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on Econometric Time Series |
| By: | Alexei Onatski; Chen Wang |
| Abstract: | Johansen’s (1988, 1991) likelihood ratio test for cointegration rank of a Gaussian VAR depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the distribution almost surely weakly converges to the so-called Wachter distribution. This finding provides a theoretical explanation for the observed tendency of Johansen’s test to find “spurious cointegration”. It also sheds light on the workings and limitations of the Bartlett correction approach to the over-rejection problem. We propose a simple graphical device, similar to the scree plot, for a preliminary assessment of cointegration in high-dimensional VARs. |
| Date: | 2016–06–15 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1637&r=ets |
| By: | Andreou, Elena |
| Abstract: | Many empirical studies link mixed data frequency variables such as low frequency macroeconomic or Â…nancial variables with high frequency Â…financial indicatorsÂ’ volatilities, especially within a predictive regression model context. The objective of this paper is threefold: First, we relate the standard Least Squares (LS) regression model with high frequency volatility predictors, with the corresponding Mixed Data Sampling Nonlinear LS (MIDAS-NLS) regression model (Ghysels et al., 2005, 2006), and evaluate the properties of the regression estimators of these models. We also consider alternative high frequency volatility measures as well as various continuous time models using their corresponding relevant higher-order moments to further analyze the properties of these estimators. Second, we derive the relative MSE efficiency of the slope estimator in the standard LS and MIDAS regressions, we provide conditions for relative efficiency and present the numerical results for different continuous time models. Third, we extend the analysis of the bias of the slope estimator in standard LS regressions with alternative realized measures of risk such as the Realized Covariance, Realized Beta and the Realized Skewness when the true DGP is a MIDAS model. |
| Keywords: | bias; efficiency; high-frequency volatility estimators; MIDAS regression model |
| JEL: | C22 C53 G22 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11307&r=ets |
| By: | Moreira, Marcelo J.; Mourão, Rafael; Moreira, Humberto |
| Abstract: | Researchers often rely on the t-statistic to make inference on parameters in statistical models. It is common practice to obtain critical values by simulation techniques. This paper proposes a novel numerical method to obtain an approximately similar test. This test rejects the null hypothesis when the test statistic islarger than a critical value function (CVF) of the data. We illustrate this procedure when regressors are highly persistent, a case in which commonly-used simulation methods encounter dificulties controlling size uniformly. Our approach works satisfactorily, controls size, and yields a test which outperforms the two other known similar tests. |
| Date: | 2016–06–06 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:778&r=ets |
| By: | Dirk Drechsel (KOF Swiss Economic Institute, ETH Zurich, Switzerland); Stefan Neuwirth (KOF Swiss Economic Institute, ETH Zurich, Switzerland) |
| Abstract: | We propose a Bayesian optimal filtering setup for improving out-of-sample forecasting performance when using volatile high frequency data with long lag structure for forecasting low-frequency data. We test this setup by using real-time Swiss construction investment and construction permit data. We compare our approach to different filtering techniques and show that our proposed filter outperforms various commonly used filtering techniques in terms of extracting the more relevant signal of the indicator series for forecasting. |
| Keywords: | Forecasting, construction, Switzerland, Bayesian, mixed data frequencies |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:kof:wpskof:16-407&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen); Bent Nielsen (Department of Economics, Nuffield College) |
| Abstract: | We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires an assumption on the frequency of small regressors. We show that this is satis?ed for a variety of deterministic and stochastic regressors, including stationary an random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results. |
| Keywords: | M-estimator, robust statistics, martingales, Huber-skip, quantile estimation. |
| Date: | 2016–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1605&r=ets |
| By: | Yanfei Kang; Rob J. Hyndman; Kate Smith-Miles |
