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on Econometrics |
| By: | Herwartz , Helmut; Siedenburg, Florian |
| Abstract: | A novel simulation based approach to unit root testing is proposed in this paper. The test is constructed from the distinct orders in probability of the OLS parameter estimates obtained from a spurious and an unbalanced regression, respectively. While the parameter estimate from a regression of two integrated and uncorrelated time series is of order Op(1), the estimate is of order Op(T-1) if the dependent variable is stationary. The test statistic is constructed as an inter quantile range from the empirical distribution obtained from regressing the standardized data sufficiently often on controlled random walks. GLS detrending (Elliott et al, 1996) and spectral density variance estimators (Perron and Ng, 1998) are applied to account for deterministic terms and residual autocorrelation in the data. A Monte Carlo study confirms that the proposed test has favorable empirical size properties and is powerful in local-to-unity neighborhoods. Testing for PPP for a sample of G6 economies, the proposed test yields results in favor of PPP for half of the sample economies while benchmark tests obtain at most one rejection of the random walk null hypothesis. |
| Keywords: | Unit root tests,simulation based test,simulation study,GLS detrending |
| JEL: | C22 C12 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cauewp:200906&r=ecm |
| By: | Isabel Casas (Aarhus University and CREATES); Irene Gijbels (Katholieke Universiteit Leuven) |
| Abstract: | The objective of this paper is to introduce the break preserving local linear (BPLL) estimator for the estimation of unstable volatility functions. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Markov switching models (Hamilton, 1989) and threshold models (Lin and Terasvirta, 1994) are amongst the most popular models to describe the behaviour of data with structural breaks. The local linear (LL) estimator is not consistent at points where the volatility function has a break and it may even report negative values for finite samples. The estimator presented in this paper generalises the classical LL. The BPLL maintains the desirable properties of the LL with regard to the bias and the boundary estimation, it estimates the breaks consistently and it ensures that the volatility estimates are always positive. |
| Keywords: | Breaks estimation, Heteroscedasticity, Local linear regression, Nonlinear time series, Volatility estimation |
| JEL: | C13 C14 C22 |
| Date: | 2009–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-48&r=ecm |
| By: | Tue Gørgens (The Australian National University); Christopher L. Skeels (The University of Melbourne); Allan H. Würtz (School of Economics and Management, University of Aarhus and CREATES) |
| Abstract: | This paper explores estimation of a class of non-linear dynamic panel data models with additive unobserved individual-specific effects. The models are specified by moment restrictions. The class includes the panel data AR(p) model and panel smooth transition models. We derive an efficient set of moment restrictions for estimation and apply the results to estimation of panel smooth transition models with fixed effects, where the transition may be determined endogenously. The performance of the GMM estimator, both in terms of estimation precision and forecasting performance, is examined in a Monte Carlo experiment. We find that estimation of the parameters in the transition function can be problematic but that there may be significant benefits in terms of forecast performance. |
| Keywords: | Dynamic panel data models, fixed effects, GMM estimation, smooth transition |
| JEL: | C13 C23 |
| Date: | 2009–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-51&r=ecm |
| By: | George Monokroussos |
| Abstract: | Estimating Limited Dependent Variable Time Series models through standard extremum methods can be a daunting computational task because of the need for integration of high order multiple integrals and/or numerical optimization of difficult objective functions. This paper proposes a classical Markov Chain Monte Carlo (MCMC) estimation technique with data augmentation that overcomes both of these problems. The asymptotic properties of the proposed estimator are established. Furthermore, a practical and flexible algorithmic framework for this class of models is proposed and is illustrated using simulated data, thus also offering some insight into the small-sample biases of such estimators. Finally, the versatility of the proposed framework is illustrated with an application of a dynamic tobit model for the Open Market Desk's Daily Reaction Function. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:nya:albaec:09-07&r=ecm |
| By: | Kyungchul Song (Department of Economics, University of Pennsylvania) |
| Abstract: | One of the approaches to compare forecasts is to test whether the loss from a benchmark prediction is smaller than the others. The test can be embedded into the general problem of testing functional inequalities using a one-sided Kolmogorov-Smirnov functional. This paper shows that such a test generally suffers from unstable power properties, meaning that the asymptotic power against certain local alternatives can be much smaller than the size. This paper proposes a general method to robustify the power properties. This method can also be applied to testing inequalities such as stochastic dominance and moment inequalities. Simulation studies demonstrate that tests based on this paper’s approach perform quite well relative to the existing methods. |
| Keywords: | Inequality Restrictions, Testing Predictive Ability, One-sided Nonparametric Tests, Power Robustification |
| JEL: | C12 C14 C52 C53 |
| Date: | 2009–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:09-035&r=ecm |
| By: | Xin Zhao; Carl John Scarrott; Marco Reale; Les Oxley (University of Canterbury) |
