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Unit Root (unit + root)
Kinds of Unit Root Terms modified by Unit Root Selected AbstractsIS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?NATURAL RESOURCE MODELING, Issue 1 2010NINA S. JONES Abstract Use of the time-series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data-generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips-Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses. [source] Trade Balance and Exchange Rate: Unit Roots, Co-integration and Long Memory in the US and the UKECONOMIC NOTES, Issue 1 2008Luis A. Gil-Alana This paper deals with the relationship between the balance of trade and the exchange rate in the US/UK case. Many authors have studied this issue for many countries, but despite the intensive research, there is still no agreement about the effectiveness of currency devaluation to increase a country's balance of trade. We first analyse the relationship between the two variables using unit roots and co-integration methods, and the results are ambiguous. We try a new approach based on fractional integration. The unit root hypothesis is rejected in case of the trade balance in favour of smaller orders of integration, while this hypothesis is not rejected for the exchange rate. Thus, the two series do not possess the same order of integration. We sort this problem out by taking the exchange rate as an exogenous variable, and including it in a regression model where the residuals might follow a fractionally integrated model. [source] On the Robustness of Unit Root Tests in the Presence of Double Unit RootsJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2002NIELS HALDRUP We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey,Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips,Perron class of semi-parametric tests is shown to diverge to plus infinity asymptotically and thus favouring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples. [source] Power of Tests for Unit Roots in the Presence of a Linear Trend,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 5 2008Bent Nielsen Abstract Dickey and Fuller [Econometrica (1981) Vol. 49, pp. 1057,1072] suggested unit-root tests for an autoregressive model with a linear trend conditional on an initial observation. TPower of tests for unit roots in the presence of a linear trendightly different model with a random initial value in which nuisance parameters can easily be eliminated by an invariant reduction of the model. We show that invariance arguments can also be used when comparing power within a conditional model. In the context of the conditional model, the Dickey,Fuller test is shown to be more stringent than a number of unit-root tests motivated by models with random initial value. The power of the Dickey,Fuller test can be improved by making assumptions to the initial value. The practitioner therefore has to trade-off robustness and power, as assumptions about initial values are hard to test, but can give more power. [source] Real exchange rates may have nonlinear trendsINTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 2 2008David O. Cushman Abstract The unit root null is tested against possible nonlinear-trend stationarity for 13 US and German bilateral real exchange rates over the floating exchange rate period. Eight tests specified with nonlinear trends are applied. Simulations are used to determine individual and joint significance levels and to help interpret the results. Unit roots can be rejected for a number of the exchange rates, and nonlinear-trend stationarity appears more plausible than mean or linear-trend stationarity as the alternative. In several cases, estimates of the trends support the nonlinear-trend conclusion with statistical and economic significance. Thus, purchasing power parity is probably violated, but real exchange rates have meaningful long-run equilibrium values. Copyright © 2007 John Wiley & Sons, Ltd. [source] Long-Term Debt and Optimal Policy in the Fiscal Theory of the Price LevelECONOMETRICA, Issue 1 2001John H. Cochrane The fiscal theory says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. I analyze long-term debt and optimal policy in the fiscal theory. I find that the maturity structure of the debt matters. For example, it determines whether news of future deficits implies current inflation or future inflation. When long-term debt is present, the government can trade current inflation for future inflation by debt operations; this tradeoff is not present if the government rolls over short-term debt. The maturity structure of outstanding debt acts as a "budget constraint" determining which periods' price levels the government can affect by debt variation alone. In addition, debt policy,the expected pattern of future state-contingent debt sales, repurchases and redemptions,matters crucially for the effects of a debt operation. I solve for optimal debt policies to minimize the variance of inflation. I find cases in which long-term debt helps to stabilize inflation. I also find that the optimal policy produces time series that are similar to U.S. surplus and debt time series. To understand the data, I must assume that debt policy offsets the inflationary impact