This function performs the Augmented Dickey-Fuller test to assess the
stationarity of a time series. The Augmented Dickey-Fuller (ADF) test is used
to determine if a given time series is stationary. This function takes a
numeric vector as input, and you can optionally specify the lag order with
the `.k`

parameter. If `.k`

is not provided, it is calculated based on the
number of observations using a formula. The test statistic and p-value are
returned.

## Arguments

- .x
A numeric vector representing the time series to be tested for stationarity.

- .k
An optional parameter specifying the number of lags to use in the ADF test (default is calculated).

## Value

A list containing the results of the Augmented Dickey-Fuller test:

`test_stat`

: The test statistic from the ADF test.`p_value`

: The p-value of the test.

## Examples

```
# Example 1: Using the AirPassengers dataset
ts_adf_test(AirPassengers)
#> $test_stat
#> [1] -7.318571
#>
#> $p_value
#> [1] 0.01
#>
# Example 2: Using a custom time series vector
custom_ts <- rnorm(100, 0, 1)
ts_adf_test(custom_ts)
#> $test_stat
#> [1] -4.565089
#>
#> $p_value
#> [1] 0.01
#>
```