The auto.arima() function handle both the seasonal and non-seasonal ARIMA model and the principal() function used for rotating and extracting the principal components.

It seems there might be a confusion in your question. The auto.arima() and principal() functions are from different packages and serve different purposes in R.

auto.arima() function:

Package: forecast

Purpose: The auto.arima() function is part of the forecast package in R and is used for automatic ARIMA (AutoRegressive Integrated Moving Average) model selection. It helps in automatically selecting the best ARIMA model for a given time series data by evaluating different combinations of parameters.

Usage:
library(forecast)
model <- auto.arima(your_time_series_data)
Explanation: The auto.arima() function uses a stepwise approach and information criteria like AIC (Akaike Information Criterion) to determine the optimal ARIMA model order (p, d, q).

principal() function:

Package: stats

Purpose: The principal() function is part of the base R package stats and is used for performing a principal components analysis (PCA). PCA is a dimensionality reduction technique that transforms the original variables into a new set of uncorrelated variables called principal components.

Usage:
result <- principal(your_data_matrix)
Explanation: The principal() function calculates the principal components of a given data matrix. It returns an object containing information about the principal components, such as eigenvalues, loadings, and other statistics.

To summarize, auto.arima() is used for time series forecasting, specifically for automatic ARIMA model selection, and it belongs to the forecast package. On the other hand, principal() is used for principal components analysis, a technique for dimensionality reduction, and it is part of the base R package stats.