Trend, seasonality, stationarity, autocorrelation, ARIMA, exponential smoothing, forecasting metrics and cross-validation for time series.
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- What is a time series?
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A sequence of observations measured at successive points in time, typically at regular intervals.- Define trend in a time series.
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The long-term general direction or movement of the data, rising, falling, or staying relatively flat over time.- What is seasonality?
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A repeating pattern that occurs at fixed, known intervals within the time series, such as monthly or annual cycles.- What does it mean for a time series to be stationary?
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The statistical properties (mean, variance, autocorrelation) do not change over time.- What is differencing?
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Taking the difference between consecutive observations to remove trends and make a time series stationary.- Define autocorrelation.
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The correlation between observations of a time series at different lags, measuring how much past values relate to current values.- What does an ACF plot display?
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Autocorrelation values at different lags, helping identify patterns and dependence in the time series.- What does a PACF plot show?
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The partial autocorrelation at each lag, removing the effect of intermediate lags, useful for identifying AR order.- What is an autoregressive (AR) process?
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A process where current values depend linearly on past values, denoted AR(p) where p is the number of past values used.- What is a moving average (MA) process?
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A process where current values depend on past forecast errors, denoted MA(q) where q is the number of past errors.- What does ARIMA stand for?
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AutoRegressive Integrated Moving Average, a model combining AR, differencing (I), and MA components.- In ARIMA(p,d,q), what do p, d, and q represent?
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p is the AR order, d is the differencing order (to achieve stationarity), and q is the MA order.- What is white noise?
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A sequence of independent random variables with constant mean and variance, with no autocorrelation.- What is a lag?
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The number of time steps back from the current observation, used to measure correlation with past values.- Define the autocorrelation function (ACF).
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A function that measures the correlation between observations at different lags, ranging from -1 to 1.
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