introduction to time series modeling
introduction to time series and forecasting
... is given 1.1 Examples of Time Series A time series is a set of observations xt , each one being recorded at a specific time t A discrete -time time series (the type to which this book is primarily ... · i · 2002 1:59 p.m Page ix Contents Preface Introduction 1.1 Examples of Time Series 1.2 Objectives of Time Series Analysis 1.3 Some Simple Time Series Models 1.3.1 Some Zero-Mean Models 1.3.2 ... Introduction 1.1 1.2 1.3 1.4 1.5 1.6 Examples of Time Series Objectives of Time Series Analysis Some Simple Time Series Models Stationary Models and the Autocorrelation Function Estimation and Elimination...
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An introduction to disk drive modeling
... their time is proportional to the square root of the seek distance plus the settle time Long seeks spend most of their time moving at a constant speed, taking time that is proportional to distance ... 41% 30.00ms 10 b Transfer time proportional to I/O size; seek -time linear in distance; random rotation time in interval [0, rotation -time) a Trivial model: constant, fixed time for each I/O fixed ... 97560 sector size 256 bytes 512 bytes cylinders 1449 1962 tracks per cylinder 19 data sectors per track 113 72 number of zones 1 track skew 34 sectors sectors cylinder skew 43 sectors 18 sectors...
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AN INTRODUCTION TO CREDIT RISK MODELING doc
... devresbo ton devresbo ton devresbo ton %33.0 devresbo ton devresbo ton devresbo ton noitaiveD-dradnatS %98.21 %69.7 %97.3 %93.2 %36.0 %96.0 %64.0 %60.0 %60.0 devresbo ton devresbo ton devresbo ton ... statistical tools provide a first indication regarding the rating of a customer, but due to the various soft factors underlying a rating, the Without going into details we would like to add that ... LLC 2.5 2.6 2.7 One-Factor/Sector Models 2.5.1 The CreditMetricsTM /KMV One-Factor Model 2.5.2 The CreditRisk+ One-Sector Model 2.5.3 Comparison of One-Factor and One-Sector Models Loss Distributions...
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an introduction to credit risk modeling phần 2 docx
... to the philosophy of its authors Gupton, Finger, and Bhatia to make credit risk methodology available to a broad audience in a fully transparent manner Both companies continue to contribute to ... Their tools are based on a modification of Merton’s asset value model, see Chapter 3, and include a tool for estimating default probabilities (Credit MonitorTM ) from market information and a tool ... underlying Factor FIGURE 1.5 Correlation induced by an underlying factor with a country factor for Germany and probably also with some other factors However, the crucial point is that factor models...
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an introduction to credit risk modeling phần 3 doc
... where the sector factor Xs(i) is common to all obligors in that sector Here s(i) denotes the sector in which obligor i takes place A possible simulation algorithm to generate default times τ1 , ... distribution then just turns out to be the convolution of the sector distributions due to the independence of the sector variables Λ(1) , , Λ(mS ) So we only have to find the sector’s default distributions ... sector as a “factor-inducing” entity, or – as the CreditRisk+ Technical Document [18] says it – every sector could be thought of as generated by a single underlying factor In this way, sectors...
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an introduction to credit risk modeling phần 4 docx
... standard deviation) In pricing tools the CM is sometimes assumed to be constant for a portfolio, even when adding new deals to it The contribution of the new deal to the total EC of the enlarged portfolio ... are going to show how to use copulas in order to construct portfolio loss variables admitting a stronger tail dependency than induced by the normal copulas But before continuing, we want to quote ... non-normal distributions to financial time series in general (see, e.g., Eberlein [33]), so far we not know about an established standard calibration methodology for fitting t-copulas to a credit portfolio...
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an introduction to credit risk modeling phần 5 pptx
... without any knowledge of stochastic calculus we recommend the book by Mikosch [87], which gives an introduction to the basic concepts of stochastic calculus with finance in view To readers with a strong ... short selling of A today, giving us A0 units of money today; buying asset B today, hereby spending B0 units of money; investing the residual A0 − B0 > in the riskless bond today At time T , we first ... asset A According to Proposition 3.2.1 we only have to show that the two portfolios have the same value at time t = T , because then their values at time t = must also agree due to the no-arbitrage...
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an introduction to credit risk modeling phần 6 pptx
... underlying factors incorporating a common systematic source of credit risk Associated with every such background factor is a so-called sector, such that every obligor i admits a breakdown into sector weights ... , mS that sector s contributes with a fraction wis to the default intensity of obligor i Here mS denotes the number of involved sectors Obviously the calibration of sectors and sector weights ... our detour and we return to the actual topic of this section The conditional distribution of the sector defaults is given by (4 19) The mixing variable is Λ(s) ∼ Γ(αs , βs ) According to our...
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an introduction to credit risk modeling phần 7 doc
... equivalent to requiring that the underlying Markov chain be stochastically monotonic Note that row and column monotony towards the diagonal (properties (vi) and (vii)) implies stochastic monotony but ... less than or equal to 0.002% are mapped to AAA, 0.002% to 0.04% corresponds to AA, etc The historical frequencies of changes from one range to another are estimated from the history of changes in ... which root to choose when more of them exist The idea is now to try to embed the time- discrete Markov ©2003 CRC Press LLC chain in a time- continuous Markov process, the latter being totally controlled...
