Time Series
Nicholas Stergiou in Nonlinear Analysis for Human Movement Variability, 2018
A basic assumption of most time series analysis is that all time series inherently possess dependence between adjacent observations. In fact, this dependence is of interest because it reveals information about the source producing the behavior. In this way, time series analysis is essential for understanding human movement variability, because time series analysis reveals how the system evolves over multiple movement repetitions. To generate a time series, repeated measurements of some property of the system are made as the system varies in time. This may imply that time series data are essentially a list of numbers, but any list of numbers cannot be considered a time series. This chapter details what constitutes time series data and describes important specific considerations that should be kept in mind when working with time series data.
Longitudinal data
Pat Dugard, John Todman, Harry Staines in Approaching Multivariate Analysis, 2010
A well developed set of methods known as time series analysis may be useful if you have a long series of data, perhaps from a monitoring program. These methods were developed for use in economics and are most effective when you have hundreds of observations. They are especially useful for dealing with seasonality. This term was first used to denote the kind of changes in economic data associated with the seasons: unemployment usually rises in winter because some jobs are only available in summer (especially in tourism and construction). Many measures show this kind of seasonal effect: ice cream sales rise in summer and fall in winter; consumer spending goes up before Christmas. Often interest focuses on whether there is some underlying trend, up or down, that seasonal variation obscures.
The role and functional components of statistical alerting methods for biosurveillance
David L. Blazes, Sheri H. Lewis in Disease Surveillance, 2016
Assuming that the filtering and aggregation processes of the previous section have produced time series that plausibly contain signals of interest, univariate and multivariate statistical hypothesis tests may still produce excessive false alarms for many reasons. Researchers have applied preconditioning strategies to reduce excess alerting. Some hypothesis tests assume input time series with Gaussian distributions, and developers have applied square root or other normalizing transformations to obtain expected background distributions (Hafen et al. 2009). The differencing stratagem of Martinez-Beneito reported above may be helpful for detrending. Some data quality issues may be treated analytically. One common problem is that of late reporting of data, so that the most recent, hence the most critical, time series entries are underestimated. Noufaily et al. applied a proportional hazards model that revealed temporal influences on relatively short delays (Noufaily et al. 2015). Another common problem is that a monitored time series may comprise data streams from multiple care facilities and may display discontinuities resulting in alerting bias when the number of data contributors changes. Burkom et al. obtained an improved alert rate by applying a provider-based regression method before using a detection algorithm (Burkom et al. 2004), though such an approach requires knowledge of the number of currently participating data sources. Levin-Rector et al. also applied trend removal as one of their refinements to the historical limits method (Levin-Rector et al. 2015).
Traffic violation analysis using time series, clustering and panel zero-truncated one-inflated mixed model
Published in International Journal of Injury Control and Safety Promotion, 2022
Zahra Rezaei Ghahroodi, Samaneh Eftekhari Mahabadi, Sara Bourbour, Helia Safarkhanloo, Shokoufa Zeynali
The monthly number of violations aggregated over all vehicles, to be analyzed both as a univariate time series and also assuming location wise data as a spatial time series. Time series constitute a series of data points collected or sampled at fixed intervals. Monthly violation counts for a certain period of time also constitute a time series data. The time series data of traffic violations is very important to study as it can reveal the future trend of violations such as the time periods that it tends to increase or decrease. Also, spatial analysis allows for future violation predictions in different locations so that preventive measures can be taken. Generally, forecasting the future trend of traffic violation, can help control traffic violation and identify the black spot of traffic violation (Button, 2014; Jiaxing et al., 2010).
Threshold single multiplicative neuron artificial neural networks for non-linear time series forecasting
Published in Journal of Applied Statistics, 2021
Asiye Nur Yildirim, Eren Bas, Erol Egrioglu
Artificial neural networks (ANNs), one of the commonly used artificial intelligence methods; are based on mathematical modelling of the learning process inspired by the human brain. ANNs are the structures formed by artificial neural neurons coming together. In general, ANNs have three layers: the input layer, hidden layer and the output layer. All layers have a significant effect on the performance of the network and especially the hidden layer has special importance since its number cannot be determined precisely. Based on this problem, Yadav et al. [34] proposed the single multiplicative neuron model artificial neural networks (SMNM-ANN). In the studies about SMNM-ANN, the model obtained from the network is only a single model and this situation can be accepted when time series is stationary. But a time series is not always stationary. It is not possible to encounter a stationary time series in real life. The time series include some components such as trend or/and seasonality. It is not realistic to explain and analyse this type of time series with a single model. Besides, using a single model assumption may have misleading results.
Dominant factors of the phosphorus regulatory network differ under various dietary phosphate loads in healthy individuals
Published in Renal Failure, 2021
Guoxin Ye, Jiaying Zhang, Zhaori Bi, Weichen Zhang, Minmin Zhang, Qian Zhang, Mengjing Wang, Jing Chen
Granger causality is a statistical test used to determine whether one time series can be used to predict another. The time series X is said to Granger-cause Y if the T-tests or F-tests on the lag value of X and Y are statistically significant, which indicates that the X value provides information for the future value of Y. Panel Granger causality [11,12], which emphasizes the causality among multi-individual data involving measure variables, is an extension of Granger causality analysis [13]. We prefer it for three keys. (1) It is suitable for time-series data. Bayesian-based methods cannot conveniently analyze time-series data because they must satisfy the assumptions of causal sufficiency, faithfulness, and causal Markov conditions must be satisfied [14]. (2) It allows us to analyze panel data. The format of our experimental data is naturally a panel format that contains multiple subjects who consumed varying amounts of dietary phosphorus in the designed time slots. (3) It supports the quantification of causality [15]. This feature enables us to present the potential regulatory relationships between variables via a weighted adjacency matrix.
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