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on Econometric Time Series |
| By: | Søren Johansen (University of Copenhagen and CREATES); Bent Nielsen (Nuffield College & Department of Economics, University of Oxford & Institute for New Economic Thinking at the Oxford Martin School) |
| 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 satisfied 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. |
| JEL: | C22 |
| Date: | 2016–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2016-18&r=ets |
| By: | Tue Gorgens; Chirok Han; Sen Xue |
| Abstract: | This paper establishes asymptotic distributions of the quadratic GMM estimator of the autoregressive parameter in simple linear dynamic panel data models with fixed effects under standard minimal assumptions. The number of time periods is assumed to be small. Focusing on settings where autoregressive parameter is uniquely identified, nonstandard convergence rates and limiting distributions arise in the well-known random walk case, as well as in other previously unrecognized cases. The paper finds that the convergence rates are slow in the nonstandard cases, and the limiting distributions are a mixture of two nonnormal distributions. The findings are illustrated using Monte Carlo simulations. |
| Keywords: | Dynamic panel data models, fixed effects, generalized method of moments, nonstandard limiting distributions |
| JEL: | C23 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2016-635&r=ets |
| By: | Mikosch, Heiner; Neuwirth, Stefan |
| Abstract: | This paper presents a MIDAS type mixed frequency VAR forecasting model. First, we propose a general and compact mixed frequency VAR framework using a stacked vector approach. Second, we integrate the mixed frequency VAR with a MIDAS type Almon lag polynomial scheme which is designed to reduce the parameter space while keeping models fexible. We show how to recast the resulting non-linear MIDAS type mixed frequency VAR into a linear equation system that can be easily estimated. A pseudo out-of-sample forecasting exercise with US real-time data yields that the mixed frequency VAR substantially improves predictive accuracy upon a standard VAR for dierent VAR specications. Forecast errors for, e.g., GDP growth decrease by 30 to 60 percent for forecast horizons up to six months and by around 20 percent for a forecast horizon of one year. |
| Keywords: | Forecasting, mixed frequency data, MIDAS, VAR, real time |
| JEL: | C53 E27 |
| Date: | 2015–04–13 |
| URL: | http://d.repec.org/n?u=RePEc:bof:bofitp:2015_013&r=ets |
| By: | Ryoko Ito |
| Abstract: | We develop the spline-DCS model and apply it to trade volume prediction, which remains a highly non-trivial task in high-frequency finance. Our application illustrates that the spline-DCS is computationally practical and captures salient empirical features of the data such as the heavy-tailed distribution and intra-day periodicity very well. We produce density forecasts of volume and compare the model's predictive performance with that of the state-of-the-art volume forecasting model, named the component-MEM, of Brownlees et al. (2011). The spline-DCS significantly outperforms the component-MEM in predicting intra-day volume proportions. |
| Keywords: | order slicing, price impact, robustness, score, VWAP trading |
| JEL: | C22 C51 C53 C58 G12 |
| Date: | 2016–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1606&r=ets |
| By: | Peter Malec |
| Abstract: | We propose a multiplicative component model for intraday volatility. The model consists of a seasonality factor, as well as a semiparametric and parametric component. The former captures the well-documented intraday seasonality of volatility, while the latter two account for the impact of the state of the limit order book, utilizing an additive structure, and fluctuations around this state by means of a unit GARCH specification. The model is estimated by a simple and easy-to-implement approach, consisting of across-day-averaging, smooth-backfitting and QML steps. We derive the asymptotic properties of the three component estimators. Further, our empirical application based on high-frequency data for NASDAQ equities investigates non-linearities in the relationship between the limit order book and subsequent return volatility and underlines the usefulness of including order book variables for out-of-sample forecasting performance. |
| Keywords: | Intraday volatility, GARCH, smooth backfitting, additive models, limit order book. |
| JEL: | C14 C22 C53 C58 |
| Date: | 2016–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1633&r=ets |
| By: | Del Barrio Castro, Tomás; Rodrigues, Paulo M M; Taylor, A M Robert |
| 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 |
| Date: | 2015–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:16807&r=ets |
| By: | Giorgia Marini (Università Sapienza di Roma - Dipartimento di Studi Giuridici, Filosofici ed Economici) |
| Abstract: | This paper enlarges on Gutierrez's (2003) results on the power of panel cointegration tests. By a comparison of power of panel cointegration tests, we show how the choice of most powerful test depends on the values of the sample statistics. Country-by-country and panel stationarity and cointegration tests are performed on a panel of 20 OECD countries over the period 1971-2004. Residual-based tests and a cointegration rank test in the system of health care expenditure and GDP are used to test cointegration. Asymptotic normal distribution of these tests allows a straightforward comparison: for some values of the sample statistics, residual-based and rank tests are not directly comparable as the power of the residual-based tests oscillates; for other values of the sample statistics, the rank test is more powerful than the residual-based tests. This suggests that a clear-cut conclusion on the most powerful test cannot be reached a priori. |
| Keywords: | Panel data, panel stationarity tests, panel cointegration tests, power of tests |
| JEL: | C12 C22 C23 I10 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:gfe:pfrp00:00021&r=ets |