4,463 research outputs found
Nonfractional Memory: Filtering, Antipersistence, and Forecasting
The fractional difference operator remains to be the most popular mechanism
to generate long memory due to the existence of efficient algorithms for their
simulation and forecasting. Nonetheless, there is no theoretical argument
linking the fractional difference operator with the presence of long memory in
real data. In this regard, one of the most predominant theoretical explanations
for the presence of long memory is cross-sectional aggregation of persistent
micro units. Yet, the type of processes obtained by cross-sectional aggregation
differs from the one due to fractional differencing. Thus, this paper develops
fast algorithms to generate and forecast long memory by cross-sectional
aggregation. Moreover, it is shown that the antipersistent phenomenon that
arises for negative degrees of memory in the fractional difference literature
is not present for cross-sectionally aggregated processes. Pointedly, while the
autocorrelations for the fractional difference operator are negative for
negative degrees of memory by construction, this restriction does not apply to
the cross-sectional aggregated scheme. We show that this has implications for
long memory tests in the frequency domain, which will be misspecified for
cross-sectionally aggregated processes with negative degrees of memory.
Finally, we assess the forecast performance of high-order and
models when the long memory series are generated by cross-sectional
aggregation. Our results are of interest to practitioners developing forecasts
of long memory variables like inflation, volatility, and climate data, where
aggregation may be the source of long memory
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
On Hodges and Lehmann's " result"
While the asymptotic relative efficiency (ARE) of Wilcoxon rank-based tests
for location and regression with respect to their parametric Student
competitors can be arbitrarily large, Hodges and Lehmann (1961) have shown that
the ARE of the same Wilcoxon tests with respect to their van der Waerden or
normal-score counterparts is bounded from above by . In
this paper, we revisit that result, and investigate similar bounds for
statistics based on Student scores. We also consider the serial version of this
ARE. More precisely, we study the ARE, under various densities, of the
Spearman-Wald-Wolfowitz and Kendall rank-based autocorrelations with respect to
the van der Waerden or normal-score ones used to test (ARMA) serial dependence
alternatives
Rank-based estimation for all-pass time series models
An autoregressive-moving average model in which all roots of the
autoregressive polynomial are reciprocals of roots of the moving average
polynomial and vice versa is called an all-pass time series model. All-pass
models are useful for identifying and modeling noncausal and noninvertible
autoregressive-moving average processes. We establish asymptotic normality and
consistency for rank-based estimators of all-pass model parameters. The
estimators are obtained by minimizing the rank-based residual dispersion
function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These
estimators can have the same asymptotic efficiency as maximum likelihood
estimators and are robust. The behavior of the estimators for finite samples is
studied via simulation and rank estimation is used in the deconvolution of a
simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Efficient Gibbs Sampling for Markov Switching GARCH Models
We develop efficient simulation techniques for Bayesian inference on
switching GARCH models. Our contribution to existing literature is manifold.
First, we discuss different multi-move sampling techniques for Markov Switching
(MS) state space models with particular attention to MS-GARCH models. Our
multi-move sampling strategy is based on the Forward Filtering Backward
Sampling (FFBS) applied to an approximation of MS-GARCH. Another important
contribution is the use of multi-point samplers, such as the Multiple-Try
Metropolis (MTM) and the Multiple trial Metropolize Independent Sampler, in
combination with FFBS for the MS-GARCH process. In this sense we ex- tend to
the MS state space models the work of So [2006] on efficient MTM sampler for
continuous state space models. Finally, we suggest to further improve the
sampler efficiency by introducing the antithetic sampling of Craiu and Meng
[2005] and Craiu and Lemieux [2007] within the FFBS. Our simulation experiments
on MS-GARCH model show that our multi-point and multi-move strategies allow the
sampler to gain efficiency when compared with single-move Gibbs sampling.Comment: 38 pages, 7 figure
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