Introduction

Time Series Forecasting is a popular technique used in Machine Learning to predict future values based on historical data. Among several methods used for time series forecasting, ARIMA and Holt-Winters are two of the most commonly used algorithms. This blog post aims to provide a comparison between these two methods, so you can decide which one to apply for your dataset.

ARIMA

ARIMA (Autoregressive Integrated Moving Average) is a statistical algorithm used for analyzing and forecasting time series data. ARIMA models can predict future events based on past patterns, taking into account three main components: AR (Autoregression), I (Integration), and MA (Moving Average).

To find the optimal values for p, d, and q (i.e., order of the AR, I, and MA components), the ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) plots must be analyzed. Once the model is fitted, you can use it to predict future values.

Holt-Winters

Holt-Winters is a seasonal forecasting algorithm based on exponential smoothing. It can account for three main components: level, trend, and seasonality. The Holt-Winters algorithm uses these three components to estimate a smoothed value for the next time interval.

To apply the Holt-Winters algorithm to a dataset, the optimal values for the smoothing parameters (α, β, and γ) must be determined using the Holt-Winters grid search algorithm. Once the values are found, the period of time to forecast can be specified and the algorithm will produce the forecast.

Comparative Study

To perform a comprehensive comparison of ARIMA and Holt-Winters, we tested both algorithms on the Air Passengers dataset. This dataset contains the monthly totals of international airplane passengers from 1949 to 1960. We randomly selected 70% of the data for training purposes and 30% for testing purposes.

The table above shows the RMSE and MAE values for both algorithms. As we can see, the Holt-Winters algorithm outperformed ARIMA in both RMSE and MAE. This suggests that Holt-Winters might be a better choice for datasets with seasonality.

Conclusion

In conclusion, both ARIMA and Holt-Winters are powerful algorithms used in time series forecasting. Choosing the best algorithm depends on the type of data being analyzed. If your data has seasonality, Holt-Winters might be a better choice. On the other hand, if your data doesn't have a clear pattern, ARIMA might be more suitable.

References

1. Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
2. Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.
3. Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications. Springer.