of cyclical surplus shocks, rather than causing price level disturbances by policy-induced shocks. Shifting the objective from price level variance to inflation variance, the optimal policy produces much less volatile inflation at the cost of a unit root in the price level; this is consistent with the stabilization of U.S. inflation after the gold standard was abandoned. [source] Convergence in West German Regional Unemployment RatesGERMAN ECONOMIC REVIEW, Issue 4 2007Christian Bayer Stochastic convergence; unemployment; structural break; unit root Abstract. Differences in regional unemployment rates are often used to describe regional economic inequality. This paper asks whether changes in regional unemployment differences in West Germany are persistent over time. Understanding the persistency of regional unemployment differences helps us to assess how effective regional policy can be. While univariate tests suggest that changes in regional unemployment differences are persistent in West Germany, more powerful panel tests lend some support to the hypothesis that regional unemployment rates converge. However, these tests reveal a moderate speed of convergence at best. Because there is a structural break following the second oil crisis, we also use tests that allow for such a break. This provides evidence for both convergence and quick adjustment to an equilibrium distribution of regional unemployment rates that is, however, subject to a structural break. [source] Heterogeneity and cross section dependence in panel data models: theory and applications introductionJOURNAL OF APPLIED ECONOMETRICS, Issue 2 2007Badi H. Baltagi The papers included in this special issue are primarily concerned with the problem of cross section dependence and heterogeneity in the analysis of panel data models and their relevance in applied econometric research. Cross section dependence can arise due to spatial or spill over effects, or could be due to unobserved (or unobservable) common factors. Much of the recent research on non-stationary panel data have focussed on this problem. It was clear that the first generation panel unit root and cointegration tests developed in the 1990's, which assumed cross-sectional independence, are inadequate and could lead to significant size distortions in the presence of neglected cross-section dependence. Second generation panel unit root and cointegration tests that take account of possible cross-section dependence in the data have been developed, see the recent surveys by Choi (2006) and Breitung and Pesaran (2007). The papers by Baltagi, Bresson and Pirotte, Choi and Chue, Kapetanios, and Pesaran in this special issue are further contributions to this literature. The papers by Fachin, and Moon and Perron are empirical studies in this area. Controlling for heterogeneity has also been an important concern for empirical researchers with panel data methods promising better handle on heterogeneity than cross-section data methods. The papers by Hsiao, Shen, Wang and Weeks, Pedroni and Serlenga and Shin are empirical contributions to this area. Copyright © 2007 John Wiley & Sons, Ltd. [source] A patent analysis of global food and beverage firms: The persistence of innovationAGRIBUSINESS : AN INTERNATIONAL JOURNAL, Issue 3 2002Oscar Alfranca We explore whether current innovation has an enduring effect on future innovative activity in large, global food and beverage (F&B) companies. We analyze a sample of 16,698 patents granted in the United States over the period 1977 to 1994 to 103 F&B firms selected from the world's largest F&B multinationals. We test whether patent time series are trend stationary or difference stationary in order to detect how large the autoregressive parameter is and how enduring the impact of past innovation in these companies is. We conclude that the patent series are not consistent with the random walk model. The null hypothesis of a unit root can be rejected at the 5% level when a constant and a time trend are considered. Both utility and design patent series are stationary around a constant and a time trend. Moreover, there is a permanent component in the patent time series. Thus, global F&B firms show a stable pattern of technological accumulation in which "success breeds success." "Old" innovators are the ones to foster both important changes and new ways of packaging products among F&B multinationals. The effect of past innovation is almost permanent. By contrast, other potential stimuli to technological change have only transitory effects on innovation. Patterns of technological accumulation vary in specific F&B industries. Past experience in design is important in highly processed foods and beverages, but not in agribusinesses and basic foodstuffs. Patterns of technological accumulation are similar in both smaller multinationals/newcomers and large, established multinationals. [EconLit citations : O330, F230, L660] © 2002 Wiley Periodicals, Inc. [source] A simultaneous test of unit root and level changeJOURNAL OF FORECASTING, Issue 3 2010Duk Bin Jun Abstract Testing the existence of unit root and/or level change is necessary in order to understand the underlying processes of time series. In many studies carried out so far, the