Missing Observations In Time Series Research Articles

Forecasting missing data in time series with the application of hybrid models – theoretical and empirical approach

The main goal of the article is to present the possibilities of forecasting missing observations in time series for hourly data with the application of hybrid models. Hybrid time series models and regression models with complex seasonal fluctuations were used in the study. Complex fluctuations for hourly data can be either a sum or a product of fluctuations of annual, weekly and daily cycles, while fluctuations the length of a cycle expressed by an even number (12-month and 24-hour ones) can be described using regular hierarchical models. The theoretical considerations were illustrated by an empirical analysis of the demand for electricity in hourly periods in a selected agglomeration. The statistical data covered three consecutive years of the first decade of the 2000s. The data were provided by an electricity distribution company and included in the Data Bank of the Department of Applied Mathematics in Economics of the West Pomeranian University of Technology in Szczecin. It was assumed that non-systematic gaps occur with regard to all types of seasonal fluctuations. The obtained results indicate the usefulness of hybrid models in forecasting economic phenomena subject to very frequent observations.

Discriminating treed and non-treed wetlands in boreal ecosystems using time series Sentinel-1 data

Wetlands are recognized for their importance to a range of ecosystem goods and services; however, detailed information on wetland presence, type, extent, and persistence is challenging to attain over large areas and/or long time periods due to the spatial complexity and temporal dynamism of wetlands. In this study we explored the potential for within-year time series of C-band Synthetic Aperture Radar (SAR) observations from the free and open Sentinel-1 data archive to improve discrimination of treed and non-treed wetlands and non-wetlands in a boreal forest environment. Through a set of 3843 classification experiments for the year 2017, we tested the influence of three factors on classification accuracy: (i) input features (two backscatter coefficients in VV and VH polarization (σVV and σVH) and four quantitative measures derived from the Stokes vector); (ii) the temporal form of features (i.e. using all within-year observations versus generalized measures such as monthly/seasonal means or annualized statistics); and (iii) missing observations in Sentinel-1 time series due to varying observation availability across space. Among the tested features, we found the greatest utility in σVV and σVH. Directly using all within-year observations yielded higher accuracy than using generalized temporal forms. Moreover, the temporal form of the features had a greater impact on classification accuracy than the features themselves. The highest overall accuracy (0.860 ± 0.002) was achieved using σVV and σVH from all within-year observations. The majority of class confusion occurred between treed wetlands and non-wetlands. We found no significant reduction in the overall accuracy by simulated missing observations in time series when using all within-year observations. With the increasing availability of free and open data from the Sentinel-1 archive, new opportunities are emerging to readily integrate within-year time series into large-area land cover mapping, particularly if analysis-ready SAR data products further reduce preprocessing requirements for end users.

AN EVOLUTIONARY APPROACH FOR IMPUTING MISSING DATA IN TIME SERIES

This paper presents a proposal based on an evolutionary algorithm for imputing missing observations in time series. A genetic algorithm based on the minimization of an error function derived from their autocorrelation function, mean, and variance is presented.All methodological aspects of the genetic structure are presented. An extended description of the design of the fitness function is provided. Four application examples are provided and solved by using the proposed method.

A note on linear combination of predictors

An important concern in statistics is the linear combination of predictors of a random variable that are based on several sources of information. In the time-series context the technique is used, for example, to forecast or estimate missing observations. At the practical level, it is well known in the combining forecasts literature that combining is a pragmatic solution to the failure to synthesize all the information into an optimal forecast. In this paper we caution against using this procedure arbitrarily, in particular with weighted averages, to obtain an overall linear predictor of the random quantity. We illustrate the results with examples about estimating the missing observations in time 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

Missing observations in time series

A method based on forecasting techniques is proposed to estimate missing observations in time series. Using mean squares, this method is compared to the minimum mean square estimate.