### Understanding Time Series Glossary

# Time Series Terms Explained

Time series data is a sequence of data points indexed in time order, typically collected at successive, equally-spaced points in time. This type of data is ubiquitous in our increasingly digital and interconnected world, appearing in diverse fields such as economics, finance, environmental science, healthcare, and technology. Time series analysis involves methods for extracting meaningful statistics and characteristics from this temporal data, with the goals of understanding past behavior and predicting future trends.

The significance of time series data and analysis has grown exponentially in recent years, driven by the surge in big data, advancements in computational power, and the development of sophisticated analytical techniques. As our world becomes increasingly data-driven, the ability to understand and analyze time series data has become an essential skill across many disciplines.

Real-world applications of time series analysis are vast. In finance, it's used for stock price prediction and risk management. Meteorologists use it for weather forecasting and climate change studies. In healthcare, time series analysis helps in monitoring patient vital signs and predicting disease outbreaks. Businesses leverage it for sales forecasting, inventory management, and customer behavior analysis. Even in fields like energy management and urban planning, time series data plays a crucial role in optimizing resource allocation and predicting future demands.

Below you'll find a list of 100 time series glossary terms with definitions.

**Additive Model:**A time series model where the components (trend, seasonality, and irregularity) are added together to make the actual time series.**Akaike Information Criterion (AIC):**A measure of the relative quality of statistical models for a given set of data, balancing goodness of fit with model simplicity.**ARCH (Autoregressive Conditional Heteroskedasticity):**A model used to characterize and model observed time series, particularly in financial contexts where volatility clustering is observed.**ARIMA (Autoregressive Integrated Moving Average):**A statistical analysis model that uses time series data to better understand the data set or predict future trends.**Augmented Dickey-Fuller Test:**A test used to determine if a unit root is present in an autoregressive model, indicating non-stationarity.**Autocorrelation:**The correlation of a signal with a delayed copy of itself as a function of delay, showing the similarity between observations as a function of the time lag between them.**Backtesting:**The process of testing a trading strategy or predictive model using historical data to see how accurately it would have predicted actual results.**Bandpass Filter:**A device or process that allows signals between two specific frequencies to pass but discriminates against signals at other frequencies.**Baxter-King Filter:**A type of band-pass filter used in macroeconomics to separate cyclical components of a time series from raw data.**Bayesian Information Criterion (BIC):**A criterion for model selection among a finite set of models, based on the likelihood function and penalizing model complexity.**Box-Jenkins Methodology:**A systematic method for identifying and estimating models that represent discrete time series data.**Census X-13 ARIMA-SEATS:**A seasonal adjustment software package produced, distributed, and maintained by the U.S. Census Bureau.**Change Point Detection:**The process of identifying points in time when the statistical properties of a time series change.**Cointegration:**A statistical property of time series variables where two or more series are non-stationary, but a linear combination of them is stationary.**Cointegration Vector:**A vector of coefficients that creates a stationary linear combination of non-stationary variables.**Coincident Indicator:**An economic indicator that changes at approximately the same time and in the same direction as the overall economy.**Cross-correlation:**A measure of similarity of two series as a function of the displacement of one relative to the other.**Cross-validation:**A model validation technique for assessing how the results of a statistical analysis will generalize to an independent data set.**Cyclical Pattern:**Regular fluctuations in a time series that do not have a fixed period, often related to economic or business cycles.**Decomposition:**The process of separating a time series into its constituent components, usually including trend, seasonal, cyclical, and irregular components.**Differencing:**A technique used to transform a non-stationary time series into a stationary one by computing the differences between consecutive observations.**Double Exponential Smoothing:**An extension of exponential smoothing that adds a trend component to the model, also known as Holt's linear trend method.**Drift:**A gradual change in the properties of a time series over time, often referring to a steady increase or decrease in the mean of the series.**Durbin-Watson Test:**A test statistic used to detect the presence of autocorrelation in the residuals from a regression analysis.**Dynamic Regression:**A regression model that includes lagged values of the dependent variable, independent variables, or both as predictors.**Dynamic Time Warping:**A technique for finding the optimal alignment between two time series, even if they are of different lengths.**Ensemble Methods:**Techniques that combine several base models to produce one optimal predictive model for time series forecasting.**Error Correction Model:**A dynamic model that estimates the speed at which a dependent variable returns to equilibrium after a change in an independent variable.**Exponential Smoothing:**A time series forecasting method that gives exponentially decreasing weights to older observations.**Exponential Trend:**A trend in a time series where the variable of interest increases or decreases by a constant percentage in each time period.**Forecast:**An estimate of a future value in a time series based on past and present data.**Fourier Transform:**A mathematical transform that decomposes a function of time into its constituent frequencies.**Frequency Domain:**A term used in signal processing and analysis to describe a domain for analysis of mathematical functions or signals with respect to frequency rather than time.**GARCH (Generalized Autoregressive Conditional Heteroskedasticity):**An extension of the ARCH model that allows for past conditional variances in the current conditional variance equation.**Granger Causality:**A statistical concept of causality based on prediction, where one time series is said to Granger-cause another if it can be shown that those time series values provide statistically significant information about future values of another time series.**Harmonic Regression:**A regression technique used when the predictor variables are trigonometric functions of a cyclical component.**Heteroscedasticity:**The circumstance in which the variability of a variable is unequal across the range of values of a second variable that predicts it.**Hodrick-Prescott Filter:**A mathematical tool used in macroeconomics to separate the cyclical component of a time series from raw data.**Holt-Winters Method:**An extension of exponential smoothing that directly models trend and seasonality in a time series.**Homoscedasticity:**The circumstance in which the variability of a variable is equal across the range of values of a second variable that predicts it.