A statistical way to describe a surface in space is by specifying the expected value and variance at each point, and their mutual covariances. The surface is assumed to consist of a trend function and a residual function. The covariances between those points are expressed in a covariance function, based on the residual function. An application of the covariance function is Kriging, an interpola...

We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover — via theoretical arguments, conjectures, and numerical simulations — how spatial covariances scale with system size, their relations to local thermodynamic quantities, and the randomizing effects of heat baths. Among our findings are t...

It is well known that least-squares (LS) method gives biased parameter estimates when the input and output measurements are corrupted by noise. One possible approach for solving this bias problem is the bias-compensation based method such as the bias-compensated least-squares (BCLS) method. In this paper, a new bias-compnesation based method is proposed for identification of noisy input-output ...

in searching a market-neutral arbitrage strategy in forex market, we took a portfolio of three major currency pairs, eur-usd, usd-jpy, and eur-jpy. there are eight approaches, different cases of short and long positions; for example buying 1st and selling two others, etc. historical daily fx rates were gathered since january 1990 until february 2011. monthly covariances between daily growth rat...

For a zero-mean Gaussian process, the covariances of zero crossings can be expressed as the sum of quadrivariate normal orthant probabilities. In this paper, we demonstrate the evaluation of zero crossing covariances using one-dimensional integrals. Furthermore, we provide asymptotics of zero crossing covariances for large time lags and derive bounds and approximations. Based on these results, ...

We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover — via theoretical arguments, conjectures, and numerical simulations — how spatial covariances scale with system size, their relations to local thermodynamic quantities, and the randomizing effects of heat baths. Among our findings are t...