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Nonlinear, NonGaussian, and Nonstationary State Space Models and Applications to Economic and Financial Time Series
https://ir.soken.ac.jp/records/781
https://ir.soken.ac.jp/records/781defecea1764f43bbbf48d0f47f0b46da
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Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20100222  
タイトル  
タイトル  Nonlinear, NonGaussian, and Nonstationary State Space Models and Applications to Economic and Financial Time Series  
タイトル  
タイトル  Nonlinear, NonGaussian, and Nonstationary State Space Models and Applications to Economic and Financial Time Series  
言語  en  
言語  
言語  eng  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_46ec  
資源タイプ  thesis  
著者名 
矢野, 浩一
× 矢野, 浩一 

フリガナ 
ヤノ, コウイチ
× ヤノ, コウイチ 

著者 
YANO, Koiti
× YANO, Koiti 

学位授与機関  
学位授与機関名  総合研究大学院大学  
学位名  
学位名  博士（統計科学）  
学位記番号  
内容記述タイプ  Other  
内容記述  総研大甲第1043号  
研究科  
値  複合科学研究科  
専攻  
値  15 統計科学専攻  
学位授与年月日  
学位授与年月日  20070323  
学位授与年度  
値  2006  
要旨  
内容記述タイプ  Other  
内容記述  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 nonGaussian heavytailed distributions. <br />These facts indicate that a nonlinear nonGaussian 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 nonstationary economy because the <br />coefficients of linear regression are fixed. This paper shows several statistical <br />approaches based on nonlinear nonGaussian state space modeling and timevarying <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 nonGaussian statespace modeling. <br /> In chapter 2, we propose a method to seek initial distributions of parameters for a <br />selforganizing state space model proposed by Kitagawa]. Our method is based on the <br />simplex NelderMead 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 nonGaussian 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 nonGaussian 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 heavytailed <br />distributions for the daily return of the Yen/Dollar exchange rate. <br /> In chapter 5, we propose a method that estimates a timevarying linear system <br />equation based on timevarying coefficients' vector autoregressive modeling <br />(timevarying 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 timevarying 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 forecastbased <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 />timevarying 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.  
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