{"product_id":"estimation-of-stochastic-processes-with-stationary-increments-and-cointegrated-sequences-hardback-9781786305039","title":"Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences (Hardback) 9781786305039","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eEstimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMaksym Luz (Author), Mikhail Moklyachuk (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781786305039, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 October 2019\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e320 pages\u003cbr\u003e23.6 x 16 x 2.3 cm, 0.658 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eEstimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences.\u003cbr\u003e \u003cbr\u003e Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eNotations ix\u003c\/p\u003e \u003cp\u003eIntroduction xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1. Stationary Increments of Discrete Time Stochastic Processes: Spectral Representation\u003c\/b\u003e \u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2. Extrapolation Problem for Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. The classical method of extrapolation 9\u003c\/p\u003e \u003cp\u003e2.2. Minimax (robust) method of extrapolation 21\u003c\/p\u003e \u003cp\u003e2.3. Least favorable spectral density in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e 24\u003c\/p\u003e \u003cp\u003e2.4. Least favorable spectral densities which admit factorization in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e 25\u003c\/p\u003e \u003cp\u003e2.5. Least favorable spectral density in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e\u003c\/i\u003e 29\u003c\/p\u003e \u003cp\u003e2.6. Least favorable spectral density which admits factorization in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e\u003c\/i\u003e 29\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3. Interpolation Problem for Stochastic Sequences with \u003c\/b\u003e\u003cb\u003eStationary \u003ci\u003en\u003c\/i\u003eth Increments\u003c\/b\u003e \u003cb\u003e31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. The classical method of interpolation 31\u003c\/p\u003e \u003cp\u003e3.2. Minimax method of interpolation 41\u003c\/p\u003e \u003cp\u003e3.3. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003e−\u003c\/sup\u003e\u003c\/i\u003e\u003csub\u003e0\u003ci\u003e,n\u003c\/i\u003e\u003c\/sub\u003e 43\u003c\/p\u003e \u003cp\u003e3.4. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003e−\u003c\/sup\u003e\u003csub\u003eM,n\u003c\/sub\u003e\u003c\/i\u003e 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4. Extrapolation Problem for Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments Based on Observations with Stationary Noise\u003c\/b\u003e \u003cb\u003e53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. The classical method of extrapolation with noise 53\u003c\/p\u003e \u003cp\u003e4.2. Extrapolation of cointegrated stochastic sequences 71\u003c\/p\u003e \u003cp\u003e4.3. Minimax (robust) method of extrapolation 75\u003c\/p\u003e \u003cp\u003e4.4. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 80\u003c\/p\u003e \u003cp\u003e4.5. Least favorable spectral densities which admit factorization in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 82\u003c\/p\u003e \u003cp\u003e4.6. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 84\u003c\/p\u003e \u003cp\u003e4.7. Least favorable spectral densities which admit factorization in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5. Interpolation Problem for Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments Based on Observations with Stationary Noise\u003c\/b\u003e \u003cb\u003e89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. The classical method of interpolation with noise 89\u003c\/p\u003e \u003cp\u003e5.2. Interpolation of cointegrated stochastic sequences 96\u003c\/p\u003e \u003cp\u003e5.3. Minimax (robust) method of interpolation 97\u003c\/p\u003e \u003cp\u003e5.4. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003e−\u003c\/sup\u003e\u003c\/i\u003e\u003csub\u003e0\u003ci\u003e,f\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e× D\u003csup\u003e−\u003c\/sup\u003e\u003c\/i\u003e\u003csub\u003e0\u003ci\u003e,g\u003c\/i\u003e\u003c\/sub\u003e 100\u003c\/p\u003e \u003cp\u003e5.5. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csub\u003e2\u003ci\u003eε\u003c\/i\u003e1\u003c\/sub\u003e\u003ci\u003e× D\u003c\/i\u003e\u003csub\u003e1\u003ci\u003eε\u003c\/i\u003e2\u003c\/sub\u003e 103\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6. Filtering Problem of Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments Based on Observations with Stationary Noise\u003c\/b\u003e \u003cb\u003e107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. The classical method of filtering 107\u003c\/p\u003e \u003cp\u003e6.2. Filtering problem for cointegrated stochastic sequences 119\u003c\/p\u003e \u003cp\u003e6.3. Minimax (robust) method of filtering 124\u003c\/p\u003e \u003cp\u003e6.4. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 129\u003c\/p\u003e \u003cp\u003e6.5. Least favorable spectral densities which admit factorization in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 131\u003c\/p\u003e \u003cp\u003e6.6. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 134\u003c\/p\u003e \u003cp\u003e6.7. Least favorable spectral densities which admit factorization in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7. Interpolation Problem for Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments Observed with Non-stationary Noise\u003c\/b\u003e \u003cb\u003e139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. The classical interpolation problem in the case of non-stationary noise 140\u003c\/p\u003e \u003cp\u003e7.2. Minimax (robust) method of interpolation 148\u003c\/p\u003e \u003cp\u003e7.3. