autocorrelation_coeff_plot {wwntests}

Plot Confidence Bounds of Estimated Functional Autocorrelation Coefficients

Description

'autocorrelation_coeff_plot' Computes the 1-alpha upper confidence bounds for the functional autocorrelation coefficients at lags h = 1:K under both weak white noise (WWN) and strong white noise (SWN) assumptions. It plots the coefficients as well as the bounds for all lags h = 1:K. Note, the SWN bound is constant, while the WWN is dependent on the lag.

Usage

autocorrelation_coeff_plot(
  f_data,
  K = 20,
  alpha = 0.05,
  M = NULL,
  wwn_bound = TRUE
)

Arguments

f_data

The functional data matrix with observed functions in the columns.

K

A positive Integer value. The maximum lag for which to compute the single-lag test (tests will be computed for lags h in 1:K).

alpha

A numeric value between 0 and 1 specifying the significance level to be used in the single-lag test. The default value is 0.05.

M

A positive Integer value. Determines the number of Monte-Carlo simulations employed in the Welch-Satterthwaite approximation of the limiting distribution of the test statistics, for each test.

wwn_bound

A Boolean value allowing the user to turn off the weak white noise bound. TRUE by default. Speeds up computation when FALSE.

Details

This function computes and plots autocorrelation coefficients at lag h, for h in 1:K. It also computes an estimated asymptotic 1 - alpha confidence bound, under the assumption that the series forms a weak white noise. Additionally, it computes a similar (constant) bound under the assumption the series form a strong white noise. Please see the vignette or the references for a more complete treatment.

Value

Plot of the estimated autocorrelation coefficients for lags h in 1:K with the weak white noise 1-alpha upper confidence bound for each lag, as well as the constant strong white noise 1-alpha confidence bound.

References

[1] Kokoszka P., & Rice G., & Shang H.L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity. Journal of Multivariate Analysis, 162, 32-50.

Examples

b <- brown_motion(75, 40)
autocorrelation_coeff_plot(b)
autocorrelation_coeff_plot(b, M = 200)