Time series

time series analysistime-seriestime-series analysistime series predictiontime-series datatime series econometricsTime-series regressionhistorical datatimetime sequence
A time series is a series of data points indexed (or listed or graphed) in time order.wikipedia
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Discrete time and continuous time

discrete timediscrete-timecontinuous-time
Thus it is a sequence of discrete-time data.
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.

Interrupted time series

interrupted time series designinterrupted time-seriesinterrupted time series analysis
Interrupted time series analysis is the analysis of interventions on a single time series.
Interrupted time series analysis, sometimes known as quasi-experimental time series analysis, is an approach for the analysis of a single time series of data known or conjectured to be affected by interventions (controlled external influences).

Statistics

statisticalstatistical analysisstatistician
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. In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting.
Inference can extend to forecasting, prediction and estimation of unobserved values either in or associated with the population being studied; it can include extrapolation and interpolation of time series or spatial data, and can also include data mining.

Line chart

lineline graphCentralograph
Time series are very frequently plotted via line charts.
A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.

Moving-average model

Moving average modelmoving averagemoving average process
The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving average model).
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series.

Regression analysis

regressionmultiple regressionregression model
While regression analysis is often employed in such a way as to test theories that the current values of one or more independent time series affect the current value of another time series, this type of analysis of time series is not called "time series analysis", which focuses on comparing values of a single time series or multiple dependent time series at different points in time.
In recent decades, new methods have been developed for robust regression, regression involving correlated responses such as time series and growth curves, regression in which the predictor (independent variable) or response variables are curves, images, graphs, or other complex data objects, regression methods accommodating various types of missing data, nonparametric regression, Bayesian methods for regression, regression in which the predictor variables are measured with error, regression with more predictor variables than observations, and causal inference with regression.

Stationary process

stationarynon-stationarystationarity
The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving average model).
Since stationarity is an assumption underlying many statistical procedures used in time series analysis, non-stationary data are often transformed to become stationary.

Forecasting

forecastforecastsprojection
In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting.
Both might refer to formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods.

Cross-sectional study

cross-sectionalcross-sectional studiescross-sectional analysis
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).
They differ from time series analysis, in which the behavior of one or more economic aggregates is traced through time.

Time domain

time-domaintimetime coordinates
Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods.
Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time.

Panel data

longitudinal datapanel(panel)
A time series is one type of panel data.
Time series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter).

Scaled correlation

In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation, thereby mitigating the need to operate in the frequency domain.
In statistics, scaled correlation is a form of a coefficient of correlation applicable to data that have a temporal component such as time series.

Seasonality

seasonal variationseasonalPeriodic variation
In time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly.

Linear trend estimation

trendTrend estimationtrends
When a series of measurements of a process are treated as, for example, a time series, trend estimation can be used to make and justify statements about tendencies in the data, by relating the measurements to the times at which they occurred.

Mathematical finance

financial mathematicsquantitative financequantitative trading
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. In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting.
Bachelier modeled the time series of changes in the logarithm of stock prices as a random walk in which the short-term changes had a finite variance.

Decomposition of time series

decomposingdecompositiondecompositional method
The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns.

Autocorrelation

autocorrelation functionserial correlationautocorrelated
The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis.
It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient.

Prediction

predictpredictionspredictive
Forecasting usually requires time series methods, while prediction is often performed on cross-sectional data.

Kalman filter

Kalman filteringunscented Kalman filterInformation Filter
See Kalman filter, Estimation theory, and Digital signal processing
Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics.

Cross-sectional data

cross-sectionalcross-sectioncross section
Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset).
Cross-sectional data differs from time series data, in which the same small-scale or aggregate entity is observed at various points in time.

Autoregressive–moving-average model

ARMAautoregressive moving average modelautoregressive moving average
Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models.
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA).

Vector autoregression

VARvector autoregressive modelstructural VAR estimation
Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression.
Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series.

Autoregressive integrated moving average

ARIMAAutoregressive integrated moving average modelAutoregressive integrated moving average (ARIMA)
Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models.
In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model.

Change detection

Change point detectionchange-point detection
One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.
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.

R (programming language)

RR programming languageCRAN
R and its libraries implement a wide variety of statistical and graphical techniques, including linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, and others.