions, and that the tests based on these statistics attain the same asymptotic local power functions as infeasible tests based on the unobserved errors, and hence there is no loss in asymptotic local power from allowing for level breaks, even where none is present. We report results from a Monte Carlo study into the finite-sample behaviour of our proposed tests, as well as several empirical examples.

We derive the properties of the periodogram local to the zero frequency for a large class of spurious long-memory processes. The periodogram is of crucial importance in this context, since it forms the basis for most commonly used estimation methods for the memory parameter. The class considered nests a wide range of processes such as deterministic or stochastic structural breaks and smooth trends as special cases. Several previous results on these special cases are generalized and extended. All of the spurious long-memory processes considered share the property that their impact on the periodogram at the Fourier frequencies local to the origin is different than that of true long-memory processes. Both types of processes therefore exhibit clearly distinct empirical features.

Several modified estimation methods of the memory parameter have been introduced in the past years. They aim to decrease the upward bias of the memory parameter in cases of low frequency contaminations or an additive noise component, especially in situations with a short-memory process being contaminated. In this paper, we provide an overview and compare the performance of nine semiparametric estimation methods. Among them are two standard methods, four modified approaches to account for low frequency contaminations and three procedures developed for perturbed fractional processes. We conduct an extensive Monte Carlo study for a variety of parameter constellations and several DGPs. Furthermore, an empirical application of the log-absolute return series of the S&P 500 shows that the estimation results combined with a long-memory test indicate a spurious long-memory process.

Karesi alınmış getirilerin gittikçe azalan otokorelasyonları, şokların uzun dönem bağımlılığı olduğuna işaret eder. Bununla birlikte, bu durum sahte uzun hafıza olarak nitelendirilen yapısal kırılmalara maruz kalan oynaklığın davranışıyla kolayca birbirine karışır. Çalışma, S&P 500'ün oynaklığındaki uzun hafızanın sahte nedenlerle açıklanıp açıklanamayacağını araştırmayı amaçlıyor.Çalışma hem zaman alanı hem de frekans alanı tahminlerini kullanmaktadır.Zaman alanında, veriler, yeni geliştirilmiş bir dalgacık (wavelet) tabanlı prosedürü kullanarak aykırı gözlemler için filtrelenir. Yapısal kırılmalar, değiştirilmiş bir ICSS algoritması kullanılarak tespit edilir. Ardından, filtreleme öncesi ve sonrası veriler için simetrik ve asimetrik GARCH modelleri tahmin edilmiştir. Frekans alanında, entegrasyon derecesi, Local Whittle tahmini kullanılarak hesaplanır, ardından sahte uzun hafızanın iki testi uygulanır.Ampirik sonuçlar, S&P 500'ün oynaklığındaki uzun hafızanın, en azından bir kısmı sahte olup oynaklık kaymasından kaynaklandığını işaret etmektedir.Aykırı gözlemlerin yok sayılması, GARCH modellerinde model kurma hatasına yol açabileceği bulundu. Buna ek olarak, frekans alanında tahmin edilen uzun hafıza parametresi zaman içinde tutarlı değildir. Bu, getiri serilerinin tutarlı bir (d) entegrasyon derecesinin kısmi olarak bütünleştirilmiş bir rejim yerine birkaç rejim tarafından daha iyi tanımlanabileceğini göstermektedir. The slowly decaying autocorrelations of squared returns imply that shocks are long-range dependent. However, this behavior is easily confused with the behavior of volatility when exposed to structural breaks that is described as spurious long memory. The study aims at investigating whether long memory in the volatility of S&P 500 can be explained by spurious reasons. The study utilizesboth time domain and frequency domain estimations.In the time domain, the data is filtered for outliers using a recently developed wavelet-based procedure. Structural breaks are detected using a modified ICSS algorithm. Then, symmetric and asymmetric GARCH models are estimated for the data before and after filtering. In the frequency domain, the degree of integration is computed using Local Whittle estimation, then two testsof spurious long memory are performed.The empirical results indicate that the long memory in the volatility of S&P500 is at least partially spuriously caused by volatility shifts. It was found that ignoring outliers can lead to misspecified GARCH models. Furthermore, the long memory parameter estimated in the frequency domain is not consistent over time. This indicates that return series might be better described by severalregimes rather than by one fractionally integrated process of a consistent degreeof integration (d) 92

The focus of the volatility literature on forecasting and the predominance of the conceptually simpler HAR model over long memory stochastic volatility models has led to the fact that the actual degree of memory estimates has rarely been considered. Estimates in the literature range roughly between 0.4 and 0.6 - that is from the higher stationary to the lower non-stationary region. This difference, however, has important practical implications - such as the existence or nonexistence of the fourth moment of the return distribution. Inference on the memory order is complicated by the presence of measurement error in realized volatility and the potential of spurious long memory. In this paper we provide a comprehensive analysis of the memory in variances of international stock indices and exchange rates. On the one hand, we find that the variance of exchange rates is subject to spurious long memory and the true memory parameter is in the higher stationary range. Stock index variances, on the other hand, are free of low frequency contaminations and the memory is in the lower non-stationary range. These results are obtained using state of the art local Whittle methods that allow consistent estimation in presence of perturbations or low frequency contaminations.