focus was only on a single aspect of unit root and level change, therefore limiting a full assessment of the given problems. Our study aims to find a solution to the given problems by testing the two hypotheses simultaneously. We derive the likelihood ratio test statistic based on the state space model, and their distributions are created by the simulation method. The performance of the proposed method is validated by simulated time series and also applied to two Korean macroeconomic time series to confirm its practical application. This analysis can provide a solution to determine the underlying structure of arguable time series. Copyright © 2009 John Wiley & Sons, Ltd. [source] Bootstrap prediction intervals for autoregressive models of unknown or infinite lag orderJOURNAL OF FORECASTING, Issue 4 2002Jae H. Kim Abstract Recent studies on bootstrap prediction intervals for autoregressive (AR) model provide simulation findings when the lag order is known. In practical applications, however, the AR lag order is unknown or can even be infinite. This paper is concerned with prediction intervals for AR models of unknown or infinite lag order. Akaike's information criterion is used to estimate (approximate) the unknown (infinite) AR lag order. Small-sample properties of bootstrap and asymptotic prediction intervals are compared under both normal and non-normal innovations. Bootstrap prediction intervals are constructed based on the percentile and percentile- t methods, using the standard bootstrap as well as the bootstrap-after-bootstrap. It is found that bootstrap-after-bootstrap prediction intervals show small-sample properties substantially better than other alternatives, especially when the sample size is small and the model has a unit root or near-unit root. Copyright © 2002 John Wiley & Sons, Ltd. [source] Stochastic Volatility in a Macro-Finance Model of the U.S. Term Structure of Interest Rates 1961,2004JOURNAL OF MONEY, CREDIT AND BANKING, Issue 6 2008PETER D. SPENCER affine term structure model; macro finance; unit root; stochastic volatility This paper generalizes the standard homoscedastic macro-finance model by allowing for stochastic volatility, using the "square root" specification of the mainstream finance literature. Empirically, this specification dominates the standard model because it is consistent with the square root volatility found in macroeconomic time series. Thus it establishes an important connection between the stochastic volatility of the mainstream finance model and macro-economic volatility of the Okun,Friedman type. This research opens the way to a richer specification of both macro-economic and term structure models, incorporating the best features of both macro-finance and mainstream finance models. [source] Unit-root testing: on the asymptotic equivalence of Dickey,Fuller with the log,log slope of a fitted autoregressive spectrumJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2010Evangelos E. Ioannidis In this article we consider the problem of testing for the presence of a unit root against autoregressive alternatives. In this context we prove the asymptotic equivalence of the well-known (augmented) Dickey,Fuller test with a test based on an appropriate parametric modification of the technique of log-periodogram regression. This modification consists of considering, close to the origin, the slope (in log,log coordinates) of an autoregressively fitted spectral density. This provides a new interpretation of the Dickey,Fuller test and closes the gap between it and log-periodogram regression. This equivalence is based on monotonicity arguments and holds on the null as well as on the alternative. Finally, a simulation study provides indications of the finite-sample behaviour of this asymptotic equivalence. [source] On the Robustness of Unit Root Tests in the Presence of Double Unit RootsJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2002NIELS HALDRUP We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey,Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips,Perron class of semi-parametric tests is shown to diverge to plus infinity asymptotically and thus favouring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples. [source] IS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?NATURAL RESOURCE MODELING, Issue 1 2010NINA S. JONES Abstract Use of the time-series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data-generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips-Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses. [source] The Analysis of Seasonal Long Memory: The Case of Spanish Inflation,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 6 2007Josu Arteche Abstract This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1,L12)d should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively. [source] Detection of Structural Change in the Long-run Persistence in a Univariate Time Series,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2 2005Eiji Kurozumi Abstract In this paper, we investigate a test for structural change in the long-run persistence in a univariate time series. Our model has a unit root with no structural change under the null hypothesis, while under the alternative it