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003e−\u003c\/sup\u003e\u003c\/i\u003e\u003csub\u003e0\u003ci\u003e,μ\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e× D\u003csup\u003e−\u003c\/sup\u003e\u003c\/i\u003e\u003csub\u003e0\u003ci\u003e,μ\u003c\/i\u003e\u003c\/sub\u003e 150\u003c\/p\u003e \u003cp\u003e7.4. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003e−\u003c\/sup\u003e\u003csub\u003eM,μ\u003c\/sub\u003e×D\u003csup\u003e−\u003c\/sup\u003e\u003csub\u003eM,μ\u003c\/sub\u003e\u003c\/i\u003e 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8. Filtering Problem for Stochastic Sequences with Stationary \u003ci\u003en\u003c\/i\u003eth Increments Observed with Non-stationary Noise\u003c\/b\u003e \u003cb\u003e155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. The classical filtering problem in the case of non-stationary noise 156\u003c\/p\u003e \u003cp\u003e8.2. Minimax filtering based on observations with non-stationary noise 170\u003c\/p\u003e \u003cp\u003e8.3. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 174\u003c\/p\u003e \u003cp\u003e8.4. Least favorable spectral densities which admit factorizations in theclass \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 175\u003c\/p\u003e \u003cp\u003e8.5. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 177\u003c\/p\u003e \u003cp\u003e8.6. Least favorable spectral densities which admit factorizations in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9. Stationary Increments of Continuous Time Stochastic Processes: Spectral Representation\u003c\/b\u003e \u003cb\u003e181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10. Extrapolation Problem for Stochastic Processes with Stationary \u003ci\u003en\u003c\/i\u003eth Increments\u003c\/b\u003e \u003cb\u003e187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1. Hilbert space projection method of extrapolation 187\u003c\/p\u003e \u003cp\u003e10.2. Minimax (robust) method extrapolation 205\u003c\/p\u003e \u003cp\u003e10.3. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 208\u003c\/p\u003e \u003cp\u003e10.4. Least favorable spectral density in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e 210\u003c\/p\u003e \u003cp\u003e10.5. Least favorable spectral density which admits factorization in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e 211\u003c\/p\u003e \u003cp\u003e10.6. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 213\u003c\/p\u003e \u003cp\u003e10.7. Least favorable spectral densities which allow factorization in the class \u003ci\u003eD\u003csub\u003eδ\u003c\/sub\u003e\u003c\/i\u003e 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11. Interpolation Problem for Stochastic Processes with Stationary \u003ci\u003en\u003c\/i\u003eth Increments\u003c\/b\u003e \u003cb\u003e217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1. Hilbert space projection method of interpolation 217\u003c\/p\u003e \u003cp\u003e11.2. Minimax (robust) method of interpolation 226\u003c\/p\u003e \u003cp\u003e11.3. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 229\u003c\/p\u003e \u003cp\u003e11.4. Least favorable spectral density in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e\u003c\/i\u003e 230\u003c\/p\u003e \u003cp\u003e11.5. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003csub\u003e1\u003ci\u003e\/f\u003c\/i\u003e\u003c\/sub\u003e × \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003csub\u003e1\u003ci\u003e\/g\u003c\/i\u003e\u003c\/sub\u003e 231\u003c\/p\u003e \u003cp\u003e11.6. Least favorable spectral density in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003csub\u003e1\u003ci\u003e\/f\u003c\/i\u003e\u003c\/sub\u003e 233\u003c\/p\u003e \u003cp\u003e11.7. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 234\u003c\/p\u003e \u003cp\u003e11.8. Least favorable spectral density in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e\u003c\/i\u003e 235\u003c\/p\u003e \u003cp\u003e11.9. Least favorable spectral density in the class \u003ci\u003eD\u003c\/i\u003e\u003csub\u003e2\u003ci\u003eε\u003c\/i\u003e\u003c\/sub\u003e 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12. Filtering Problem for Stochastic Processes with Stationary \u003ci\u003en\u003c\/i\u003eth Increments\u003c\/b\u003e \u003cb\u003e239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1. Hilbert space projection method of filtering 239\u003c\/p\u003e \u003cp\u003e12.2. Minimax (robust) method of filtering 246\u003c\/p\u003e \u003cp\u003e12.3. Least favorable spectral densities in the class \u003ci\u003eD\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ef\u003c\/sub\u003e × D\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e\u003ci\u003e\u003csub\u003eg\u003c\/sub\u003e\u003c\/i\u003e 248\u003c\/p\u003e \u003cp\u003e12.4. Least favorable spectral densities in the class \u003ci\u003eD\u003csup\u003eu\u003c\/sup\u003e\u003csub\u003ev\u003c\/sub\u003e × D\u003csub\u003eε\u003c\/sub\u003e\u003c\/i\u003e 250\u003c\/p\u003e \u003cp\u003eProblems to Solve 253\u003c\/p\u003e \u003cp\u003eAppendix 259\u003c\/p\u003e \u003cp\u003eReferences 267\u003c\/p\u003e \u003cp\u003eIndex 281\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52446737531160,"sku":"9781786305039","price":100.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781786305039.jpg?v=1785112490","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/estimation-of-stochastic-processes-with-stationary-increments-and-cointegrated-sequences-hardback-9781786305039","provider":"Freshly Printed Books","version":"1.0","type":"link"}