What is ARIMA, and what does the "I" in ARIMA stand for?
What is ARIMA, and what does the "I" in ARIMA stand for?
ARIMA stands for AutoRegressive Integrated Moving Average, which is a popular statistical model used for time series forecasting. ARIMA combines three key components:
AR (AutoRegressive): This part of the model uses the relationship between an observation and a number of lagged (previous) observations. It shows how current values in the series depend on its past values.
MA (Moving Average): This part incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations. It helps to smooth out noise and capture the patterns in the data.
I (Integrated): The "I" in ARIMA stands for Integrated, which refers to the process of differencing the time series data to make it stationary. Stationarity means that the statistical properties of the series (like mean, variance, and autocorrelation) are constant over time, which is often required for time series modeling. Integration involves subtracting current observations from previous ones to remove trends or make the data suitable for modeling.
ARIMA(p, d, q):
p: The number of lag observations used in the model (auto-regressive part).
d: The number of times the data have been differenced to achieve stationarity (integrated part).
q: The size of the moving average window (moving average part).
Thus, ARIMA is a flexible model used for capturing a variety of time series patterns, especially when data exhibit trends and require differencing to become stationary.
Comentários