| Abstract: | A new extreme value mixture modelling approach for estimating Value-at-Risk (VaR) is proposed, overcoming the key issues of determining the threshold which defines the distribution tail and accounts for uncertainty due to threshold choice. A two-stage approach is adopted: volatility estimation followed by conditional extremal modelling of the independent innovations. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially overcoming the inherent sparsity of extremal data. Simulations show the reliability and flexibility of the proposed mixture model, followed by VaR forecasting for capturing returns during the current financial crisis. |
| Keywords: | Extreme values; Bayesian; Threshold estimation; Value-at-Risk |
| JEL: | C11 G12 |
| Date: | 2009–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:09/15&r=ecm |
| By: | Knüppel, Malte |
| Abstract: | Multi-step-ahead forecasts of forecast uncertainty in practice are often based on the horizon-specific sample means of recent squared forecast errors, where the number of available past forecast errors decreases one-to-one with the forecast horizon. In this paper, the efficiency gains from the joint estimation of forecast uncertainty for all horizons in such samples are investigated. Considering optimal forecasts, the efficiency gains can be substantial if the sample is not too large. If forecast uncertainty is estimated by seemingly unrelated regressions, the covariance matrix of the squared forecast errors does not have to be estimated, but simply needs to have a certain structure. In Monte Carlo studies it is found that seemingly unrelated regressions mostly yield estimates which are more efficient than the sample means even if the forecasts are not optimal. Seemingly unrelated regressions are used to address questions concerning the inflation forecast uncertainty of the Bank of England. |
| Keywords: | Multi-step-ahead forecasts,forecast error variance,GLS,SUR |
| JEL: | C13 C32 C53 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdp1:200928&r=ecm |
| By: | Herwartz , Helmut; Siedenburg, Florian |
| Abstract: | Noting that many economic variables display occasional shifts in their second order moments, we investigate the performance of homogenous panel unit root tests in the presence of permanent volatility shifts. It is shown that in this case, panel unit root tests derived under time invariant innovation variances lose control over actual significance levels while the test proposed by Herwartz and Siedenburg (2008) retains size control. A simulation study of the finite sample properties confirms the theoretical results in finite samples. As an empirical illustration, we reassess evidence on the Fisher hypothesis. |
| Keywords: | Panel unit root tests,variance breaks,cross sectional dependence,Fisher hypothesis |
| JEL: | C23 C12 E40 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cauewp:200907&r=ecm |
| By: | Torben G. Andersen (Kellogg School of Management, Northwestern University and CREATES); Viktor Todorov (Kellogg School of Management, Northwestern University) |
| Abstract: | This paper reviews basic notions of return variation in the context of a continuous-time arbitrage-free asset pricing model and discusses some of their applications. We first define return variation in the infeasible continuous-sampling case. Then we introduce realized measures obtained from high-frequency observations which provide consistent and asymp- totically normal estimates of the underlying return variation. The paper discusses applications of these measures for reduced-form volatility mod- eling and forecasting as well as testing for the presence of jumps. |
| Keywords: | realized volatility, multipower variation, jumps, quadratic variation, volatility estimation, volatility forecasting, jump testing, continuous-time stochastic volatility model. |
| JEL: | C22 C51 C52 G12 |
| Date: | 2009–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-49&r=ecm |
| By: | Le, Vo Phuong Mai (Cardiff Business School); Minford, Patrick (Cardiff Business School); Wickens, Michael |
| Abstract: | We review the methods used in many papers to evaluate DSGE models by comparing their simulated moments with data moments. We compare these with the method of Indirect Inference to which they are closely related. We illustrate the comparison with contrasting assessments of a two-country model in two recent papers. We conclude that Indirect Inference is the proper end point of the puzzles methodology. |
| Keywords: | Bootstrap; US-EU model; DSGE; VAR; indirect inference; Wald statistic; anomaly; puzzle |
| JEL: | C12 C32 C52 E1 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2009/22&r=ecm |
| By: | Robinson Kruse (Aarhus University and CREATES); Michael Frömmel (Ghent University); Lukas Menkhoff (Leibniz University Hannover); Philipp Sibbertsen (Leibniz University Hannover) |
| Abstract: | This research points to the serious problem of potentially misspecified alternative hypotheses when testing for unit roots in real exchange rates. We apply a popular unit root test against nonlinear ESTAR and develop a Markov Switching unit root test. The empirical power of these tests against correctly and misspecified non-linear alternatives is analyzed by means of a Monte Carlo study. The chosen parametrization is obtained by real-life exchange rates. The test against ESTAR has low power against all alternatives whereas the proposed unit root test against a Markov Switching autoregressive model performs clearly better. An empirical application of these tests suggests that real exchange rates may indeed be explained by Markov-Switching dynamics. |
| Keywords: | real exchange rates, unit root test, ESTAR, Markov Switching, PPP |
| JEL: | C12 C22 F31 |
| Date: | 2009–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-50&r=ecm |
| By: | James W. Taylor; Ralph D. Snyder |
