"In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order."
The study of how economic data changes over time and the methods used to analyze this data.
time series: A sequence of observations over time.
stationarity: A property of a time series where the mean, variance and autocorrelation structure do not vary over time.
autocorrelation: The correlation between a time series and a delayed version of itself.
partial autocorrelation: The partial correlation between a time series and a lagged version of itself, controlling for the contributions of all other lags.
seasonality: The presence of patterns that repeat at fixed intervals of time.
trend: The long-term direction of a time series.
white noise: A sequence of uncorrelated random variables.
ARIMA: A statistical model for time series that incorporates autoregressive, differencing and moving average components.
seasonal ARIMA: An extension of ARIMA that includes seasonal components.
exponential smoothing: A family of models that uses weighted averages of past observations to forecast the next observation.
Holt-Winters method: A popular exponential smoothing method that includes components for level, trend and seasonality.
SARIMA: An extension of seasonal ARIMA that incorporates seasonal differencing and seasonal autoregressive and moving average components.
spectral analysis: A method for decomposing a time series into its underlying frequencies.
Fourier Transform: A mathematical transformation that converts a time series from the time domain to the frequency domain.
wavelet analysis: A method for time-frequency analysis that uses wavelets to decompose a signal into its frequency components.
cointegration: A property of two or more non-stationary time series that allows them to be expressed as a stationary linear combination.
"Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average."
"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 analysis is distinct from cross-sectional studies, in which there is no natural ordering of the observations."
"Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations."
"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."
"Values for a given period will be expressed as deriving in some way from past values, rather than from future values."
"Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data."
"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."
"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."
"The use of a model to predict future values based on previously observed values."
"time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility)."
"Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics."
"Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies."
"Time series are used in...econometrics, mathematical finance..."
"Time series are used...in any domain of applied science and engineering which involves temporal measurements."