Type:	Package
Title:	Hypothesis Testing for Dependent Variables with Unbalanced Data
Version:	0.2.0
Description:	Implements hierarchical Bayesian inference, robust frequentist inference, and distribution-free inference for dependent and unbalanced data under strong-mixing conditions. Supports triangular-array, weighted-sum and mixingale convergence regimes with Whittle and composite likelihoods, heteroskedasticity-and-autocorrelation-consistent variance estimation, block bootstrap with automatic block length, fixed-bandwidth HAR inference, adaptive conformal prediction, Bayesian decision under Region of Practical Equivalence, bridge-sampling Bayes factors, and predictive comparison via the Widely Applicable Information Criterion and leave-future-out cross-validation. Methods follow Andrews (1991) <doi:10.2307/2938229>, Kiefer and Vogelsang (2005) <doi:10.1017/S0266466605050565>, Patton, Politis and White (2009) <doi:10.1080/07474930802459016>, Vehtari, Gelman and Gabry (2017) <doi:10.1007/s11222-016-9696-4>, Kruschke (2018) <doi:10.1177/2515245918771304>, and Gibbs and Candes (2021) <doi:10.48550/arXiv.2106.00170>.
License:	MIT + file LICENSE
Encoding:	UTF-8
LazyData:	true
Depends:	R (≥ 4.1.0)
Imports:	rstan (≥ 2.26.0), stats, parallel,
Suggests:	bayesplot, bridgesampling, knitr, loo, posterior, readxl, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
RoxygenNote:	7.3.3
URL:	https://github.com/IsadoreNabi/HTDV
BugReports:	https://github.com/IsadoreNabi/HTDV/issues
NeedsCompilation:	no
Packaged:	2026-04-29 15:05:39 UTC; ROG
Author:	Jose Mauricio Gomez Julian [aut, cre]
Maintainer:	Jose Mauricio Gomez Julian <isadorenabi@pm.me>
Repository:	CRAN
Date/Publication:	2026-05-02 09:50:14 UTC

HTDV: Hypothesis Testing for Dependent Variables with Unbalanced Data

Description

Implements hierarchical Bayesian inference, robust frequentist inference, and distribution-free inference for dependent and unbalanced data under strong-mixing conditions.

Main functions

• htdv_fit: unified hierarchical Bayesian fit via HMC.

• htdv_tac, htdv_wsc, htdv_mpc: convergence-regime-specific fits.

• htdv_whittle, htdv_composite: likelihood surrogates for dependent data.

• htdv_envelope: Berger-robust posterior envelope.

• htdv_lrv: long-run variance with Newey-West and Andrews bandwidth.

• htdv_fixedb: fixed-bandwidth HAR inference (Kiefer-Vogelsang 2005).

• htdv_boot: block bootstrap with Patton-Politis-White automatic block length.

• htdv_conformal: adaptive conformal inference (Gibbs-Candes 2021).

• htdv_rope: posterior decision under Region of Practical Equivalence (Kruschke 2018).

• htdv_bf: bridge-sampling Bayes factor.

• htdv_waic_lfo: WAIC and leave-future-out cross-validation.

• htdv_stack: predictive stacking across models.

• htdv_diagnostics, htdv_ppc: MCMC diagnostics and posterior-predictive checks.

• htdv_equivalence_constants: explicit numerical constants for TAC/WSC/MPC metric equivalence.

Author(s)

Maintainer: Jose Mauricio Gomez Julian isadorenabi@pm.me (ORCID)

See Also

Useful links:

• https://github.com/IsadoreNabi/HTDV

• Report bugs at https://github.com/IsadoreNabi/HTDV/issues

Bridge-Sampling Bayes Factor

Description

Computes the Bayes factor between two fitted htdv_fit objects via bridge sampling. Requires the bridgesampling package.

Usage

htdv_bf(fit1, fit0, ...)

Arguments

Value

A list with bf10, log_bf10, logml1, logml0, and error_percentage.

References

Meng, X.-L., & Wong, W.H. (1996). Simulating Ratios of Normalizing Constants. Statistica Sinica 6(4): 831-860. Gronau, Q.F. et al. (2017). A Tutorial on Bridge Sampling. JMP 81: 80-97.

Examples

if (requireNamespace("bridgesampling", quietly = TRUE)) {
  x <- rnorm(50)
  f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 1)
  f0 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 2)
  htdv_bf(f1, f0)$bf10
}

Block Bootstrap with Automatic Block Length

Description

Implements circular and stationary block bootstraps (Politis-Romano 1992, 1994) with Patton-Politis-White (2009) automatic block length selection.

