|
on Econometric Time Series |
| By: | Shin Kanaya (Aarhus University and CREATES) |
| Abstract: | In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya-Watson type with introducing a new technical device called a damping function. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also have an independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non/semiparametric estimation and testing problems of diffusion processes. |
| Keywords: | Diffusion process, uniform convergence, kernel estimation, nonparametric. |
| JEL: | C14 C32 C58 |
| Date: | 2015–11–12 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-50&r=ets |
| By: | Tommaso Proietti (University of Rome “Tor Vergata” and Creates) |
| Abstract: | Extracting and forecasting the volatility of financial markets is an important empirical problem. The paper provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, and proposes a new predictor that can be seen as extension of the very popular and successful forecasting and signal extraction scheme, known as exponential smoothing (ES). First, we derive a generalization of the Beveridge-Nelson result, decomposing the series into the sum of fractional noise processes with decreasing orders of integration. Secondly, we consider three models that are natural extensions of ES: the fractionally integrated first order moving average (FIMA) model, a new integrated moving average model formulated in terms of the fractional lag operator (FLagIMA), and a fractional equal root integrated moving average (FerIMA) model, proposed originally by Hosking. We investigate the properties of the volatility components and the forecasts arising from these specification, which depend uniquely on the memory and the moving average parameters. For statistical inference we show that, under mild regularity conditions, the Whittle pseudo-maximum likelihood estimator is consistent and asymptotically normal. The estimation results show that the log-realized variance series are mean reverting but nonstationary. An out-of-sample rolling forecast exercise illustrates that the three generalized ES predictors improve significantly upon commonly used methods for forecasting realized volatility, and that the estimated model confidence sets include the newly proposed fractional lag predictor in all occurrences. |
| Keywords: | Realized Volatility, Volatility Components, Fractional lag models, Fractional equal-root IMA model, Model Confidence Set |
| JEL: | C22 C53 G17 |
| Date: | 2015–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-51&r=ets |
| By: | Matyas Barczy; Balazs Nyul; Gyula Pap |
| Abstract: | We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1511.05948&r=ets |
| By: | Tamara Burdisso (Central Bank of Argentina); Máximo Sangiácomo (Central Bank of Argentina) |
| Abstract: | The document focuses on the econometric treatment of macro panels, known in literature as panel time series. This new approach rejects the assumption of slopes’ homogeneity and handles nonstationarity. It also recognizes that the presence of crosssection dependence (CSD), i.e. some correlation structure in the error term between units due to the presence of unobservable common factors, squanders efficiency gains by operating with a panel. This led to a new set of estimators known in literature as Common Correlated Effect (CCE), which essentially consists of increasing the model to be estimated by adding the averages of the individuals in each time t, of both the dependent variable and the specific regressors of each individual. Finally, two Stata codes developed for the evaluation and treatment of the cross-section dependence are presented. |
| Keywords: | panel time series, nostationarity, panel unit root, mean group estimator, cross-section dependence, common correlated effect |
| JEL: | C13 C23 C87 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:bcr:wpaper:201568&r=ets |
| By: | Jair N. Ojeda-Joya (Banco de la República de Colombia); Oscar Jaulin-Mendez (Banco de la República de Colombia); Juan C. Bustos-Peláez (Universidad Nacional de Colombia) |
| Abstract: | We study the interdependence between real commodity prices and world real GDP using long-term annual data since 1870, by performing two empirical exercises. First, we compute long-term and medium-term cycles and measure their degree of synchronization for different leads and lags. Second, we perform several causality tests in order to better understand the nature of their interdependence. Our results show that GDP and commodity-price cycles are correlated, and there is evidence of short-term causality between them. However, there is no evidence of Granger causality from GDP to medium and long term cycles of commodity prices. This finding is consistent with the technology-based theories of commodity-price cycles. Searching for a supply-side determinant, we study the interdependence between oil-price and the remaining commodity-price cycles. Our results imply that oil prices are key drivers of metal price cycles for all fluctuation frequencies. Classification JEL: C22, E32, Q02 |
| Keywords: | medium-term cycles, commodity prices, frequency domain, super cycles. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:bdr:borrec:913&r=ets |
| By: | Levent Bulut (Department of Economics, Ipek University) |
| Abstract: | In Monte Carlo experiment with simulated data, I show that, as a point forecast criterion, the Clark and West's (2006) unconditional test of mean squared prediction errors (MSPE) fails to reflect the relative performance of a superior model over a relatively weaker model. The simulation results show that, even though the MSPE of a superior model is far below a weaker alternative, the Clark and West's (2006) test does not reflect this in their test statistics. Therefore, studies that use this statistics in testing the predictive accuracy of alternative exchange rate models, equity risk premium predictions, stock return predictability, inflation forecasting and unemployment forecasting should not weight too much on the magnitude of the statistically significant Clark and West's (2006) tests statistics. |