changes from a unit-root process to a stationary one or vice versa. We propose a Lagrange multiplier-type test, a test with the quasi-differencing method, and ,demeaned versions' of these tests. We find that the demeaned versions of these tests have better finite-sample properties, although they are not necessarily superior in asymptotics to the other tests. [source] Seasonal unit root tests and the role of initial conditionsTHE ECONOMETRICS JOURNAL, Issue 3 2008David I. Harvey Summary, In the context of regression-based (quarterly) seasonal unit root tests, we examine the impact of initial conditions (one for each quarter) of the process on test power. We investigate the behaviour of the well-known OLS detrended HEGY seasonal unit root tests together with their quasi-differenced (QD) detrended analogues, when the initial conditions are not asymptotically negligible. We show that the asymptotic local power of a test at a given frequency depends on the value of particular linear (frequency specific) combinations of the initial conditions. Consistent with previous findings in the nonseasonal case, the QD detrended test at a given spectral frequency dominates on power for relatively small values of this combination, while the OLS detrended test dominates for larger values. Since, in practice, the seasonal initial conditions are not observed, in order to maintain good power across both small and large initial conditions, we develop tests based on a union of rejections decision rule; rejecting the unit root null at a given frequency (or group of frequencies) if either of the relevant QD and OLS detrended HEGY tests rejects. This procedure is shown to perform well in practice, simultaneously exploiting the superior power of the QD (OLS) detrended HEGY test for small (large) combinations of the initial conditions. Moreover, our procedure is particularly adept in the seasonal context since, by design, it exploits the power advantage of the QD (OLS) detrended HEGY tests at a particular frequency when the relevant initial condition is small (large) without imposing that same method of detrending on tests at other frequencies. [source] Joint hypothesis specification for unit root tests with a structural break,THE ECONOMETRICS JOURNAL, Issue 2 2006Josep Lluís Carrion-i-Silvestre Summary, Several tests based on a t -ratio have been proposed in the literature to decide the order of integration of a time series allowing for a structural break. However, another approach based on testing a joint hypothesis of unit root and the irrelevance of some nuisance parameters is also feasible. This paper proposes new unit root tests consistent with the presence of a structural break applying this second perspective. Our approach deals both with the case where the break is not allowed under the null hypothesis, and where it is allowed. Simulations investigate the performance of this proposal compared to the existing tests and show important gains in terms of power. [source] Moment approximation for least-squares estimators in dynamic regression models with a unit root,THE ECONOMETRICS JOURNAL, Issue 2 2005Jan F. Kiviet Summary, To find approximations for bias, variance and mean-squared error of least-squares estimators for all coefficients in a linear dynamic regression model with a unit root, we derive asymptotic expansions and examine their accuracy by simulation. It is found that in this particular context useful expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. Surprisingly, the large-sample and small-disturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. We specialize our general expressions for moment approximations to the case of the random walk with drift model and find that they are unsatisfactory when the drift is small. Therefore, we develop what we call small-drift asymptotics which proves to be very accurate, especially when the sample size is very small. [source] Testing for stationarity in heterogeneous panel dataTHE ECONOMETRICS JOURNAL, Issue 2 2000Kaddour Hadri This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed. Finite sample sizes and powers are considered in a Monte Carlo experiment. The empirical sizes of the tests are close to the true size even in small samples. The testing procedure is easy to apply, including, to panel data models with fixed effects, individual deterministic trends and heterogeneous errors across cross-sections. It is also shown how to apply the tests to the more general case of serially correlated disturbance terms. [source] The Effect of Time-Series and Cross-Sectional Heterogeneity on Panel Unit Root Test PowerTHE JOURNAL OF FINANCIAL RESEARCH, Issue 3 2002John M. Geppert Abstract Panel unit root tests represent a significant advancement in addressing the low power of unit root tests by exploiting cross-sectional and time-series information. In this article we employ Monte Carlo techniques to quantify the power improvements due to cross-sectional information and assess test sensitivity to heterogeneous data. Pooling the data alleviates negative effects of slowly adjusting equilibrium relations as well as persistence in the forcing variable. However, if the panel contains a mixture of unit root and stationary series, the power