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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hodrick–Prescott filter ： ウィキペディア英語版 Hodrick–Prescott filter The Hodrick–Prescott filter (also known as Hodrick–Prescott decomposition) is a mathematical tool used in macroeconomics, especially in real business cycle theory, to remove the cyclical component of a time series from raw data. It is used to obtain a smoothed-curve representation of a time series, one that is more sensitive to long-term than to short-term fluctuations. The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier $\backslash lambda$. The filter was popularized in the field of economics in the 1990s by economists Robert J. Hodrick and Nobel Memorial Prize winner Edward C. Prescott. However, it was first proposed much earlier by E. T. Whittaker in 1923.〔 - as quoted in (Philips 2010 )〕 ==The equation== The reasoning for the methodology uses ideas related to the decomposition of time series. Let $y\_t\backslash ,$ for $t\; =\; 1,\; 2,\; ...,\; T\backslash ,$ denote the logarithms of a time series variable. The series $y\_t\backslash ,$ is made up of a trend component, denoted by $\backslash tau\backslash ,$ and a cyclical component, denoted by $c\backslash ,$ such that $y\_t\backslash \; =\; \backslash tau\_t\backslash \; +\; c\_t\backslash \; +\; \backslash epsilon\_t\backslash ,$.〔Kim, Hyeongwoo. "(Hodrick–Prescott Filter )" March 12, 2004〕 Given an adequately chosen, positive value of $\backslash lambda$, there is a trend component that will solve :$\backslash min\_\backslash left(\backslash sum\_^T\; +\; \backslash lambda\; \backslash sum\_^\; )\; )^2\; \}\backslash right).\backslash ,$ The first term of the equation is the sum of the squared deviations $d\_t=y\_t-\backslash tau\_t$ which penalizes the cyclical component. The second term is a multiple $\backslash lambda$ of the sum of the squares of the trend component's second differences. This second term penalizes variations in the growth rate of the trend component. The larger the value of $\backslash lambda$, the higher is the penalty. Hodrick and Prescott suggest 1600 as a value for $\backslash lambda$ for quarterly data. Ravn and Uhlig (2002) state that $\backslash lambda$ should vary by the fourth power of the frequency observation ratio; thus, $\backslash lambda$ should equal 6.25 for annual data and 129,600 for monthly data. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hodrick–Prescott filter」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.