ARIMA Model

An ARIMA (autoregressive integrated moving average) model is a time series model that forecasts a variable from its own past values and past forecast errors after differencing to remove trends.

ARIMA(자기회귀누적이동평균) 모형은 추세를 제거하기 위해 차분한 뒤 변수의 과거 값과 과거 예측오차로 미래 값을 예측하는 시계열 모형이다.

How do I forecast a single time series from its own past values?

하나의 시계열을 그 자체의 과거 값으로 어떻게 예측하나요?

An ARIMA(p, d, q) model combines autoregressive terms, differencing to achieve stationarity and moving-average error terms to model a univariate series. It fits regularly spaced series with autocorrelation, and seasonal ARIMA extends it to repeating seasonal patterns.

When to use ARIMA Model

• Forecasting a single regularly spaced series such as monthly sales or daily demand
• Series with trend that becomes stationary after differencing
• Seasonal series, using the seasonal ARIMA extension

When to use something else

• Several series influence each other: use a vector autoregression (VAR) model
• You want to estimate the effect of a specific intervention: use interrupted time series analysis

Assumptions and requirements

• Stationarity after differencing
• Regularly spaced observations
• Residuals that are uncorrelated white noise
• Stable model structure over the sample

What the analysis reports

• Model order (p, d, q) and coefficients
• AIC/BIC
• ACF and PACF plots
• Ljung–Box test of residuals
• Forecasts with prediction intervals

How to report it

An ARIMA([p], [d], [q]) model was selected by AIC, and the Ljung–Box test indicated no remaining residual autocorrelation, Q([df]) = [value], p = [value].

Related methods

• Exponential Smoothing
• SARIMA
• Vector Autoregression (VAR)

Run ARIMA Model on Quorant