of the test decreases substantially and the interpretation of the results becomes tenuous. [source] OPTIMAL AND ADAPTIVE SEMI-PARAMETRIC NARROWBAND AND BROADBAND AND MAXIMUM LIKELIHOOD ESTIMATION OF THE LONG-MEMORY PARAMETER FOR REAL EXCHANGE RATES,THE MANCHESTER SCHOOL, Issue 2 2005SAEED HERAVI The nature of the time series properties of real exchange rates remains a contentious issue primarily because of the implications for purchasing power parity. In particular are real exchange rates best characterized as stationary and non-persistent; nonstationary but non-persistent; or nonstationary and persistent? Most assessments of this issue use the I(0)/I(1) paradigm, which only allows the first and last of these options. In contrast, in the I(d) paradigm, d fractional, all three are possible, with the crucial parameter d determining the long-run properties of the process. This study includes estimation of d by three methods of semi-parametric estimation in the frequency domain, using both local and global (Fourier) frequency estimation, and maximum likelihood estimation of ARFIMA models in the time domain. We give a transparent assessment of the key selection parameters in each method, particularly estimation of the truncation parameters for the semi-parametric methods. Two other important developments are also included. We implement Tanaka's locally best invariant parametric tests based on maximum likelihood estimation of the long-memory parameter and include a recent extension of the Dickey,Fuller approach, referred to as fractional Dickey,Fuller (FD-F), to fractionally integrated series, which allows a much wider range of generating processes under the alternative hypothesis. With this more general approach, we find very little evidence of stationarity for 10 real exchange rates for developed countries and some very limited evidence of nonstationarity but non-persistence, and none of the FD-F tests leads to rejection of the null of a unit root. [source] Real Exchange Rate Dynamics Under The Current Float: A Re,ExaminationTHE MANCHESTER SCHOOL, Issue 2 2003Michael Bleaney Augmented Dickey,Fuller regressions on pooled (but not individual) real exchange rates for the post,1973 period consistently reject the unit root null, even after accounting for cross,sectional dependence. The inference that the series is stationary, however, is not necessarily correct, because these tests strongly over,reject the null in certain circumstances, particularly when the series has a stochastic unit root. We find that bilateral real exchange rates against the US dollar have a stochastic unit root. Out,of,sample prediction exercises for an autoregressive model confirm these findings. [source] THE AGRICULTURAL TERMS OF TRADE IN BANGLADESH: AN ECONOMETRIC ANALYSIS OF TRENDS AND MOVEMENTS, 1952,2006AUSTRALIAN ECONOMIC PAPERS, Issue 1 2008AKHAND AKHTAR HOSSAINArticle first published online: 21 APR 200 This paper investigates the trends and movements of agricultural prices, industrial prices and the agricultural terms of trade in Bangladesh with annual data for the period 1952,2006. The ADF and KPSS tests results suggest that both agricultural and industrial prices have a unit root while the agricultural terms of trade is trend-stationary. These results remain unchanged if allowance is made in the unit root test for the possibility of a structural break during 1971,1975 (when Bangladesh gained independence from Pakistan and experienced economic shocks) by applying the two-step procedure of Perron (1989). A simple Nerlovian agricultural price determination model is specified within the framework of aggregate demand and aggregate supply. The Johansen cointegration test results for the periods 1953,2006 and 1973,2006 suggest that there exists a cointegral relationship between agricultural prices, industrial prices, per-capita real income and the real exchange rate between the Bangladeshi taka and the US dollar under the restriction that per-capita real income and the real exchange rate are ,long-run forcing variables' in the sense of Pesaran and Shin (1995), and Pesaran, Shin and Smith (1996). The paper estimates a four-variable vector error-correction (VEC) model and conducts an impulse response analysis for the post-independence period, 1973,2006. [source] Evidence from panel unit root and cointegration tests that the Environmental Kuznets Curve does not existAUSTRALIAN JOURNAL OF AGRICULTURAL & RESOURCE ECONOMICS, Issue 3 2003Roger Perman The Environmental Kuznets Curve (EKC) hypothesis , an inverted U-shape relation between various indicators of environmental degradation and income per capita , has become one of the ,stylised facts' of environmental and resource economics. This is despite considerable criticism on both theoretical and empirical grounds. Cointegration analysis can be used to test the validity of such stylised facts when the data involved contain stochastic trends. In the present paper, we use cointegration analysis to test the EKC hypothesis using a panel dataset of sulfur emissions and GDP data for 74 countries over a span of 31 years. We find that the data is stochastically trending in the time-series dimension. Given this, and interpreting the EKC as a long run equilibrium