R Code for SAUTS

In each file of R code for reproducing the contents of the figures and tables for a particular chapter, you should first evaluate all the R code from the beginning of the file up to a line with the comment `BEGINNING OF CODE TO REPRODUCE CONTENT OF FIGURES/TABLES'. After the preliminary code has been evaluated, you can reproduce the content of a particular figure/table by searching for the number of the figure/table and evaluating the associated code.

R functions (eventually to be put into an R package)

acvs (computes ACVS or ACS)
acvs_to_lag_window_sdf_est (calculate lag window SDF estimate from ACVS)
AICC_given_acvs (computes AICC given ACVS, time series and number of parameters)
AICC_given_ar_coeffs (computes AICC given AR coefficients and time series)
amt_sdf_est (computes adaptive multitaper SDF estimate from time series)
arma_coeffs_to_sdf (computes SDF for ARMA process given AR and MA coefficients and white noise variance)
ar_coeffs_to_acvs (computes ACVS for AR process given AR coefficients and innovation variance)
ar_coeffs_to_sdf (computes SDF for AR process over a grid of frequencies given AR coefficients and innovation variance)
ar_coeffs_to_sdf_single_freqs (computes SDF for AR process over one or more selected frequencies given AR coefficients and innovation variance)
ar_fls, ar_bls, ar_fbls and ls_innov_var_est (computes AR parameter estimates using various least squares methods)
ar_reduced_likelihood (computes reduced likelihood for AR process given time series and AR coefficients)
bartlett_priestley_design_window (compute Bartlett_Priestley design window)
beta_W_swb_exact (smoothing window bandwidth)
break_up_sw (break up smoothing window with negative sidelobes into pos/neg components)
burg_algorithm (computes AR parameter estimates using Burg's algorithm)
B_H (standard bandwidth measure for direct spectral estimate)
B_H_bar (standard bandwidth measure for multitaper spectral estimate)
B_U (standard bandwidth measure for lag window spectral estimate)
B_U_ds_dse (standard bandwidth measure for discretely smoothed direct spectral estimates)
B_U_ds_pgram (standard bandwidth measure for discretely smoothed periodogram)
B_W_swb_exact (smoothing window bandwidth due to Jenkins)
B_W_P_swb_exact (smoothing window bandwidth due to Parzen)
circular_shift (circularly shifts vector)
compute_cD_and_Im (compute lag window estimate of cepstrum and cross_validation measure)
compute_slepian_eigenvalue (computes eigenvalue corresponding to Slepian eigenvector (multitaper))
cosine_taper (cosine data taper)
create_tapered_series (tapers a time series)
cumulative_pgram (cumulative_periodogram white_noise test)
dB, careful_dB and convert_from_dB (convert to or from decibels)
daniell_design_window (compute Daniell design window)
default_taper (default data taper (same as rectangular data taper))
dft and inverse_dft (interfaces to R function fft)
direct_sdf_est (calculate direct spectral estimate)
dirichlet_kernel (Dirichlet's kernel as per Equation (17c))
do_crisscross_dse (creates bandwidth/CI crisscross for direct spectral estimate)
do_crisscross_lwe (creates bandwidth/CI crisscross for lag window spectral estimate)
do_crisscross_mt (creates bandwidth/CI crisscross for multitaper spectral estimate)
do_crisscross_wosa (creates bandwidth/CI crisscross for WOSA spectral estimate)
do_crisscross_hanning_50_wosa (creates bandwidth/CI crisscross for Hanning_based WOSA spectral estimate with 50% overlap)
do_it_innov_var (used for Monte Carlo study that is focus of Figure 406)
do_OLS_pgram_mt (used for Monte Carlo study that is focus of Tables 411a and 411b)
evaluate_gcv_dse and m_to_measure (functions for evaluating GCV scheme)
ev_lag_window_sdf_estimator (given ACVS, computes expected value of lag window SDF estimator)
ev_shp (computes expected value of biased estimator of ACVS)
ev_shp_squared (computes expected value of square of biased estimator of ACVS)