| Keywords: | Model comparison, predictive accuracy, point-forecast criterion, the Clark and West test. |
| JEL: | F37 F47 G17 C52 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:ipk:wpaper:1509&r=ets |
| By: | Boriss Siliverstovs (KOF Swiss Economic Institute, ETH Zurich, Switzerland) |
| Abstract: | In this paper we suggest an approach to comparison of models’ forecasting performance in unstable environments. Our approach is based on combination of the Cumulated Sum of Squared Forecast Error Differential (CSSFED) suggested earlier in Welch and Goyal (2008) and the Bayesian change point analysis based on Barry and Hartigan (1993). The latter methodology provides the formal statistical analysis of the CSSFED time series which turned out to be a powerful graphical tool for tracking how the relative forecasting performance of competing models evolves over time. We illustrate the suggested approach by using forecasts of the GDP growth rate in Switzerland. |
| Keywords: | Forecasting, Forecast Evaluation, Change Point Detection, Bayesian Estimation |
| JEL: | C22 C53 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:kof:wpskof:15-397&r=ets |
| By: | Karol Szafranek |
| Abstract: | The global economy is highly dependent on commodity prices, which are, by and large, the outcome of market-specific supply and demand fundamentals. As a result, driven by different determinants, financial assets and commodity prices should be negligibly correlated. However, systematically growing engagement of noncommercial investors equipped with financial engineering innovations on commodity markets, generous inflow of capital resulting from the necessity for wider diversification of investment portfolios combined with the strengthening influence of purely financial and speculative motives have led in the 2000’s to a much stronger correlation between the financial and commodity markets, sparking a heated debate on the commodity markets financialisation. The empirical analysis presented here supports the claim that since 2005 commodity markets have been under heavier influence of macroeconomic, financial and speculative determinants. However, the process loses on strength since 2011. Results of the Varx Dcc Garch model with leverage effect and multivariate t error distribution demonstrate that the inclusion of the commodity markets’ growing sensitivity to macroeconomic conditions, financial markets turmoil and the impact of speculative aspects alters the dynamic conditional correlation path between commodities and the financial markets from 2005 to 2011 signaling the process of financialisation. Additional conclusions are drawn regarding the stability of the market interdependence as well as the parameter estimates. |
| Keywords: | Icommodity markets, financialisation, Varx, Dcc, price dynamics determinants |
| JEL: | C32 C58 E44 Q02 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:nbp:nbpmis:213&r=ets |
| By: | Sutton, M; Vasnev, A; Gerlach, R |
| Abstract: | This paper proposes an ex-post volatility estimator, called generalized variance, that uses high frequency data to provide measurements robust to the idiosyncratic noise of stock markets caused by market microstructures. The new volatility estimator is analyzed theoretically, examined in a simulation study and evaluated empirically against the two currently dominant measures of daily volatility: realized volatility and realized range. The main finding is that generalized variance is robust to the presence of microstructures while delivering accuracy superior to realized volatility and realized range in several circumstances. The empirical study features Australian stocks from the ASX 20. |
| Keywords: | Volatility ; Robust estimator |
| Date: | 2015–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/13263&r=ets |
| By: | Hill, Jonathan B.; Prokhorov, Artem |
| Abstract: | We construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to non-leverage points. We derive a higher order expansion for GEL with imbedded tail-trimming (GELITT), which reveals higher order bias and efficiency properties, available when the GARCH error has a finite second moment. Higher order asymptotics for GEL without tail-trimming requires the error to have moments of substantially higher order. We use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample. We also present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation. Finally, we present a broad simulation study for GEL and GELITT, and demonstrate profile weighted expected shortfall for the Russian Ruble - US Dollar exchange rate. We show that tail-trimmed CUE-GMM dominates other estimators in terms of bias, mse and approximate normality. AMS classifications : 62M10 , 62F35. |
| Keywords: | GEL ; GARCH ; tail trimming ; heavy tails ; robust inference ; efficient moment estimation ; expected shortfall ; Russian Ruble |
| JEL: | C13 C49 |
| Date: | 2015–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/13795&r=ets |
| By: | Hill, Jonathan B.; Prokhorov, Artem |
| Abstract: | The following supplemental material contains an omitted simulation experiment, and omitted proofs of theorems and preliminary lemmata. Section S contains simulation results, and Section A contains an appendix with omitted proofs. |
| Keywords: | GARCH ; Heavy-Tailed ; GEL |
| Date: | 2015–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/13797&r=ets |
| By: | Gerlach, Richard; Wang, Chao |