| Abstract: | It is common practice to evaluate the strength of forecasting methods using collections of well-studied time series datasets, such as the M3 data. But how diverse are these time series, how challenging, and do they enable us to study the unique strengths and weaknesses of different forecasting methods? In this paper we propose a visualisation method for a collection of time series that enables a time series to be represented as a point in a 2-dimensional instance space. The effectiveness of different forecasting methods can be visualised easily across this space, and the diversity of the time series in an existing collection can be assessed. Noting that the M3 dataset is not as diverse as we would ideally like, this paper also proposes a method for generating new time series with controllable characteristics to fill in and spread out the instance space, making generalisations of forecasting method performance as robust as possible. |
| Keywords: | M3-Competition, time series visualisation, time series generation, forecasting algorithm comparison |
| JEL: | C52 C53 C55 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2016-10&r=ets |
| By: | Hamidi Sahneh, Mehdi |
| Abstract: | Non-fundamentalness arises when observed variables do not contain enough information to recover structural shocks. This paper propose a new test to empirically detect non-fundamentalness, which is robust to the conditional heteroskedasticity of unknown form, does not need information outside of the specified model and could be accomplished with a standard F-test. A Monte Carlo study based on a DSGE model is conducted to examine the finite sample performance of the test. I apply the proposed test to the U.S. quarterly data to identify the dynamic effects of supply and demand disturbances on real GNP and unemployment. |
| Keywords: | Non-Fundamentalness; Invertibility; Vector Autoregressive. |
| JEL: | C32 C5 E3 |
| Date: | 2016–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:71924&r=ets |
| By: | Ciccarelli, Nicola |
| Abstract: | Financial data sets exhibit conditional heteroskedasticity and asymmetric volatility. In this paper we derive a semiparametric efficient adaptive estimator of a conditional heteroskedasticity and asymmetric volatility GARCH-type model (i.e., the PTTGARCH(1,1) model). Via kernel density estimation of the unknown density function of the innovation and via the Newton-Raphson technique applied on the root-n-consistent quasi-maximum likelihood estimator, we construct a more efficient estimator than the quasi-maximum likelihood estimator. Through Monte Carlo simulations, we show that the semiparametric estimator is adaptive for parameters in- cluded in the conditional variance of the model with respect to the unknown distribution of the innovation. |
| Keywords: | Semiparametric adaptive estimation; Power-transformed and threshold GARCH. |
| JEL: | C14 C22 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:72021&r=ets |
| By: | Degiannakis, Stavros; Filis, George; Hassani, Hossein |
| Abstract: | This study provides a new approach for implied volatility indices forecasting. We assess whether non-parametric techniques provide better predictions of implied volatility compared to standard forecasting models, such as AFRIMA and HAR. A combination of Singular Spectrum Analysis (SSA) and Holt-Winters (HW) model is applied on eight implied volatility indices for the period from February, 2001 to July, 2013. The findings confirm that the SSA-HW provides statistically superior one trading day and ten trading days ahead implied volatility forecasts world widely. Model-averaged forecasts suggest that the forecasting accuracy is further enhanced, for the ten-days ahead, when the SSA-HW is combined with an ARI(1,1) model. Additionally, the trading game reveals that the SSA-HW and the ARI-SSA-HW are able to generate significant average positive net daily returns in the out-of-sample period. The results are important for option pricing, portfolio management, value-at-risk and economic policy. |
| Keywords: | Implied Volatility, Volatility Forecasting, Singular Spectrum Analysis, ARFIMA, HAR, Holt-Winters, Model Confidence Set, Combined Forecasts. |
| JEL: | C14 C22 C52 C53 G15 |
| Date: | 2015–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:72084&r=ets |
| By: | Davide De Gaetano |
| Abstract: | In this paper the problem of instability due to changes in the parameters of some Realized Volatility (RV) models has been addressed. The analysis is based on 5-minute RV of four U.S. stock market indices. Three different representations of the log-RV have been considered and, for each of them, the parameter instability has been detected by using the recursive estimates test. In order to analyse how instabilities in the parameters affect the forecasting performance, an out-of-sample forecasting exercise has been performed. In particular, several forecast combinations, designed to accommodate potential structural breaks, have been considered. All of them are based on different estimation windows, with alternative weighting schemes, and do not take into account explicitly estimated break dates. The model con_dence set has been used to compare the forecasting performances of the proposed approaches. Our analysis gives empirical evidences of the effectiveness of the combinations which make adjustments for accounting the possible most recent break point. |
| Keywords: | Forecast combinations, Structural breaks, Realized volatility |
| JEL: | C53 C58 G17 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:rtr:wpaper:0208&r=ets |