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on Econometric Time Series |
| By: | Andrew Papanicolaou |
| Abstract: | These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of the Research Training Group, with the author being partially supported by NSF grant DMS-0739195. |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1406.1936&r=ets |
| By: | Guillén, Osmani; Hecq, Alain; Issler, João Victor; Saraiva, Diogo |
| Abstract: | This paper has two original contributions. First, we show that the presentvalue model (PVM hereafter), which has a wide application in macroeconomicsand fi nance, entails common cyclical feature restrictions in the dynamics of thevector error-correction representation (Vahid and Engle, 1993); something thathas been already investigated in that VECM context by Johansen and Swensen (1999, 2011) but has not been discussed before with this new emphasis. Wealso provide the present value reduced rank constraints to be tested within thelog-linear model. Our second contribution relates to forecasting time seriesthat are subject to those long and short-run reduced rank restrictions. Thereason why appropriate common cyclical feature restrictions might improveforecasting is because it finds natural exclusion restrictions preventing theestimation of useless parameters, which would otherwise contribute to theincrease of forecast variance with no expected reduction in bias. We applied the techniques discussed in this paper to data known to besubject to present value restrictions, i.e. the online series maintained and up-dated by Shiller. We focus on three different data sets. The fi rst includes thelevels of interest rates with long and short maturities, the second includes thelevel of real price and dividend for the S&P composite index, and the thirdincludes the logarithmic transformation of prices and dividends. Our exhaustive investigation of several different multivariate models reveals that betterforecasts can be achieved when restrictions are applied to them. Moreover,imposing short-run restrictions produce forecast winners 70% of the time fortarget variables of PVMs and 63.33% of the time when all variables in thesystem are considered. |
| Date: | 2014–06–02 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:753&r=ets |
| By: | Chudik, Alexander (Federal Reserve Bank of Dallas); Pesaran, M. Hashem (University of Southern California and Trinity College) |
| Abstract: | The Global Vector Autoregressive (GVAR) approach has proven to be a very useful approach to analyze interactions in the global macroeconomy and other data networks where both the cross-section and the time dimensions are large. This paper surveys the latest developments in the GVAR modeling, examining both the theoretical foundations of the approach and its numerous empirical applications. We provide a synthesis of existing literature and highlight areas for future research. |
| Keywords: | Global Vector Autoregressive; global macroeconomy |
| JEL: | C32 E17 |
| Date: | 2014–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddgw:180&r=ets |
| By: | Yamamoto, Yohei |
| Abstract: | Elliott and Müller (2007) (EM) provides a method to construct a confidence set for the structural break date by inverting a locally best test statistic. Previous studies show that the EM method produces a set with an accurate coverage ratio even for a small break, however, the set is often overly lengthy. This study proposes a simple modification to rehabilitate their method. Following the literature, we provide an asymptotic justification for the modified method under a nonlocal asymptotic framework. A Monte Carlo simulation shows that like the original method, the modified method exhibits a coverage ratio that is very close to the nominal level. More importantly, it achieves a much shorter confidence set. Hence, when the break is small, the modified method serves as a better alternative to Bai's (1997) confidence set. We apply these methods to a small level shift in post-1980s Japanese inflation data. |
| Keywords: | coverage ratio, nonlocal asymptotics, heteroskedasticity and autocorrelation consistent covariance, condence set |
| JEL: | C12 C38 |
| Date: | 2014–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2014-08&r=ets |
| By: | Rob J Hyndman; Alan Lee; Earo Wang |
| Abstract: | We describe some fast algorithms for reconciling large collections of time series forecasts with aggregation constraints. The constraints arise due to the need for forecasts of collections of time series with hierarchical or grouped structures to add up in the same manner as the observed time series. We show that the least squares approach to reconciling hierarchical forecasts can be extended to more general non-hierarchical groups of time series, and that the computations can be handled efficiently by exploiting the structure of the associated design matrix. Our algorithms will reconcile hierarchical forecasts with hierarchies of unlimited size, making forecast reconciliation feasible in business applications involving very large numbers of time series. |
| Keywords: | combining forecasts, grouped time series, hierarchical time series, reconciling forecasts, weighted least squares. |
| JEL: | C32 C53 C63 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-17&r=ets |
| By: | Yuanhua Feng (University of Paderborn); Chen Zhou (University of Paderborn) |
| Abstract: | This paper discusses forecasting of long memory and a nonparametric scale function in nonnegative financial processes based on a fractionally integrated Log-ACD (FI-Log-ACD) and its semiparametric extension (Semi-FI-Log-ACD). Necessary and sufficient conditions for the existence of a stationary solution of the FI-Log-ACD are obtained. Properties of this model under log-normal assumption are summarized. A linear predictor based on the truncated AR(oo) form of the logarithmic process is proposed. It is shown that this proposal is an approximately best linear predictor. Approximate variances of the prediction errors for an individual observation and for the conditional mean are obtained. Forecasting intervals for these quantities in the log- and the original processes are calculated under log-normal assumption. The proposals are applied to forecasting daily trading volumes and daily trading numbers in financial market. |
| Keywords: | Approximately best linear predictor, FI-Log-ACD, financial forecasting, long memory time series, nonparametric methods, Semi-FI-Log-ACD |
| Date: | 2013–04 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:59&r=ets |
| By: | Yuanhua Feng (University of Paderborn) |
| Abstract: | This paper introduces a spatial framework for high-frequency returns and a faster double-conditional smoothing algorithm to carry out bivariate kernel estimation of the volatility surface. A spatial multiplicative component GARCH with random effects is proposed to deal with multiplicative random effects found from the data. It is shown that the probabilistic properties of the stochastic part and the asymptotic properties of the kernel volatility surface estimator are all strongly affected by the multiplicative random effects. Data example shows that the volatility surface before, during and after the 2008 financial crisis forms a volatility saddle. |
| Keywords: | Spatial multiplicative component GARCH, high-frequency returns, double-conditional smoothing, multiplicative random effect, volatility arch, volatility saddle. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:65&r=ets |
| By: | Eric Ghysels; J. Isaac Miller (Department of Economics, University of Missouri-Columbia) |
| Abstract: | We analyze the sizes of standard cointegration tests applied to data subject to linear interpolation, discovering evidence of substantial size distortions induced by the interpolation. We propose modifications to these tests to effectively eliminate size distortion from such tests conducted on data interpolated from end-of-period sampled low-frequency series. Our results generally do not support linear interpolation when alternatives such as aggregation or mixed-frequency-modified tests are possible. |
| Keywords: | linear interpolation, cointegration, trace test, residual-based cointegration tests |
| JEL: | C12 C32 |
| Date: | 2014–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1403&r=ets |