http://swrc.ontoware.org/ontology#Thesis
Nonlinear, Non-Gaussian, and Non-stationary State Space Models and Applications to Economic and Financial Time Series
en
矢野 浩一
ヤノ コウイチ
YANO Koiti
総研大甲第1043号
Financial markets and the economy are changing rapidly. On financial markets, many <br />financial time series exhibit changes of volatility (variance) over time. Moreover, many <br />financial time series are well known to have non-Gaussian heavy-tailed distributions. <br />These facts indicate that a nonlinear non-Gaussian time series analysis is needed. <br />Regarding the economy, as one example, the Japanese economy has the experience of <br />the "bubble economy" in the late 1980s. After bursting of the "bubble economy", the <br />economy entered a decade o,f economic stagnation, which is often called "the lost <br />decade". These facts indicate that conventional linear regression based on ordinary <br />least squares might be ineffective to analyze a non-stationary economy because the <br />coefficients of linear regression are fixed. This paper shows several statistical <br />approaches based on nonlinear non-Gaussian state space modeling and time-varying <br />coefficient autoregressive modeling. These approaches are novel studies of financial <br />markets and the economy. <br /> In chapter 1, the Monte Carlo filter is introduced. It is a minimal introduction to <br />nonlinear non-Gaussian state-space modeling. <br /> In chapter 2, we propose a method to seek initial distributions of parameters for a <br />self-organizing state space model proposed by Kitagawa]. Our method is based on the <br />simplex Nelder-Mead algorithm for solving nonlinear and discontinuous optimization <br />problems. We show the effectiveness of our method by applying it to a linear Gaussian <br />model, a linear non-Gaussian Model, a nonlinear Gaussian model, and a stochastic <br />volatility model. <br /> In chapter 3, we propose a smoothing algorithm based on the Monte Carlo filter and <br />the inverse function of a system equation (an inverse system function). Our method is <br />applicable to any nonlinear non-Gaussian state space model if an inverse system <br />equation is given analytically. Moreover, we propose a filter initialization algorithm <br />based on a smoothing distribution obtained by our smoothing algorithm and an <br />inverse system equation. <br /> In chapter 4, we illustrate the effectiveness of our approach by applying it to <br />stochastic volatility models and stochastic volatility models with heavy-tailed <br />distributions for the daily return of the Yen/Dollar exchange rate. <br /> In chapter 5, we propose a method that estimates a time-varying linear system <br />equation based on time-varying coefficients' vector autoregressive modeling <br />(time-varying VAR), and which controls the system. In our framework, an optimal <br />feedback is determined using linear quadratic dynamic programming in each period.<br />The coeffients of time-varying VAR are assumed to change gradually (this <br />assumption is widely known as smoothness priors of the Bayesian procedure). The <br />coefficients are estimated using the Kalman filter. In our empirical analyses, we show <br />the effectiveness of our approach by applying it to monetary policy, in particular, the <br />inflation targeting of the United Kingdom and the nominal growth rate targeting of <br />Japan. Furthermore, we emphasize that monetary policy must be forecast-based <br />because transmission lags pertain from monetary policy to the economy. Our approach <br />is convenient and effective for central bank practitioners when they are unaware of <br />the true model of the economy. Additionally, we find that the coefficients of <br />time-varying VAR change in response to changes of monetary policy. <br /> In chapter 6, we estimate the β of a single factor model that is ofben used by <br />financial practitioners. In this chapter, we assume that β changes "gradually" over <br />time; this assumption is identical to that in chapter 5. Using our approach, we can <br />estimate β, even if it is time varying. We apply our approach to the Japanese Stock <br />Markets and show its effectiveness. Although we adopt a very restrictive method (we <br />assume smoothness priors and use the Kalman fiker, which is based on linear state <br />space modeling and the Gaussian distribution), we can obtain good estimates of β.