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Time series
Sequence of observations of a variable measured at regular or irregular time intervals, used to analyze trends and temporal patterns. Time series are fundamental in finance, meteorology, and economics for modeling evolving phenomena.
Stationarity
Statistical property where the mean, variance, and autocorrelation of a time series remain constant over time. Stationarity is essential for applying many statistical models and ensuring the validity of forecasts.
Dickey-Fuller test
Statistical test checking for the presence of a unit root in a time series to determine its stationarity. The augmented Dickey-Fuller test (ADF) is commonly used to validate the stationarity hypothesis before modeling.
Exponential smoothing
Forecasting technique weighting past observations with exponentially decreasing weights to capture recent trends. This method is effective for series without strong seasonality and easily calculates short-term forecasts.
White noise
Stochastic process where observations are independent, identically distributed with zero mean and constant variance. White noise serves as a reference for evaluating model adequacy and represents pure unpredictability.
Differencing
Transformation subtracting each observation from the previous one to eliminate trend and achieve stationarity. Differencing is a crucial preliminary step before applying ARIMA models to non-stationary series.
Fourier transform
Mathematical tool decomposing a time series into elementary frequencies to analyze cyclical components. The FFT allows identification of hidden periodicities and harmonics in temporal data.
Volatility
Measure of the variation in prices or values in a time series, quantifying uncertainty and risk. Volatility is particularly studied in finance to assess market instability and calibrate GARCH models.
Change point
Moment when the statistical properties of a time series undergo a significant change. Change point detection allows for identifying structural breaks and adapting predictive models.
Partial autocorrelation function
Measure of correlation between an observation and its past values while controlling for the effect of intermediate lags. The PACF is essential for determining the order of autoregressive processes in ARIMA modeling.
Temporal interpolation
Technique estimating missing values in a time series using adjacent observations. Interpolation preserves temporal continuity and enables the application of analysis methods requiring complete data.
Power spectrum
Frequency representation of the variance of a time series indicating the energy at each frequency. The spectrum reveals dominant components and helps characterize underlying data cycles.
Residual
Difference between observed values and values predicted by a temporal model, measuring the fitting error. Residual analysis allows for model validation and identification of uncaptured patterns.