| Abstract: | A new framework named Realized Conditional Autoregressive Expectile (Realized- CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a framework analogous to Realized-GARCH. The Range and realized measures (Realized Variance and Realized Range) are employed as the dependent variables of the measurement equation, since they have proven more efficient than return for volatility estimation. The dependence between Range & realized measures and expectile can be modelled with this measurement equation. The grid search accuracy of the expectile level will be potentially improved with introducing this measurement equation. In addition, through employing a quadratic fitting target search, the speed of grid search is significantly improved. Bayesian adaptive Markov Chain Monte Carlo is used for estimation, and demonstrates its superiority compared to maximum likelihood in a simulation study. Furthermore, we propose an innovative sub-sampled Realized Range and also adopt an existing scaling scheme, in order to deal with the micro-structure noise of the high frequency volatility measures. Compared to the CARE, the parametric GARCH and the Realized-GARCH models, Value-at-Risk and Expected Shortfall forecasting results of 6 indices and 3 assets series favor the proposed Realized-CARE model, especially the Realized-CARE model with Realized Range and sub-sampled Realized Range. |
| Keywords: | Realized-CARE ; Realized Variance ; Realized Range ; Subsampling Realized Range ; Markov Chain Monte Carlo ; Target Search ; Value-at-Risk ; Expected Shortfall |
| Date: | 2015–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/13800&r=ets |
| By: | Tomás del Barrio Castro (Universitat de les Illes Balears); Paulo M. M. Rodrigues (Bank of Portugal); A. M. Robert Taylor (University of Essex) |
| Abstract: | It is well known that (seasonal) unit root tests can be seriously affected by the presence of weak dependence in the driving shocks when this is not accounted for. In the non-seasonal case both parametric (based around augmentation of the test regression with lagged dependent variables) and semi-parametric (based around an estimator of the long run variance of the shocks) unit root tests have been proposed. Of these, the M class of unit root tests introduced by Stock (1999), Perron and Ng (1996) and Ng and Perron (2001), appear to be particularly successful, showing good finite sample size control even in the most problematic (near-cancellation) case where the shocks contain a strong negative moving average component. The aim of this paper is threefold. First we show the implications that neglected weak dependence in the shocks has on lag un-augmented versions of the well known regression-based seasonal unit root tests of Hylleberg et al. (1990). Second, in order to complement extant parametrically augmented versions of the tests of Hylleberg et al. (1990), we develop semi-parametric seasonal unit root test procedures, generalising the methods developed in the non-seasonal case to our setting. Third, we compare the finite sample size and power properties of the parametric and semi-parametric seasonal unit root tests considered. Our results suggest that the superior size/power trade-off offered by the M approach in the non-seasonal case carries over to the seasonal case. |
| Keywords: | Seasonal unit roots, weak dependence, lag augmentation, long run variance estimator, demodulated process. |
| JEL: | C12 C22 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:ubi:deawps:72&r=ets |
| By: | Tomás del Barrio Castro (Universitat de les Illes Balears); Andrii Bodnar; Andreu Sansó Rosselló (Universitat de les Illes Balears) |
| Abstract: | This paper implements the approach introduced by MacKinnon (1994, 1996) to estimate the response surface of the test statistics of seasonal unit root tests with OLS and GLS detrending for quarterly and monthly time series. The Gauss code that is available in the supplementary material of the paper produces p-values for five test statistics depending on the sample size, deterministic terms and frequency of the data. A comparison with previous studies is undertaken, and an empirical example using airport passenger arrivals to a tourist destination is carried out. Quantile function coefficients are reported for simple computation of critical values for tests at 1%, 5% and 10% significance levels. |
| Keywords: | HEGY test, GLS detrending, response surfaces |
| JEL: | C12 C22 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:ubi:deawps:73&r=ets |
| By: | Marczak, Martyna; Proietti, Tommaso; Grassi, Stefano |
| Abstract: | This article presents a robust augmented Kalman filter that extends the data-cleaning filter (Masreliez and Martin, 1977) to the general state space model featuring nonstationary and regression effects. The robust filter shrinks the observations towards their one-step-ahead prediction based on the past, by bounding the effect of the information carried by a new observation according to an influence function. When maximum likelihood estimation is carried out on the replacement data, an M-type estimator is obtained. We investigate the performance of the robust AKF in two applications using as a modeling framework the basic structural time series model, a popular unobserved components model in the analysis of seasonal time series. First, a Monte Carlo experiment is conducted in order to evaluate the comparative accuracy of the proposed method for estimating the variance parameters. Second, the method is applied in a forecasting context to a large set of European trade statistics series. |
| Keywords: | robust filtering,augmented Kalman filter,structural time series model,additive outlier,innovation outlier |
| JEL: | C32 C53 C63 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:hohdps:132015&r=ets |