| Abstract: | This paper concerns the forecasting of seasonal intraday time series. An extension of Holt-Winters exponential smoothing has been proposed that smoothes an intraday cycle and an intraweek cycle. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce an exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms than the other two exponential smoothing methods. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. By contrast with the previously proposed exponential smoothing methods, our new method can model in a straightforward way this situation, where the number of periods on each day of the week is not the same. |
| Keywords: | Exponential smoothing; Intraday data; Electricity load; Call centre arrivals. |
| JEL: | C22 |
| Date: | 2009–10–02 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2009-9&r=ecm |
| By: | Kajal Lahiri; Fushang Liu |
| Abstract: | Abstract: We consider how to use information from reported density forecasts from surveys to identify asymmetry in forecasters' loss functions. We show that, for the three common loss functions - Lin-Lin, Linex, and Quad-Quad - we can infer the direction of loss asymmetry by just comparing point forecasts and the central tendency (mean or median) of the underlying density forecasts. If we know the entire distribution of the density forecast, we can calculate the loss function parameters based on the first order condition of forecast optimality. This method is applied to forecasts for annual real output growth and inflation obtained from the Survey of Professional Forecasters (SPF). We find that forecasters treat underprediction of real output growth more dearly than overprediction, reverse is true for inflation. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:nya:albaec:09-03&r=ecm |
| By: | Ulrich Kirchner |
| Abstract: | We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to the effects of slope, which might appear at first counter-intuitive. We then show how Bayesian methods can be used to deal with sparse real market data. With each skew in a parametric model we associate a probability. This is illustrated with an example, for which multivariate parameter distributions are derived. We introduce the fuzzy smile (or fuzzy skew) as a visual illustration of the skew distribution. |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0911.0805&r=ecm |
| By: | Anthony Garratt; James Mitchell; Shaun P. Vahey (School of Economics, Mathematics & Statistics, Birkbeck) |
| Abstract: | We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:0909&r=ecm |
| By: | Kyungchul Song (Department of Economics, University of Pennsylvania) |
| Abstract: | This paper focuses on a situation where the decision-maker prefers to make a point-decision when the object of interest is interval-identified. Such a situation frequently arises when the interval-identified parameter is closely related to an optimal policy decision. To obtain a reasonable decision, this paper slices asymptotic normal experiments into subclasses corresponding to localized interval lengths, and finds a local asymptotic minimax decision for each subclass. Then, this paper suggests a decision that is based on the subclass minimax decisions, and explains the sense in which the decision is reasonable. One remarkable aspect of this solution is that the optimality of the solution remains intact even when the order of the interval bounds is misspecified. A small sample simulation study illustrates the solution’s usefulness. |
| Keywords: | Partial Identification, Inequality Restrictions, Local Asymptotic Minimax Estimation, Semiparametric Efficiency |
| JEL: | C01 C13 C14 C44 |
| Date: | 2009–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:09-036&r=ecm |
| By: | Beneki, Christina; Eeckels, Bruno; Leon, Costas |
| Abstract: | We present and apply the Singular Spectrum Analysis (SSA), a relatively new, non-parametric and data-driven method used for signal extraction (trends, seasonal and business cycle components) and forecasting of the UK tourism income. Our results show that SSA outperforms slightly SARIMA and time-varying parameter State Space Models in terms of RMSE, MAE and MAPE forecasting criteria. |
| Keywords: | Singular Spectrum Analysis; Singular Value Decomposition; Business Cycle Decomposition; Tourism Income; United Kingdom; Signal Extraction; Forecasting |
| JEL: | C53 E32 C14 |
| Date: | 2009–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:18354&r=ecm |
| By: | Julie Byrne (Economics,Finance and Accounting, National University of Ireland, Maynooth); Denis Conniffe (Economics,Finance and Accounting, National University of Ireland, Maynooth) |
| Keywords: | Econometrics, Macroeconomics, Growth, Volatility |
| JEL: | C51 E32 O40 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:may:mayecw:n2030809.pdf&r=ecm |
| By: | Kajal Lahiri; Xuguang Sheng |
| Abstract: | Using a standard decomposition of forecasts errors into common and idiosyncratic shocks, we show that aggregate forecast uncertainty can be expressed as the disagreement among the forecasters plus the perceived variability of future aggregate shocks. Thus, the reliability of disagreement as a proxy for uncertainty will be determined by the stability of the forecasting environment, and the length of the forecast horizon. Using density forecasts from the Survey of Professional Forecasters, we find direct evidence in support of our hypothesis. Our results support the use of GARCH-type models, rather than the ex post squared errors in consensus forecasts, to estimate the ex ante variability of aggregate shocks as a component of aggregate uncertainty. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:nya:albaec:09-06&r=ecm |
| By: | Kajal Lahiri; Xuguang Sheng |
| Abstract: | Using a Bayesian learning model with heterogeneity across agents, our study aims to identify the relative importance of alternative pathways through which professional forecasters disagree and reach consensus on the term structure of inflation and real GDP forecasts, resulting in different patterns of forecast accuracy. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement, and help to explain the relative forecasting accuracy of these two macroeconomic variables. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:nya:albaec:09-05&r=ecm |