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Rounding Errors and Volatility Estimation
 Journal of Financial Econometrics 2014
"... ABSTRACT Financial prices are often discretizedwith smallest tick size of one cent, for example. Thus prices involve rounding errors. Rounding errors affect the estimation of volatility, and understanding them is critical, particularly when using high frequency data. We study the asymptotic behavi ..."
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ABSTRACT Financial prices are often discretizedwith smallest tick size of one cent, for example. Thus prices involve rounding errors. Rounding errors affect the estimation of volatility, and understanding them is critical, particularly when using high frequency data. We study the asymptotic
Exponential sums and rounding error
 London Math. Soc
, 1991
"... Let F(x) be a real function with sufficiently many derivatives existing and satisfying certain nonvanishing conditions for 1 ̂ x ^ 2. The roundingerror sum where p(t) is —t for 0 < / < 1, and has period one, can be estimated by exponentialsum methods. We give order of magnitude bounds; th ..."
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Let F(x) be a real function with sufficiently many derivatives existing and satisfying certain nonvanishing conditions for 1 ̂ x ^ 2. The roundingerror sum where p(t) is —t for 0 < / < 1, and has period one, can be estimated by exponentialsum methods. We give order of magnitude bounds
Automatic Linear Correction Of Rounding Errors
, 1999
"... A new automatic method to correct the firstorder effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a confidence threshold are computed using automatic differentiation, computation of elementary rounding error and running error analys ..."
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Cited by 11 (2 self)
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A new automatic method to correct the firstorder effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a confidence threshold are computed using automatic differentiation, computation of elementary rounding error and running error
Rounding error in numerical solution of stochastic differential equations
, 2003
"... ABSTRACT The present investigation is concerned with estimating the rounding error in numerical solution of stochastic differential equations. A statistical rounding error analysis of Euler's method for stochastic differential equations is performed. In particular, numerical evaluation of the ..."
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Cited by 2 (1 self)
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ABSTRACT The present investigation is concerned with estimating the rounding error in numerical solution of stochastic differential equations. A statistical rounding error analysis of Euler's method for stochastic differential equations is performed. In particular, numerical evaluation
Reliable computing: numerical and rounding errors
"... Computer representation of real numbers The arithmetic performed in a machine involves numbers with only a finite number of digits, with the results that many calculations are performed with approximate representations of the actual numbers. In typical computer, only a relatively small subset of the ..."
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Computer representation of real numbers The arithmetic performed in a machine involves numbers with only a finite number of digits, with the results that many calculations are performed with approximate representations of the actual numbers. In typical computer, only a relatively small subset of the real number system is used for the representation of all real numbers. This subset contains only rational numbers, both positive and negative, and stores a fractional part, called the mantisa, together with an exponential part, called the characteristic. Floating point systems are specified by four parameters, Fl(B,p,L,U) , and elements of these systems are specified by three parameters, (s,m,e): • s is the sign of a floatingpoint number, • m is its (unsigned) mantissa, and • e is its exponent. Certain values of these parameters are reserved for special values (i.e., to represent objects within the system that do not have interpretations as numbers). Otherwise, the number represented is
Rounding Errors in Solving Block Hessenberg Systems
, 1994
"... A rounding error analysis is presented for a divideandconquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a backward stable solution. The algorithm is shown to be stable for diagonally dominant matrices and for Mmatri ..."
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A rounding error analysis is presented for a divideandconquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a backward stable solution. The algorithm is shown to be stable for diagonally dominant matrices and for Mmatrices.
Perturbation simulations of rounding errors in the evaluation of Chebyshev series
"... Abstract: This paper presents some numerical simulations of rounding errors produced during evaluation of Chebyshev series. The simulations are based on perturbation theory and use recent software called Aquarels. They give more precise results than the theoretical bounds (the di erence is of some o ..."
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Abstract: This paper presents some numerical simulations of rounding errors produced during evaluation of Chebyshev series. The simulations are based on perturbation theory and use recent software called Aquarels. They give more precise results than the theoretical bounds (the di erence is of some
Regression Discontinuity Applications with Rounding Errors in the Running Variable
 Forthecoming, Journal of Applied Econometrics
, 2014
"... Many empirical applications of regression discontinuity (RD) models use a running variable that is rounded and hence is discrete, e.g., age in years, or birth weight in ounces. This paper shows that standard RD estimation using a rounded discrete running variable leads to inconsistent estimates of ..."
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regarding the distribution of rounding errors, which is easily obtained and often close to uniform. The proposed approach is applied to estimate the effect of Medicare on insurance coverage in the US, and to investigate the retirementconsumption puzzle in China, utilizing the Chinese mandatory retirement
Perturbation Analyses for the Cholesky Factorization with Backward Rounding Errors
, 1996
"... This paper gives perturbation analyses for the Cholesky factorization A = R T R of a real symmetric positive definite matrix A, with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations on finite precision floating point c ..."
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bound on the condition of the problem is derived. Key Words. Cholesky factorization, perturbation analysis, backward rounding error, condition estimation, pivoting AMS Subject Classifications: 15A23, 65F35 1.
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 537 (0 self)
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The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through
Results 1  10
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1,896