Interpolation Of Time Series Research Articles

An improved scheme for time-dependent boundary conditions in atmospheric general circulation models

Atmospheric general circulation models (AGCMs) are often “coupled” with time varying observations of boundary conditions or some other aspect of the climate system. A typical example is the Atmospheric Model Intercomparison Project (AMIP) experimental protocol, which required the specification of sea surface temperature and sea-ice extent from observed monthly means. AGCMs ordinarily incorporate the prescribed conditions by evaluating an interpolating function at each time step. Typical schemes, such as that used in the second generation GCM (GCM2) of the Canadian Centre for Climate Modelling and Analysis (CCC), do not preserve monthly means and have a smoothing effect on the interpolated time series which tends to reduce the amplitude of annual cycle and interannual variability of sea surface temperature (SST). By solving a large set of linear equations, a simple linear time-interpolation scheme that preserves the observed monthly mean SST and hence its variability can be obtained. The new scheme improves upon that used previously in CCC GCM2 by eliminating the substantial loss of interannual variability (up to 20%) and the small attenuation of the annual cycle (less than 4% on average) incurred with the old scheme. The improved linear interpolation scheme is easily adapted to other quantities.

An objective interpolation method for spatiotemporal distribution of marine plankton

A Lagrangian-Eulerian interpolation method for the objective analysis of marine plankton data was developed. Based on the Gauss-Markov theorem, this method takes into account the advection effect on the distribution of passive marine plankton, and yields an estimate and confidence at every interpolating point (X, y, z, t ) which is optimal in the least squares error This method was demonstrated in the analysis of plankton data collected in the California Current region during June 1993. The interpolated time series of spatial distributions of plankton revealed areas where plankton features were more permanent due to weak advection and areas where plankton features were more timedependent due to the existence of strong currents. Results show north-south transports and exchanges of plankton populations produced by the complex flow system in the California Current region This Lagrangian-Eulerian interpolation produces synoptic spat~al distributions of plankton at given times and their error fields, and can be used as a basic analytical tool to understand advection effects in plankton distributions.

Multirate processing of time series exhibiting higher order cyclostationarity

The paper investigates the effects of multirate systems on the higher order wide-sense cyclostationarity (WSCS) properties of discrete-time series. To this end, definitions and properties of the cyclic higher order statistics, which were introduced for continuous-time series in the fraction-of-time probability framework, are first extended to discrete-time series. Then, starting from the consideration of the basic multirate building blocks, viz., M-fold decimators and L-fold interpolators, results for typical interconnections are derived. The problem of eliminating the images in the cyclic higher order spectra of an interpolated time series is addressed. Moreover, the problem of avoiding aliasing (in both cycle and spectral frequency domains) in the cyclic higher order spectra of a decimated time series is considered. Finally, a sufficient condition to avoid both aliasing and imaging effects in the cyclic higher order spectra of a time series decimated by a fractional factor is derived.

Similarities and differences between one-sided and two-sided linear prediction

Provides a comparison between one-sided linear prediction (OSP) and two-sided linear prediction (TSP) with respect to prediction error, relationships to AR modeling and to two-sided AR modeling, and the application to time series interpolation, linear-phase filter design, and spectral estimation. Although some of these results have appeared previously in scattered references, the authors present a unified framework for deriving all of these results, as well as new, additional results. New contributions of the paper include: (i) proof that TSP produces smaller, nonwhite residuals than OSP, extending previous results; (ii) specification of the frequency-domain error criterion minimized by TSP, and comparison with the analogous OSP criterion; (iii) demonstration that TSP and two-sided AR modeling are different problems, unlike OSP; (iv) interpretation of performance of TSP interference-rejection filters. >

Periodic properties of interpolated time series

Although linearly interpolated series are often used in economics, little has been done to examine the effects of interpolation on time-series properties and on statistical inference. We show that linear interpolation of a trend stationary series superimposes a ‘periodic’ structure on the moments of the series. Using conventional time-series methods to make inference about the interpolated series may therefore be invalid. Also, the interpolated series may exhibit more shock persistence than the original trend stationary series.

