A Novel Fréchet Distribution for Inflation Rate Modeling and Comparative Machine Learning Forecasting

The complexity of inflation rate fluctuations poses a significant challenge to traditional statistical models, requiring the development of more dependable and adaptable methods. The primary objectives of this paper are to predict and model inflation rate data. We propose the novel Fréchet (NF) via the logarithmic transformation approach from the conventional Fréchet distribution. Its density function might be nearly symmetric, bimodal, right-skewed, or left-skewed. The hazard function of the NF distribution is highly flexible, capable of increasing, decreasing, being upside-down bathtub-shaped, or increasing-decreasing, which is not possible with the traditional Fréchet distribution. We derive key statistical features of this distribution and obtain parameter estimates using various estimation methods. Monte Carlo simulations are used to demonstrate the accuracy of the parameter estimates. The potential of the NF distribution is empirically validated using monthly inflation rate data. Additionally, we conduct a comparative analysis of various time series approaches using statistical methods as well as machine learning models for predicting inflation rates, including ARIMA, recurrent neural networks (RNN), and support vector regression (SVR). The findings reveal that SVR outperforms other methods by achieving the lowest errors across all metrics, with a root mean squared error (RMSE) of 0.2225, a mean absolute error (MAE) of 0.1394, and a mean absolute percentage error (MAPE) of 0.020101, underscoring its effectiveness in modeling and predicting inflation rate data.