In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.
A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements.
Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series.
Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart.
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Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, w
In statistical analysis, change detection or change point detection tries to identify times when the probability distribution of a stochastic process or time series changes. In general the problem concerns both detecting whether or not a change has occurred, or whether several changes might have occurred, and identifying the times of any such changes. Specific applications, like step detection and edge detection, may be concerned with changes in the mean, variance, correlation, or spectral density of the process.
In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series. A time series is integrated of order d if is a stationary process, where is the lag operator and is the first difference, i.e. In other words, a process is integrated to order d if taking repeated differences d times yields a stationary process. In particular, if a series is integrated of order 0, then is stationary.
Maximum entropy spectral estimation is a method of spectral density estimation. The goal is to improve the spectral quality based on the principle of maximum entropy. The method is based on choosing the spectrum which corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values. This assumption, which corresponds to the concept of maximum entropy as used in both statistical mechanics and information theory, is maximally non-committal with regard to the unknown values of the autocorrelation function of the time series.
Covers parametric signal models and practical Matlab applications for Markov chains and AutoRegressive processes.
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.
In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.
Digital image processing is the use of a digital computer to process s through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over . It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems.
We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the 1-loop corrections from charged particles to the photon energy-momentum tensor - the sel
2022
This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which i
Accurate traffic density estimations is essential for numerous purposes like the developing successful transit policies or to forecast future traffic conditions for navigation. Current developments in