Time series interpolation via global optimization of moments fitting

Abstract

Most time series forecasting methods assume the series has no missing values. When missing values exist, interpolation methods, while filling in the blanks, may substantially modify the statistical pattern of the data, since critical features such as moments and autocorrelations are not necessarily preserved.In this paper we propose to interpolate missing data in time series by solving a smooth nonconvex optimization problem which aims to preserve moments and autocorrelations. Since the problem may be multimodal, Variable Neighborhood Search is used to trade off quality of the interpolation (in terms of preservation of the statistical pattern) and computing times.Our approach is compared with standard interpolation methods and illustrated on both simulated and real data.

Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment

“…Carrizosa et al [13] have proposed a method based on the preservation of moments and autocorrelation between observations and predictions: this method requires a smooth non-convex optimization problem to be solved. Authors have compared this method to other existing ones.…”

“…These methods are statistical parametric models [13,33] based on a Markovian process. Schlegel et al [16] explained the basic idea of those methods: a stochastic signal X(t) can be extracted from white noise (ε(t), with an average equal to 0) through smoothing processes.…”

“…All of those models need to be defined by a user with expertise in the concerned topic. Logistic regressions can be used to predict the missing values of a binary variable [13].…”

“…Interpolated data by this method are discontinuous [16]. This method often yields the worst results [13,16], and should not be confused with the k-nearest-neighbors methods.…”

“…The nearest neighbor or proximal interpolation, introduced by [14], is the easiest method [13,15]: the value of the closest known (existing) neighbor is assigned to the missing value (such as Equation (1)). Interpolated data by this method are discontinuous [16].…”