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an introduction to credit risk modeling phần 8 pps
... payment times the discount factor for time t times the probability to default “around” t summed up from time zero to maturity Similarly, for a classic default swap we have spread payments ∆i s at time ... correlated default times via the copula approach ©2003 CRC Press LLC time, < meani [τi ] >, the average first -to- default -time < mini [τi ] >, and the average last -to- default -time < maxi [τi ] >, ... the default times < stdi [τi ] > ( ), the average first -to- default time < mini [τi ] > (+), and the average last -to- default -time < maxi [τi ] > (◦) in units of the average default time < meani...
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an introduction to credit risk modeling phần 9 pot
... has access to this particular credit exposure offers a way to evade the problems hindering the investor to purchase the exposure he is interested in The issuer sells a note to the investor with ... outcome has to be reported to the trustee and to the investors The collection of tests and criteria varies from deal to deal, and not all tests included in the monthly reports automatically have ... loan needs to be backed by regulatory capital, the capital costs associated with a loan to a customer can be too high for making the lending business profitable But if loans are pooled into portfolios...
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an introduction to credit risk modeling phần 3 pptx
... where the sector factor Xs(i) is common to all obligors in that sector Here s(i) denotes the sector in which obligor i takes place A possible simulation algorithm to generate default times τ1 , ... distribution then just turns out to be the convolution of the sector distributions due to the independence of the sector variables Λ(1) , , Λ(mS ) So we only have to find the sector’s default distributions ... sector as a “factor-inducing” entity, or – as the CreditRisk+ Technical Document [18] says it – every sector could be thought of as generated by a single underlying factor In this way, sectors...
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an introduction to credit risk modeling phần 5 pps
... without any knowledge of stochastic calculus we recommend the book by Mikosch [87], which gives an introduction to the basic concepts of stochastic calculus with finance in view To readers with a strong ... short selling of A today, giving us A0 units of money today; buying asset B today, hereby spending B0 units of money; investing the residual A0 − B0 > in the riskless bond today At time T , we first ... asset A According to Proposition 3.2.1 we only have to show that the two portfolios have the same value at time t = T , because then their values at time t = must also agree due to the no-arbitrage...
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an introduction to credit risk modeling phần 7 pot
... equivalent to requiring that the underlying Markov chain be stochastically monotonic Note that row and column monotony towards the diagonal (properties (vi) and (vii)) implies stochastic monotony but ... less than or equal to 0.002% are mapped to AAA, 0.002% to 0.04% corresponds to AA, etc The historical frequencies of changes from one range to another are estimated from the history of changes in ... which root to choose when more of them exist The idea is now to try to embed the time- discrete Markov ©2003 CRC Press LLC chain in a time- continuous Markov process, the latter being totally controlled...
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an introduction to credit risk modeling phần 8 ppsx
... payment times the discount factor for time t times the probability to default “around” t summed up from time zero to maturity Similarly, for a classic default swap we have spread payments ∆i s at time ... correlated default times via the copula approach ©2003 CRC Press LLC time, < meani [τi ] >, the average first -to- default -time < mini [τi ] >, and the average last -to- default -time < maxi [τi ] >, ... the default times < stdi [τi ] > ( ), the average first -to- default time < mini [τi ] > (+), and the average last -to- default -time < maxi [τi ] > (◦) in units of the average default time < meani...
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an introduction to credit risk modeling phần 9 pdf
... has access to this particular credit exposure offers a way to evade the problems hindering the investor to purchase the exposure he is interested in The issuer sells a note to the investor with ... outcome has to be reported to the trustee and to the investors The collection of tests and criteria varies from deal to deal, and not all tests included in the monthly reports automatically have ... loan needs to be backed by regulatory capital, the capital costs associated with a loan to a customer can be too high for making the lending business profitable But if loans are pooled into portfolios...
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an introduction to credit risk modeling phần 10 docx
... simulation step from time t to time t + will always be conditioned on the already realized path (the “history” up to time t) This very much reflects the approach an investor would follow during ... Investors Service Moody’s Approach to rating multisector CDOs, September 2000 [94] Moody’s Investors Service Moody’s Approach to Rating Multisector CDOs, September 2000 [95] Moody’s Investors ... overview and introduction to CDOs [69] – The JPM guide to credit derivatives, also introducing synthetic CDOs [68] ©2003 CRC Press LLC • Deutsche Bank: – CDO introduction [27] – Introduction to the...
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An introduction to the unified modeling language
... because he or she has to go to jail A player moves on the board because he or she has to go to Free Parking This scenario involves a player moving However, sometimes a player has to deal with “exceptional” ... Table 1: Multiplicity notation Cardinality and modality One -to- one and mandatory One -to- one and optional One -to- many and mandatory One -to- many and optional With lower bound l and upper bound u ... dimension represents time; the horizontal dimension represents different objects Initiation of the sequence starts in the top-left corner, and time proceeds down the page (from top to bottom) The vertical...
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