Usage

htdv_boot(
  x,
  statistic,
  R = 1999L,
  type = c("circular", "stationary"),
  block_length = "auto",
  level = 0.95
)

Arguments

Value

A list with t0 (statistic on original data), t_star (bootstrap distribution), ci_percentile, ci_basic, ci_studentized, and block_length.

References

Politis, D.N., & Romano, J.P. (1994). The Stationary Bootstrap. JASA 89(428): 1303-1313. Patton, A., Politis, D.N., & White, H. (2009). Correction to Automatic Block-Length Selection for the Dependent Bootstrap. Econometric Reviews 28(4): 372-375.

Examples

set.seed(1)
x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
out <- htdv_boot(as.numeric(x), mean, R = 500, type = "stationary")
out$ci_percentile

Composite Log-Likelihood for Dependent Data

Description

Pairwise or k-tuple composite log-likelihood (Varin, Reid and Firth 2011) for strictly stationary sequences.

Usage

htdv_composite(x, density_fun, theta, k = 1L, log = FALSE)

Arguments

Value

A list with loglik (scalar), n_blocks, and block_values.

References

Varin, C., Reid, N., & Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21(1), 5-42.

Examples

x <- arima.sim(model = list(ar = 0.4), n = 200, rand.gen = rnorm)
gauss_ar1 <- function(block, theta) {
  phi <- theta[1]; sigma2 <- theta[2]
  a <- block[1]; b <- block[2]
  dnorm(a, 0, sqrt(sigma2 / (1 - phi^2)), log = TRUE) +
    dnorm(b, phi * a, sqrt(sigma2), log = TRUE)
}
htdv_composite(as.numeric(x), gauss_ar1, c(0.4, 1), k = 1, log = TRUE)$loglik

Adaptive Conformal Inference for Dependent Data

Description

Online adaptive conformal prediction intervals with gradient update on the miscoverage rate (Gibbs-Candes 2021). Provides long-run marginal coverage without exchangeability.

Usage

htdv_conformal(
  x,
  predictor,
  residual_fun = function(e) abs(e),
  alpha_target = 0.1,
  lambda = 0.05,
  burn_in = 20L
)

Arguments

Value

A list with intervals (matrix of lower/upper), coverage (empirical), alpha_path, and point_predictions.

References

Gibbs, I., & Candes, E. (2021). Adaptive Conformal Inference under Distribution Shift. NeurIPS 34: 1660-1672.

Examples

x <- arima.sim(model = list(ar = 0.6), n = 200, rand.gen = rnorm)
pred <- function(hist) if (length(hist) >= 1) hist[length(hist)] else 0
out <- htdv_conformal(as.numeric(x), pred, alpha_target = 0.1,
                      lambda = 0.05, burn_in = 20)
out$coverage

MCMC Diagnostics for htdv_fit Objects

Description

Computes split-Rhat, bulk and tail ESS, E-BFMI, divergence count, and treedepth saturation; all standard HMC diagnostics (Vehtari et al. 2021, Betancourt 2016).

Usage

htdv_diagnostics(
  fit,
  rhat_threshold = 1.01,
  ess_threshold = 400,
  bfmi_threshold = 0.3
)

Arguments

Value

A list with rhat, ess_bulk, ess_tail, bfmi, divergences, max_treedepth, passed (logical), and failures (character vector).

References

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Buerkner, P.-C. (2021). Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC. Bayesian Analysis 16(2): 667-718. Betancourt, M. (2016). Diagnosing Suboptimal Cotangent Disintegrations. <doi:10.48550/arXiv.1604.00695>.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_diagnostics(fit)$passed

HTDV Empirical Benchmarks Against Published References

Description

Output of the three-dataset external validation protocol of Section 12-ter of the companion paper. Each dataset is run against a pre-existing reference result from the published literature on the same vintage, with the three HTDV inferential layers (HAR, bootstrap, hierarchical Bayesian) reporting their point estimate, 95% interval, and a Bayesian diagnostic-pass flag.

Usage

htdv_empirical_benchmarks

Format

A data frame with three rows (one per dataset) and the following columns:

dataset

Name of the benchmark dataset.

reference

Citation of the reference paper.

n

Sample size after preprocessing.

sample

Sample window (string).

reference_value

Reference point value.

reference_se

Reference standard error (NA when the reference does not provide one).

har_point, har_ci_lo, har_ci_hi

HAR-Wald point and 95% CI.

bayes_point, bayes_ci_lo, bayes_ci_hi

Bayesian point and 95% credible interval.

bayes_diag_pass, bayes_rhat_max, bayes_ess_min, bayes_divergences

Bayesian HMC diagnostics.

boot_point, boot_ci_lo, boot_ci_hi

Stationary block bootstrap point and 95% percentile CI.

agreement_har, agreement_bayes, agreement_boot

Per-layer agreement verdict: "agreement", "htdv-strict (above ref)", or "htdv-strict (below ref)".

