Simulate an Individual (Augmented) Dickey-Fuller Model

sim_df_mod() is designed as a helper function, to be used internally in this package in sadf_test(). But, you can use it here to simulate a time series and perform a(n Augmented) Dickey-Fuller test.

Usage

sim_df_mod(x, ts_type, df_lags = NULL, classic_df = FALSE, wn = FALSE)

Arguments

x: a numeric vector corresponding to a series to replicate/simulate
ts_type: a type of time-series to simulate (either 'ndnt', 'dnt', or 'dt')
df_lags: a numeric vector for the number of lags to calculate for the test.
classic_df: logical, defaults to FALSE. If FALSE, the function calculates an "Augmented" Dickey-Fuller test on a simulated series with the number of lagged first differences requested in the df_lags argument. If TRUE, the classic Dickey-Fuller test is executed without the lagged first differences.
wn: logical, defaults to FALSE. If FALSE, generates a random walk of some description for a DF/ADF test. If TRUE, series to be simulated for a DF/ADF test is white noise.

Value

sim_df_mod() returns the output of a linear model (with class lm) that performs a(n Augmented) Dickey-Fuller test on a simulated time series. This is mostly for internal use, but it might pique the user's interest to see such a test in action independent of simulated summaries generated by sadf_test().

Details

classic_df = TRUE suppresses the need to specify df_lags = 0, but df_lags cannot be 0 if classic_df = FALSE.

This might change in future iterations, but it's worth clarifying the values assigned to the parameters of a drift and trend. The drift is randomly generated from a Rademacher distribution for both the times series with drift and drift-and-trend. The series with a deterministic trend divides the value from the Rademacher distribution by 10. My rationale is largely based on what I've seen other pedagogical guides do, the extent to which they talk about simulating values for these types of random walks.

Author

Steven V. Miller

Examples


set.seed(8675309) # don't want new numbers in documentation every time...

sim_df_mod(rnorm(25), ts_type = 'ndnt', classic_df = TRUE)
#> 
#> Call:
#> lm(formula = f_d_x ~ l1_fx - 1)
#> 
#> Coefficients:
#>    l1_fx  
#> -0.01491  
#> 

sim_df_mod(rnorm(25), ts_type = 'ndnt', df_lags = 2, classic_df = FALSE)
#> 
#> Call:
#> lm(formula = d_fx_t ~ l1_fx - 1 + adf_diff_lags_fake)
#> 
#> Coefficients:
#>               l1_fx  adf_diff_lags_fake1  adf_diff_lags_fake2  
#>              0.1184              -0.4047              -0.4403  
#>