Autoregressive integrated moving average (ARIMA)
Autoregressive integrated moving average (ARIMA) is a statistical model that is used to forecast future values of a time series. It is a generalization of the autoregressive moving average (ARMA) model, which only considers the autocorrelations between the current value and the past values of the time series. ARIMA also considers the moving average of the residuals of the ARMA model, which helps to improve the accuracy of the forecasts.
ARIMA models the time series as a combination of three components:
Autoregression (AR): The AR component models the dependence between the current value and the past values of the time series.
Moving average (MA): The MA component models the dependence between the current value and the errors of the previous predictions.
Integration (I): The I component models the non-stationarity of the time series by differencing the data.
The ARIMA model is specified by three integers: p, d, and q.
p: The number of lags in the AR component.
d: The number of times the data is differenced to make it stationary.
q: The number of lags in the MA component.
ARIMA models are commonly used to forecast financial data, such as stock prices and exchange rates. They are also used to forecast other types of time series data, such as customer demand, sales, and inventory levels.
The ARIMA model can be used to forecast the stock price for a specific date, or it can be used to forecast the stock price over a period of time. The forecast can be used to make investment decisions, such as whether to buy or sell the stock.
ARIMA models are a powerful tool for forecasting time series data. They are relatively easy to understand and implement, and they can be used to forecast a variety of time series data.