AR(1) — predição
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The AR(1) predictor calculates the future value of a time series based on the current value and the correlation coefficient. The AR(1) formula is simple and effective for forecasting future values in time series that exhibit trend patterns.
This calculator uses the AR(1) formula: y_{t+1} = c + φ·y_t, where c is the trend constant and φ is the correlation coefficient. The future value y_{t+1} is calculated by multiplying the current value (y_t) by the correlation coefficient (φ) and adding the trend constant (c).
The AR(1) predictor is useful in various applications, including demand forecasting, temperature forecasting, and other variables that exhibit trend patterns. However, note that the accuracy of the forecast depends on the quality of the data and the correct choice of the correlation coefficient.
Be careful when choosing the value of the correlation coefficient (φ) and the trend constant (c), as these values directly affect the accuracy of the forecast. Additionally, it is recommended to use a sufficient period of data to ensure the accuracy of the forecast.
Frequently asked questions
What is a correlation coefficient (φ)?
The correlation coefficient (φ) is a value between -1 and 1 that indicates the strength of the relationship between the current value and the future value. A value of 1 indicates a perfect correlation, while a value of -1 indicates an inverse correlation.
How do I choose the value of the trend constant (c)?
The trend constant (c) is a value that represents the overall trend of the time series. The ideal value for c depends on the specific context and can be found by exploring the data or using regression models.
Why does the accuracy of the forecast depend on the quality of the data?
The accuracy of the forecast depends on the quality of the data because the AR(1) formula is sensitive to errors or distortions in the data. Therefore, it is essential to ensure that the data is accurate and representative of the time series.
What is the period of data required for accurate forecasting?
The period of data required for accurate forecasting depends on the specific context and the quality of the data. However, it is generally recommended to use a sufficient period of data to ensure the accuracy of the forecast.