**Impulse Response Function:**A function that describes how a system reacts over time when it receives a brief input signal or impulse.**Irregular Component:**The residual variation in a time series after the trend, seasonal, and cyclical components have been removed.**Intervention Analysis:**A type of time series analysis used to assess the impact of a special event on the values in a time series.**Kalman Filter:**An algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone.**KPSS Test:**A statistical test of the null hypothesis that an observable time series is stationary around a deterministic trend.**Lag:**The number of time periods separating two observations in a time series.**Lagging Indicator:**An economic indicator that changes after the overall economy has changed.**Lead-lag Relationship:**A relationship between two time series where one series consistently changes before the other.**Leading Indicator:**An economic indicator that changes before the overall economy changes.**Level Shift:**A sudden, persistent change in the level of a time series.**Ljung-Box Test:**A statistical test of whether any of a group of autocorrelations of a time series are different from zero.**Logistic Trend:**A trend model where growth is slowest at the start and end of a time period, with the maximum growth occurring in the middle.**Long Memory Process:**A process in which observations in the distant past continue to have a noticeable effect on current observations.**Longitudinal Data:**Data that tracks the same sample at different points in time.**Mean Reversion:**The theory suggesting that asset prices and other market indicators tend to move towards the average or mean over time.**Momentum:**The rate of acceleration of a security's price or volume, often used in technical analysis of stocks.**Moving Average:**A calculation used to analyze data points by creating a series of averages of different subsets of the full data set.**Multiplicative Model:**A time series model where the components (trend, seasonality, and irregularity) are multiplied together to make the actual time series.**Multivariate Time Series:**A time series that consists of more than one variable changing over time.**Non-stationarity:**The quality of a time series whose statistical properties change over time.**Nowcasting:**The prediction of the present, the very near future, and the very recent past in economics.**Outlier:**An observation point that is distant from other observations in a time series.**Panel Data:**Data that contains observations of multiple phenomena obtained over multiple time periods for the same firms or individuals.**Partial Autocorrelation:**The autocorrelation of a time series with its own lagged values, controlling for the values of the time series at all shorter lags.**Periodogram:**A graph showing the magnitude of different frequency components in a time series.**Periodic Regression:**A regression model that incorporates periodic (usually sinusoidal) components to capture cyclical patterns in the data.**Prediction Interval:**An estimate of an interval in which a future observation will fall with a certain probability.**Prophet:**An open-source forecasting tool developed by Facebook, designed to handle time series with strong seasonal effects and multiple seasons of historical data.**Random Walk:**A time series model where each observation is equal to the previous observation plus a random shock.**Regime Switching:**A model that allows for abrupt changes in the behavior of a time series, often used to model economic or financial time series that exhibit sudden changes in their dynamic properties.**Residual Analysis:**The examination of the differences between observed values and values predicted by a model to assess model adequacy.**Rolling Forecast:**A forecasting method where the forecast is updated as new data becomes available, always forecasting the same number of periods into the future.**SARIMA (Seasonal ARIMA):**An extension of ARIMA that supports univariate time series data with a seasonal component.**Seasonal Adjustment:**The process of estimating and removing seasonal effects from a time series to reveal non-seasonal features.**Seasonality:**Regular and predictable patterns in a time series that repeat over fixed intervals of time.**Short Memory Process:**A process in which the effect of an observation on future observations decreases rapidly as the time lag between them increases.**Smoothing Parameter:**A value in smoothing algorithms that controls the degree of smoothing applied to the data.**Spectral Analysis:**The process of determining the frequency content of a signal.**State Space Model:**A mathematical model that represents a physical system as a set of input, output, and state variables related by first-order differential equations.**Stationarity:**A property of a time series where statistical properties such as mean, variance, and autocorrelation are constant over time.**Structural Break:**A sudden change in the fundamental structure of a time series, often due to external factors.**STL Decomposition:**A method for decomposing a time series into trend, seasonal, and remainder components (Seasonal and Trend decomposition using Loess).**Temporal Aggregation:**The process of combining data from shorter time intervals into longer intervals (e.g., daily to monthly).**Temporal Causal Modeling:**A method for automatically detecting causal relationships in time series data.**Temporal Disaggregation:**The process of estimating higher frequency data from lower frequency data.**Time Domain:**A term used in signal processing and analysis to describe the analysis of mathematical functions or signals with respect to time.**Time Series:**A sequence of data points measured at successive points in time, typically at uniform intervals.**Time Series Cross-section Data:**Data that combines time series data and cross-sectional data, often used in econometrics.**Time Series Database:**A specialized database system optimized for handling time-stamped or time series data. It is designed to efficiently store, retrieve, and process large volumes of time-indexed data points.**Transfer Function Model:**A model that relates an input time series to an output time series, often used in control theory and signal processing.**Trend:**The long-term movement or change in the mean level of a time series.**Trend Extrapolation:**A method of forecasting that extends past trends into the future.**Trend Stationarity:**A type of stationarity where the time series fluctuates around a deterministic trend.**Triple Exponential Smoothing:**An extension of exponential smoothing that adds both trend and seasonal components to the model, also known as the Holt-Winters method.**Unit Root:**A feature of some stochastic processes that can cause problems in statistical inference involving time series models.**Vector Autoregression (VAR):**A statistical model used to capture the linear interdependencies among multiple time series.**Volatility:**A statistical measure of the dispersion of returns for a given security or market index.**Volatility Clustering:**The tendency of large changes in asset prices to cluster together, resulting in periods of high or low volatility.**Wavelet Analysis:**A method of analyzing localized variations of power within a time series.**White Noise:**A random signal with a constant power spectral density, often used as a model for random noise in signal processing.