Details

The three benchmarks (E1, E2, E3) and their references are:

• E1. Post-1984 US CPI inflation against Stock and Watson (2007). FRED-MD vintage 2026-03, variable CPIAUCSL transformed to annualized monthly inflation.

• E2. Long-run mean of log-CAPE against Campbell and Shiller (1998). Robert Shiller's online historical dataset.

• E3. US vs. Canada 10-year government bond yield differential against the iid Welch baseline. FRED series GS10 and IRLTLT01CAM156N, common sample 1990-01 to latest.

Source

Generated by run_benchmarks.R of the companion paper repository. See vignette("HTDV-validation") for the methodological narrative and the persistence-ladder reading.

Berger-Robust Envelope Posterior

Description

Builds an envelope posterior over a list of htdv_fit objects by entropy-maximizing mixture weights subject to predictive consistency (Berger 1994).

Usage

htdv_envelope(fits, target = "theta")

Arguments

Value

A list with draws (envelope draws for the target parameter), weights, intervals, and component_intervals.

References

Berger, J.O. (1994). An Overview of Robust Bayesian Analysis. Test 3(1): 5-124.

Examples

x <- rnorm(50)
f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
               refresh = 0, seed = 1)
f2 <- htdv_fit(x, model = "wsc", chains = 2, iter = 500,
               refresh = 0, seed = 2)
htdv_envelope(list(f1, f2), target = "theta")$intervals

Numerical Constants for TAC/WSC/MPC Metric Equivalence

Description

Computes the explicit finite-sample constants K_TAC(gamma, q), K_MPC(gamma) and the unified two-sided envelope (c_L, c_U) from Theorems 5-8 of the companion paper.

Usage

htdv_equivalence_constants(gamma, q = 6, n = 100, C_alpha = 1)

Arguments

Value

A list with components K_TAC, K_MPC, c_L, c_U, b_optimal, m_optimal, and regime (a short label describing which method is favored).

Examples

htdv_equivalence_constants(gamma = 2, q = 6, n = 60)

Hierarchical Bayesian Fit for Dependent Variables

Description

Fits the hierarchical Bayesian model described in the companion paper via Hamiltonian Monte Carlo (NUTS) using rstan. Nuisance parameters sigma_inf, gamma_mix, and (for WSC) b carry priors and are integrated over.

Usage

htdv_fit(
  x,
  model = c("tac", "wsc", "mpc", "whittle", "composite"),
  chains = 4L,
  iter = 4000L,
  warmup = iter%/%2L,
  refresh = max(iter%/%10L, 1L),
  adapt_delta = 0.99,
  max_treedepth = 12L,
  seed = NULL,
  ...
)

htdv_tac(x, ...)

htdv_wsc(x, ...)

htdv_mpc(x, ...)

Arguments

Value

An object of class htdv_fit, a list with components stanfit, model, data, n, call.

References

Hoffman, M.D., & Gelman, A. (2014). The No-U-Turn Sampler. JMLR 15(1): 1593-1623. Betancourt, M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in HMC. <doi:10.48550/arXiv.1604.00695>.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
class(fit)

Fixed-Bandwidth HAR Inference (Kiefer-Vogelsang 2005)

Description

Fixed-b HAR Wald test where the bandwidth is a fixed fraction of the sample size. Critical values are obtained by simulation from the asymptotic functional distribution.

Usage

htdv_fixedb(
  x,
  theta0 = 0,
  B = 0.1,
  kernel = c("bartlett", "parzen", "qs"),
  sims = 5000L,
  alpha = 0.05
)

Arguments

Value

A list with statistic, critical_value, p_value, reject, bandwidth, and kernel.

References

Kiefer, N.M., & Vogelsang, T.J. (2005). A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests. Econometric Theory 21(6): 1130-1164.

Examples

set.seed(1)
x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
htdv_fixedb(as.numeric(x), theta0 = 0, B = 0.2, sims = 1000)$p_value

Long-Run Variance Estimation (HAC)

Description

Heteroskedasticity-and-autocorrelation-consistent long-run variance with data-driven Andrews (1991) optimal bandwidth, Bartlett, Parzen, and Quadratic-Spectral kernels.

Usage

htdv_lrv(
  x,
  kernel = c("bartlett", "parzen", "qs"),
  bandwidth = "andrews",
  prewhiten = FALSE
)

Arguments

Value

A list with components lrv (long-run variance estimate), bandwidth, kernel, and ar_coef (only if prewhitened).

References

Andrews, D.W.K. (1991). Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 59(3): 817-858. Newey, W.K. & West, K.D. (1987). A Simple, Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55(3): 703-708.

