Kamakura Seminar Jan 8-9, 2014
ＫＫＲ, Kamakura Wakamiya
January 8, 2014
14:00 - 14:50
Asymptotics of Realized Volatility with Non-Gaussian ARCH(¥infty) Microstructure Noise
By Hiroyuki TANIAI ( Waseda University;
Joint work with Usami, T., Suto, N. and Taniguchi, M. )
15:00 - 15:50
Universal Portfolios with Optimal Categorized Side Information
By Hiroshi Shiraishi ( Jikei Medical Univ. )
16:00 - 16:50
Vector autoregressive modeling in presence of time-varying covariance.
By Hamdi Raissi ( Univ. Europeenne de Bretagne, France )
17:00 - 18:30 :
Discussion on “ Future Developments in High Dimensional Statistical Analysis”
By all the members
January 9, 2014
9:00 - 9:50
FCLT for long memory process in frequency domain
By Junichi Hirukawa ( Niigata Univ. )
10:00 - 10:50
Semiparametric Models and Estimation for Nonlinear Regression of Irregularly
Located Spatial Time-series Data
By Zudi Lu ( University of Southampton, U.K. )
11:00 - 11:50
Aggregation and dynamic macroeconomics
By Marco Lippi ( Università di Roma - La Sapienza and EIEF )
Abstract ( Kamakura Seminar )
(1) Asymptotics of Realized Volatility with Non-Gaussian ARCH(¥infty) Microstructure
Noise
By Hiroyuki TANIAI ( Waseda University;
Joint work with Usami, T., Suto, N. and Taniguchi, M. )
Abstract.
In order to estimate the conditional variance of some specific day, the sum of squared
intradayreturns, as known as ``realized volatility" or ``realized variance", is often used.
Although this estimator does not converge to the true volatility when the observed price
involves market microstructure noise, some subsample-based estimator is known to
resolve this problem. In this paper, we will study the asymptotics of this estimator,
assuming that market microstructure noise follows a non-Gaussian autoregressive
conditional heteroskedastic model of order $¥infty$ (ARCH($¥infty$)). There we
elucidate the asymptotics of realized volatility and subsample estimator, which are
influenced by the non-Gaussianity and dependent structure of the noise. Some
numerical studies are given, and they illuminate interesting features of the
asymptotics.
(2) Universal Portfolios with Optimal Categorized Side Information
By Hiroshi Shiraishi ( Jikei Medical Univ. )
Abstract.
Cover (1991) proposed a ``universal portfolio" (UP) strategy which is a sequential
portfolio selection procedure for investing in the stock market. He showed that the
strategy achieves, to first order in the exponent, the same wealth as the best constant
rebalanced portfolio (BCRP) without any distributional assumption. Cover and
Ordentlich (1996) extended his result to the case with side information. They showed
that the UP with side information strategy achieves asymptotically the same wealth as
the best state-constant rebalanced portfolio (BSCRP) which invests in the market using
one of k distinct portfolios depending on the current state of side information. We
consider a UP with Optimal Categorized Side Information which is the same as Cover
and Ordentlich's UP, but the number of states k is estimated at each time. We also
shows that the UP achieves asymptotically the same wealth as the BSCRP with an
optimal number of states (k*).
(3) Vector autoregressive modeling in presence of time-varying covariance.
By Hamdi Raissi ( Univ. Europeenne de Bretagne, France )
The statistical analysis of vector autoregressive (VAR) models with nonconstant
covariance is investigated. The covariance structure is deterministic and quite general,
including piecewise constant structure or cyclical behaviors as special cases.
In this framework we propose ordinary least squares (OLS), generalized least squares
(GLS) and adaptive least squares (ALS) procedures. The GLS estimator requires the
knowledge of the time-varying variance structure while in the ALS approach the
unknown covariance is estimated by kernel smoothing with the outer product of the
OLS residuals vectors. We derive the asymptotic distribution of the proposed estimators
for the AR parameters and compare their properties. Using these results we build tests
for the linear Granger causality which take into account non stationary covariance.
Identification and validation tools are proposed for the selection of the lag length of
VAR models with nonconstant covariance. The theoretical outputs are illustrated
analyzing the dynamics of US macroeconomic data sets.
(4) FCLT for long memory process in frequency domain
By Junichi Hirukawa ( Niigata Univ. )
Abstract.
Since the work of McLeish (1974) many different sets of conditions for the central limit
theorems (CLT) and invariance principles (FCLT) for discrete time series have been
considered. The key to the approach for linear process is an algebraic decomposition of
the linear filter that is known in the econometric literature as the Beveridge-Nelson
(BN) decomposition. However such decomposition in frequency domain is not often
discussed. In this talk we would like to consider FCLT for long memory process in
frequency domain.
(5) Semiparametric Models and Estimation for Nonlinear Regression of Irregularly
Located Spatial Time-series Data
By Zudi Lu ( University of Southampton, U.K. )
Abstract.
Nonparametric and semiparametric approaches have been popular in nonlinear
modelling of univariate or small number multivariate time series data. However, they
become increasingly challenging when applied to nonlinear analysis of big spatial
time-series network data. Bigger time-series data with more complex structures
collected at irregularly spaced sampling locations are becoming more prevalent in a
wide range of disciplines. With few exceptions, however, practical statistical methods
for modeling and analysis of such data remain elusive. Here, we propose a class of
spatio-temporal autoregressive partially linear regression models, which permits
possibly nonlinear relationships between responses and covariates.
(6) Aggregation and dynamic macroeconomics
By Marco Lippi ( Università di Roma - La Sapienza and EIEF )
Abstract.
As a rule, macroeconometric models are based on the representative agent. However, if
heterogeneity across agents is allowed, the micro and the macro dynamics may differ
dramatically. I show that the classic results by Theil on static models can be generalized
to dynamic relationships. I illustrate this point with the case of VAR models and show
the way heterogeneity and fundamentalness crucially determine the aggregate result.