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The process of utilizing the auto.arima() function in Jupyter notebook(R) is as follows:

1. First, install the forecast package in R Studio by running the following command: install.packages("forecast")

2. Load the forecast package by running the following command: library(forecast)

3. Import your time series data into Jupyter notebook using the relevant data import methods such as read.csv, read_excel, etc.

4. Convert the imported data into a time series object using the ts() function. Ensure that the object has the correct frequency and start date.

5. Use the auto.arima() function to automatically determine the optimal ARIMA parameters for your time series. The function accepts the time series object, as well as several additional arguments that allow you to configure the model selection process. For example, you can specify the maximum order of the ARIMA model, the maximum number of differencing required, and whether the function should perform a stepwise search.

6. The auto.arima() function will return the best-fitting ARIMA model for your time series. You can then use this model to make forecasts, perform diagnostics, and analyze the results of your time series analysis.

7. Finally, visualize your time series and the forecasted values using the relevant R visualization packages such as ggplot2, plotly, etc.