{"product_id":"9789811939693","title":"Evolutionary Economics and Social Complexity Science: Practical Applications of RMT-Based Technique","description":"\u003ch1\u003eEvolutionary Economics and Social Complexity Science: Practical Applications of RMT-Based Technique\u003c\/h1\u003e \u003ch2\u003eTanaka-Yamawaki, Mieko; Ikura, Yumihiko\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book presents the novel approach of analyzing large-sized rectangular-shaped numerical data (so-called big data). The essence of this approach is to grasp the \"meaning\" of the data instantly, without getting into the details of individual data. Unlike conventional approaches of principal component analysis, randomness tests, and visualization methods, the authors' approach has the benefits of universality and simplicity of data analysis, regardless of data types, structures, or specific field of science.\u003cbr\u003e \u003cbr\u003e First, mathematical preparation is described. The RMT-PCA and the RMT-test utilize the cross-correlation matrix of time series, \u003ci\u003eC \u003c\/i\u003e= \u003ci\u003eXX\u003csup\u003eT\u003c\/sup\u003e\u003c\/i\u003e, where \u003ci\u003eX\u003c\/i\u003e represents a rectangular matrix of \u003ci\u003eN\u003c\/i\u003e rows and \u003ci\u003eL\u003c\/i\u003e columns and \u003ci\u003eX\u003csup\u003eT\u003c\/sup\u003e\u003c\/i\u003e represents the transverse matrix of \u003ci\u003eX\u003c\/i\u003e. Because \u003ci\u003eC\u003c\/i\u003e is symmetric, namely, \u003ci\u003eC \u003c\/i\u003e= \u003ci\u003eC\u003csup\u003eT\u003c\/sup\u003e\u003c\/i\u003e, it can be converted to a diagonal matrix of eigenvalues by a similarity transformation \u003ci\u003eSCS\u003c\/i\u003e\u003csup\u003e-1\u003c\/sup\u003e = \u003ci\u003eSCS\u003csup\u003eT\u003c\/sup\u003e\u003c\/i\u003e using an orthogonal matrix \u003ci\u003eS\u003c\/i\u003e. When \u003ci\u003eN\u003c\/i\u003e is significantly large, the histogram of the eigenvalue distribution can be compared to the theoretical formula derived in the context of the random matrix theory (RMT, in abbreviation).\u003cbr\u003e \u003cbr\u003e Then the RMT-PCA applied to high-frequency stock prices in Japanese and American markets is dealt with. This approach proves its effectiveness in extracting \"trendy\" business sectors of the financial market over the prescribed time scale. In this case, \u003ci\u003eX\u003c\/i\u003e consists of \u003ci\u003eN\u003c\/i\u003e stock- prices of length \u003ci\u003eL\u003c\/i\u003e, and the correlation matrix \u003ci\u003eC\u003c\/i\u003e is an \u003ci\u003eN\u003c\/i\u003e by \u003ci\u003eN\u003c\/i\u003e square matrix, whose element at the \u003ci\u003ei\u003c\/i\u003e-th row and \u003ci\u003ej\u003c\/i\u003e-th column is the inner product of the price time series of the length \u003ci\u003eL\u003c\/i\u003e of the \u003ci\u003ei\u003c\/i\u003e-th stock and the \u003ci\u003ej\u003c\/i\u003e-th stock of the equal length \u003ci\u003eL\u003c\/i\u003e.\u003cbr\u003e \u003cbr\u003e Next, the RMT-test is applied to measure randomness of various random number generators, including algorithmically generated random numbers and physically generated random numbers.\u003cbr\u003e \u003cbr\u003eThe book concludes by demonstrating two applications of the RMT-test: (1) a comparison of hash functions, and (2) stock prediction by means of randomness, including a new index of off-randomness related to market decline.\u003cbr\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2024-05-25\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811939693\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-19-3967-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 152\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44521854632076,"sku":"9789811939693","price":107.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811939693.jpg?v=1776539930","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789811939693","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}