Daisuke Nagakura

Testing for Symmetry of Distribution

In this paper, we propose a test for symmetry of distribution. Our test is robust against the existence of outlier. We confirm this by simulation study.

A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component simultaneously. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data.

Inconsistency of a unit root test against stochastic unit root processes

In this paper, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process against the alternative of a stochastic unit root (STUR) process, is inconsistent against a class of ERCA models. This class includes a class of STUR processes as special cases. We show, however, that the well-known Dickey-Fuller (DF) UR tests and an LBI test of Lee (1998) are consistent against a particular case of this class of ERCA models.

On the relationship between the matrix operators, vech and vecd

ABSTRACT We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively.

Further Results on the VECD Operator and Its Application

In this paper, we consider the matrix vectorization operator termed the vecd operator, which has recently been introduced in the literature. This operator stacks up distinct elements of a symmetric matrix in a way that differs from that of the well-known vech operator; it stacks up not columns, but diagonals. We give further consideration to the vecd operator and related matrices, and derive their various useful properties. We provide some statistical applications of the vecd operator to illustrate its usefulness.

Asymmetry in Government Bond Returns

Is there asymmetry in the distribution of government bond returns in developed countries? Can asymmetries be predicted using financial and macroeconomic variables? To answer the first question, we provide evidence for asymmetry in government bond returns in particular for short maturities. This finding has important implications for modelling and forecasting government bond returns. For example, widely used models for yield curve analysis such as the affine term structure model assume symmetrically distributed innovations. To answer the second question, we find that liquidity in government bond markets predicts the coefficient of skewness with a positive sign, meaning that the probability of a large and negative excess return is more likely in a less liquid market. In addition, a positive realized return is associated with a negative coefficient of skewness, or a small probability of a large and negative return in the future. *We thank Toni Braun, Karen Lewis, Masao Ogaki, Tatsuyoshi Okimoto, participants at the Bank of Japan seminar and the 8th Conference for Applied Financial Economics for their helpful comments.

A Note on How to Impose Stationarity and Invertibility Conditions in ARMA Model Estimation: A Review

In this note, I review how to impose the stationarity and invertibility conditions in estimating ARMA models with unconstrained optimization. Specifically, I reintroduce a convenient transformation of unconstrained variables proposed by Jones (1980), illustrating how to compute its inverse transformation and partial derivatives.