relationship, support for the hypothesis requires that an appropriate model cointegrates and that sulfur emissions are a concave function of income. Individual and panel cointegration tests cast doubt on the general applicability of the hypothesised relationship. Even when we find cointegration, many of the relationships for individual countries are not concave. The results show that the EKC is a problematic concept, at least in the case of sulfur emissions. [source] Trade Balance and Exchange Rate: Unit Roots, Co-integration and Long Memory in the US and the UKECONOMIC NOTES, Issue 1 2008Luis A. Gil-Alana This paper deals with the relationship between the balance of trade and the exchange rate in the US/UK case. Many authors have studied this issue for many countries, but despite the intensive research, there is still no agreement about the effectiveness of currency devaluation to increase a country's balance of trade. We first analyse the relationship between the two variables using unit roots and co-integration methods, and the results are ambiguous. We try a new approach based on fractional integration. The unit root hypothesis is rejected in case of the trade balance in favour of smaller orders of integration, while this hypothesis is not rejected for the exchange rate. Thus, the two series do not possess the same order of integration. We sort this problem out by taking the exchange rate as an exogenous variable, and including it in a regression model where the residuals might follow a fractionally integrated model. [source] Tourism demand modelling: some issues regarding unit roots, co-integration and diagnostic testsINTERNATIONAL JOURNAL OF TOURISM RESEARCH, Issue 5 2003Paresh Kumar Narayan Abstract This paper investigates the all important issue of diagnostic tests, including unit roots and cointegration, in the tourism demand modelling literature. The origins of this study lie in the apparent lack in the tourism economics literature of detail concerning the diagnostic test aspect. Study of this deficiency has suggested that previous literature on tourism demand modelling may be divided into two categories: the pre-1995 and post-1995 studies. It was found that the pre-1995 and some post-1995 studies have ignored unit root tests and co-integration and, hence, are vulnerable to the so-called ,spurious regression' problem. In highlighting the key diagnostic tests reported by post-1995 studies, this paper contends that there is no need to report the autoregressive conditional heteroskedasticity (ARCH) test, which is applicable only to financial market analysis where the dependent variable is return on an asset. More generally, heteroskedasticity is not seen as a problem in time-series data. However, the reporting of a greater than necessary range of diagnostic tests,,,some of which do not have any theoretical justification with regard to tourism demand analysis,,,does not diminish the precision of the results or the model. This paper should appeal to scholars involved in tourism demand modelling. Copyright © 2003 John Wiley & Sons, Ltd. [source] Bootstrapping Financial Time SeriesJOURNAL OF ECONOMIC SURVEYS, Issue 3 2002Esther Ruiz 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. [source] Estimation and forecasting in first-order vector autoregressions with near to unit roots and conditional heteroscedasticityJOURNAL OF FORECASTING, Issue 7 2009Theologos Pantelidis Abstract This paper investigates the effects of imposing invalid cointegration restrictions or ignoring valid ones on the estimation, testing and forecasting properties of the bivariate, first-order, vector autoregressive (VAR(1)) model. We first consider nearly cointegrated VARs, that is, stable systems whose largest root, lmax, lies in the neighborhood of unity, while the other root, lmin, is safely smaller than unity. In this context, we define the ,forecast cost of type I' to be the deterioration in the forecasting accuracy of the VAR model due to the imposition of invalid cointegration restrictions. However, there are cases where misspecification arises for the opposite reasons, namely from ignoring cointegration when the true process is, in fact, cointegrated. Such cases can arise when lmax equals unity and lmin is less than but near to unity. The effects of this type of misspecification on forecasting will be referred to as ,forecast cost of type II'. By means of Monte Carlo simulations, we measure both types of forecast cost in actual situations, where the researcher is led (or misled) by the usual unit root tests in choosing the unit root structure of the system. We consider VAR(1) processes driven by i.i.d. Gaussian or GARCH innovations. To distinguish between the effects of nonlinear dependence and those of leptokurtosis, we also consider processes driven by i.i.d. t(2) innovations. The simulation results reveal that the forecast cost of imposing invalid cointegration restrictions is substantial, especially for small samples. On the other hand, the forecast cost of ignoring valid cointegration restrictions is small but not negligible. In all the cases considered, both types of forecast cost increase with the intensity of GARCH effects. 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