Optimization methods in time series interpolation

The problem of estimating missing observations in time series with a known model is studied. An approach based directly on the minimization of a suitable criterion holding the residuals as free variables is discussed. The optimization problem can be solved by methods of nonlinear optimization, and utilizing its special structure. The method may also be utilized under various constraints set on the variables. Explicit algorithms based on the method are given and demonstrated to produce accurate results

Parametric modelling of stochastic wave effects on offshore platforms

The time histories of stochastic ocean wave-related processes are simulated by means of computationally efficient parametric models. The parametric models utilized here include the autoregressive and moving averages (ARMA) algorithms for the simulation of wave height fluctuations, discrete convolution models for linear transformations of given time histories, discrete differentiation models for obtaining derivatives, discrete interpolation models for interpolating time series at intermediate time increments and their hybrid combination. The recursive simulation of fluctuation in wave height is accomplished by ARMA algorithm based on a two-stage model-fitting approach that provides simulated processes consistent with the prescribed spectral descriptions. The sensitivity of the model order to the wave spectral description is presented. The parametric simulation schemes of linearly related processes, e.g. wave load effects, are conducted by means of discrete convolution models utilizing finite and infinite wave forms. A parametric model representing differentiation in the context of a linear transformation is employed to simulate derivatives of response processes. A hybrid combination of discrete convolution and differentiation models provides an efficient simulation scheme for evaluating wave loads at the instantaneous position of compliant platforms. Interpolation of time histories is carried out utilizing double subscripted digital filters. The selection of appropriate models and their orders is discussed in the context of their stability, accuracy and robustness. Detailed examples are given to illustrate the practical features of these models.

Robust Hypothesis Testing and Robust Time Series Interpolation And Regression

Abstract. Recent results on minimax robust time series interpolation and regression coefficient estimation are generalized and extended through a relationship with robust hypothesis testing. The spectral uncertainty classes in the time series problems are assumed to be convex and to satisfy an integral constraint such as on the variance of the process. It is shown that robust solutions in such cases can always be obtained from the least‐favourable probability density functions for corresponding hypothesis testing problems. A specific class, the bounded spectral densities from the band model, is considered to illustrate the results.

Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand

SUMMARY The least squares principle is applied to the problem of estimating missing points in a time series represented by a Box-Jenkins seasonal model. The procedure developed is used to estimate the effect of one-day national holidays on hourly electricity demand. This is done by interpolating over the holiday period using unaffected demand observations from both before and after this period. The ratio of the actual demand to the estimated normal demand, recorded for the same holiday period over successive years, may then be used to forecast the effect on demand of future holidays.

The Interpolation of Time Series by Related Series

The Interpolation of Time Series by Related Series

The Interpolation of Time Series by Related Series

Abstract The construction of most comprehensive economic time series involves the estimation of some components for some dates by interpolation between values (“benchmarks”) for earlier and later dates. This is often done by using a related series known for all relevant dates. In practice, the bulk of such interpolation uses only a single related series, its values for only three dates—the interpolation date, one prior date, and one later date—and the values of the given series for only the prior and later dates. For this special case, some current methods are defective on formal grounds and all may frequently yield less accurate estimates than straight-line or other mathematical interpolation. Converting the problem into a simple bivariate regression problem suggests a generalization of current methods that takes account of the correlation between the movements of the given series and the related series.

The Interpolation of Time Series by Related Series

Abstract The construction of most comprehensive economic time series involves the estimation of some components for some dates by interpolation between values (“benchmarks”) for earlier and later dates. This is often done by using a related series known for all relevant dates. In practice, the bulk of such interpolation uses only a single related series, its values for only three dates—the interpolation date, one prior date, and one later date—and the values of the given series for only the prior and later dates. For this special case, some current methods are defective on formal grounds and all may frequently yield less accurate estimates than straight-line or other mathematical interpolation. Converting the problem into a simple bivariate regression problem suggests a generalization of current methods that takes account of the correlation between the movements of the given series and the related series.