ARIMA Forecasting Tool (Simplified)
Define Pre-Trained ARIMA Model & Recent Data
Forecast Output
Forecasted Values Table
| Time Step (Relative to Last Obs.) | Forecasted Value |
|---|
Understanding ARIMA & Export
ARIMA (AutoRegressive Integrated Moving Average) Models
ARIMA models are a class of statistical models for analyzing and forecasting time series data. They aim to describe the autocorrelations in the data.
An ARIMA(p,d,q) model is defined by three orders:
- p (AR - AutoRegressive order): The number of lag observations included in the model. It indicates that the current value of the series depends on its own p-previous values. (φ coefficients)
- d (I - Integrated order): The number of times the raw observations are differenced to make the time series stationary. This tool assumes you have already differenced your data if d > 0 and are providing coefficients for the differenced series.
- q (MA - Moving Average order): The size of the moving average window. It indicates that the current value depends on q-previous error terms (residuals between actuals and forecasts). (θ coefficients)
The general form (for a non-seasonal ARIMA model, after differencing if d > 0) can be complex, but conceptually for Y't (the differenced series):
Y't = c + φ₁Y't-1 + ... + φpY't-p + εt + θ₁εt-1 + ... + θqεt-q
- Y't is the (differenced) series value at time t.
- c is a constant/intercept.
- φ are the AR coefficients.
- θ are the MA coefficients.
- εt is the white noise error term at time t.
Forecasting: Involves using the historical values and estimated error terms (for MA components) to predict future values one step at a time.
Note on this Tool: This is a highly simplified tool for applying a pre-defined ARIMA model. It does not perform model identification (choosing p,d,q), parameter estimation, or diagnostic checking, which are critical steps in a full time series analysis workflow and require specialized statistical software.