F_2_nu_alpha and F_2_nu_percentage_point (F_distribution with DOFs of 2 and nu)
fejer_kernel and fejer_kernel_single_freq (Fejer's kernel)
find_ar_3_dB_width (find 3 dB width down from peak in AR SDF)
find_max_peaks_ar (find locations of largest peaks in AR SDF)
find_max_peaks_ar (find locations of largest peaks in direct SDF estimate)
find_pgram_3_dB_width (find 3 dB width down from peak in periodogram)
fisher_g_statistic (Fisher's g statistic and related functions)
gcv_dsp (GCV_based bandwidth selection for discretely smoothed periodogram)
gcv_lw (GCV_based bandwidth selection for lag window estimates based on periodogram)
gen_cis_for_ar_sdf (generate CIs based on AR SDF estimate)
get_dse_freqs (compute frequencies associated with direct SDF estimate)
hanning_taper (Hanning data taper)
h_parzen_lag_window along with many other tapers derived from lag windows (h_bartlett_lag_window etc_)
is_even (tests for even integer)
is_odd (tests for odd integer)
is_power_of_2 (tests for power of 2)
J_multiple_freq (used for Thomson's F_test)
kllk (argument_invariant version fo Kullback_Leibler discrepancy measure)
lag_window_to_smoothing_window
lk (argument_reversed version fo Kullback_Leibler discrepancy measure)
ma_coeffs_to_sdf (computes SDF for MA process given MA coefficients and white noise variance)
ma_acvs_to_sdf (computes SDF for MA(q) process given ACVS out to at least lag q)
max_abs_dB (maximum absolute dB discrepancy measure)
mse (mean square error discrepancy measure)
msle (mean square log error discrepancy measure)
mt_innov_var (computes multitaper_based estimate of innovation variance)
mt_sdf_est (computes multitaper SDF estimate from time series)
m_to_dsdse (computes discretely smoothed direct spectral estimate)
next_power_of_2 (computes smallest power of 2 greater than or equal to a number)
nmse (normalized mean square error discrepancy measure)
parzen_lag_window along with many other lag windows (bartlett_lag_window etc_)
parzen_smoothing_window (calculate periodogram over a range of frequencies or at a single frequency)
pgram (calculate periodogram over a grod of frequencies)
pgram_single_freqs (calculate periodogram at one or more specified frequencies)
rectangular_taper (rectangular data taper (same as default data taper))
reshaped_mt_sdfe (form reshaped multitaper SDF estimate)
siegel_t_distribution_via_M (distribution for Siegel's T statistic and related functions)
sim_ar_process (simulation of AR process with stationary initial conditions)
sim_arma_process (simulation of ARMA process with stationary initial conditions)
sin_t_over_t_taper (sin(t)/t data taper)
sine_taper (kth_order sine data taper)
spec_window and spec_window_central_lobe (compute spectral window for direct spectral estimate)
slepian_taper (zeroth_order Slepian data taper as approximated by Equation (196b))
step_down_LD_recursions (Levinson_Durbin recursions)
svd_harmonic_analysis (computations needed to SVD_based harmonic analysis)
thomson_chave_miller_jackknife (multitaper_based CIs for SDF based on two types of jackknifing)
thomson_F_test (compute Thomson's F_test for significant peaks in multitaper SDF estimate)
trapezoidal_taper (trapezoidal data taper)
ts_to_lag_window_sdf_est (calculate lag window SDF estimate from time series)
var_biased (biased estimator of sample variance (division by N instead of N_1))
var_power_law_alpha_mt (variance of multitaper_based estimator of power_law exponent)
var_power_law_alpha_pgram (variance of periodogram_based estimator of power_law exponent)
width_e.R_mt (alternative bandwidth measure of Equation (355a) for multitaper spectral estimate)
wosa_sdf_est (calculate WOSA spectral estimate)
yule_walker_algorithm_given_acvs (computes Yule_Walker AR parameter estimates based on an ACVS estimate)
yule_walker_algorithm_given_data (computes Yule_Walker AR parameter estimates based on time series)

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