We consider a large class of structural change processes that generate spurious long memory. Among others, this class encompasses structural breaks as well as random level shift processes and smooth trends. The properties of these processes are studied based on a simple representation of their discrete Fourier transform. We find, that under very general conditions all of the models nested in this class generate poles in the periodogram at the zero frequency. These are of order O(T), instead of the usual O(T2d) for long memory processes and O(T2) for a random walk. This order arises whenever both the mean changes and sample fractions at which they occur are non-degenerate, asymptotically

The persistence of inflation rates is of major importance to central banks due to the fact that it determines the costs of monetary policy according to the Phillips curve. This article is motivated by newly available econometric methods which allow for a consistent estimation of the persistence parameter under low frequency contaminations and consistent break point estimation under long memory without a priori assumptions on the presence of breaks. In contrast to previous studies, we allow for smooth trends in addition to breaks as a source of spurious long memory. We support the fi nding of reduced memory parameters in monthly inflation rates of the G7 countries as well as spurious long memory, except for the US. Nevertheless, only a few breaks can be located. Instead, all countries exhibit signi cant trends at the 5 percent level with the exception of the US.

The focus of the volatility literature on forecasting and the predominance of the conceptually simpler HAR model over long memory stochastic volatility models has led to the fact that the actual degree of memory estimates has rarely been considered. Estimates in the literature range roughly between 0.4 and 0.6 - that is from the higher stationary to the lower non-stationary region. This difference, however, has important practical implications - such as the existence or non-existence of the fourth moment of the return distribution. Inference on the memory order is complicated by the presence of measurement error in realized volatility and the potential of spurious long memory. In this paper we provide a comprehensive analysis of the memory in variances of international stock indices and exchange rates. On the one hand, we find that the variance of exchange rates is subject to spurious long memory and the true memory parameter is in the higher stationary range. Stock index variances, on the other hand, are free of low frequency contaminations and the memory is in the lower non-stationary range. These results are obtained using state of the art local Whittle methods that allow consistent estimation in presence of perturbations or low frequency contaminations.

This paper provides a multivariate score-type test to distinguish between true and spurious long memory. The test is based on the weighted sum of the partial derivatives of the multivariate local Whittle likelihood function. This approach takes phase shifts in the multivariate spectrum into account. The resulting pivotal limiting distribution is independent of the dimension of the process, which makes it easy to apply in practice. We prove the consistency of our test against the alternative of random level shifts or monotonic trends. A Monte Carlo analysis shows good finite sample properties of the test in terms of size and power. Additionally, we apply our test to the log-absolute returns of the S&P 500, DAX, FTSE, and the NIKKEI. The multivariate test gives formal evidence that these series are contaminated by level shifts.

A two-stage forecasting approach for long memory time series is introduced. In the first step we estimate the fractional exponent and, applying the fractional differencing operator, we obtain the underlying weakly dependent series. In the second step, we perform the multi-step ahead forecasts for the weakly dependent series and obtain their long memory counterparts by applying the fractional cumulation operator. The methodology applies to stationary and nonstationary cases. Simulations and an application to seven time series provide evidence that the new methodology is more robust to structural change and yields good forecasting results.

Certain “spurious long memory” processes mimic the behavior of fractional integration in that the variance of their sample mean behaves like that of a fractionally integrated process of some order D. We show, however, experimentally that a fractional integration test may discriminate between spurious long memory of order D and integration of order D. Further, we suggest a test for the null hypothesis that the order of integration does not change from one subperiod to another. It simply builds on the difference of the estimates from the respective subsamples that are split exogenously. Upon appropriate normalization a limiting standard normal distribution arises. With these methods we tackle the question whether international and sectoral bank equity index returns are fractionally integrated and whether the memory parameters have changed. The daily data are split into three regimes: one pre-crises subsample, a second including the collapse of the Lehman Brothers bank, and a third covering the Euro area sovereign debt crisis. In particular, we provide evidence that both turmoils had differing international effects. Financial support from ECO2011-29751 and ECO2012-33619 projects.

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We have developed a new test against spurious long memory based on the invariance of long memory parameter to aggregation. By using the local Whittle estimator, the statistic takes the supremum among combinations of paired aggregated series. Simulations show that the test performs good in finite sample sizes, and is able to distinguish long memory from spurious processes with excellent power. Moreover, the empirical application gives further evidence that the observed long memory in German stock returns is spurious.

I discuss mean reversion in the first and the second moment of the return distribution. After a discussion of the concepts and a summary of the findings in the literature, I show that investor´s perceptions of mean reversion play a role in stock market crashes. Turning to the second moment of the return distribution, expected volatility, I consider mean reversion using GARCH. The main finding is that in order to properly measure mean reversion, it is crucial to take parameter regime shifts into account. This can but need not necessarily be done by solving the change point detection problem. I present evidence that stock price volatility contains more than a single mean reversion time. After showing that the expectation of the sum of the estimates of the autoregressive coefficients of a GARCH(1,1) model is one when there are unknown parameter changes, I explore the phenomenon in simulations. For parameter changes within realistic ranges for stock price volatility I obtain global estimates indicating high persistence while the average data-generating mean reversion is of the order of a few days. Spectral analysis of the Dow Jones Industrial Average and the S&$P500 index between 1985 and 2001 reveals a short time scale of the magnitude of 5-10 days present in the data. I generalize these results to GARCH(p,q) models with p=1,2 and q=1,2.