Examples

set_seed_user <- 42
x <- arima.sim(model = list(ar = 0.6), n = 200, rand.gen = rnorm)
out <- htdv_lrv(as.numeric(x), kernel = "qs", bandwidth = "andrews")
out$lrv

Posterior-Predictive Checks on Dependence Statistics

Description

Replicates autocorrelation, Ljung-Box, spectral discrepancy, and a detrended-fluctuation Hurst exponent under the posterior and computes posterior-predictive p-values.

Usage

htdv_ppc(fit, x_obs, lag_max = 10L)

Arguments

Value

A list with p_acf, p_ljung_box, p_spectral, p_hurst.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_ppc(fit, x)

Region-of-Practical-Equivalence (ROPE) Decision

Description

Posterior decision under Kruschke's (2018) Region of Practical Equivalence.

Usage

htdv_rope(draws, rope, level = 0.95)

Arguments

Value

A list with decision ("accept", "reject", "undecided"), hdi, rope, and prob_in_rope.

References

Kruschke, J.K. (2018). Rejecting or Accepting Parameter Values in Bayesian Estimation. Advances in Methods and Practices in Psychological Science 1(2): 270-280.

Examples

draws <- rnorm(4000, mean = 0.05, sd = 0.1)
htdv_rope(draws, rope = c(-0.1, 0.1), level = 0.95)$decision

Aggregated Output of the HTDV Factorial Simulation Study

Description

Sign-corrected aggregated results of the factorial Monte Carlo study described in Section 12-bis of the companion paper. The study crosses five factors at four levels each (sample size, AR(1) coefficient, innovation tail, imbalance ratio, location shift) for 1024 cells, each replicated 500 times against three inferential layers (HAR, bootstrap, hierarchical Bayesian). One cell (n=500, phi=0.85, t3, imb=1, delta=0) was lost to an I/O collision and is excluded; the table contains 1023 cells x 3 layers = 3069 rows.

Usage

htdv_sim_summary

Format

A data frame with one row per (cell, layer) and the following columns:

n

Per-group primary sample size (40, 80, 200, 500).

phi

AR(1) coefficient (0, 0.3, 0.6, 0.85).

tail

Innovation distribution: "normal", "t5", "t3", "t2_1".

imb

Imbalance ratio n1/n2 (1, 1.5, 3, 6).

delta

Location shift in units of sigma_inf (0, 0.1, 0.25, 0.5).

layer

Inferential layer: "har", "boot", "bayes".

n_reps

Number of replications aggregated (500 for all cells).

reject_rate

Empirical rejection rate at nominal alpha = 0.05.

coverage

Fraction of replications whose 95% interval covered the true parameter (sign-corrected for HAR and bootstrap).

mean_ci_length

Average length of the 95% interval.

mean_runtime

Mean per-replication runtime in seconds.

diag_pass_rate

Fraction of replications passing all HMC diagnostic gates (Bayesian layer only; NA otherwise).

Source

Generated by run_simstudy.R of the companion paper repository on master seed 20260422, with sign-corrected coverage produced by recover_coverage.R. Total wall-clock 31.1 hours on a 16-core Linux workstation. See vignette("HTDV-validation") for the full report.

Factorial Monte Carlo Simulation Study for Dependent-Unbalanced Data

Description

Runs the pre-registered factorial Monte Carlo study of Section 12-bis of the companion paper. The study crosses four factors (per-group sample size, AR(1) coefficient, innovation tail, imbalance ratio) and evaluates three inferential layers (HAR-Wald, stationary block bootstrap, hierarchical Bayesian HMC) on each replication.

Usage

htdv_simstudy(
  n_grid = c(40L, 80L, 200L, 500L),
  phi_grid = c(0, 0.3, 0.6, 0.85),
  tail_grid = c("normal", "t5", "t3", "t2_1"),
  imb_grid = c(1, 1.5, 3, 6),
  delta_grid = c(0, 0.1, 0.25, 0.5),
  R = 500L,
  seed = 20260422L,
  n_cores = 1L,
  layers = c("har", "boot", "bayes"),
  bayes_chains = 2L,
  bayes_iter = 600L,
  bayes_warmup = 300L,
  boot_R = 999L,
  rope = c(-0.1, 0.1),
  alpha = 0.05,
  out_dir = NULL,
  progress = TRUE
)

Arguments

Value

A data frame with one row per (cell, replication, layer). Columns: cell_id, n, phi, tail, imb, n1, n2, delta, sigma_inf, layer, replicate, reject, ci_lo, ci_hi, estimate, covered, ci_length, rhat_max, ess_min, divergences, diag_pass, runtime_sec.

Data-generating process

Two independent AR(1) series x^{(1)}_t of length n_1=n and x^{(2)}_t of length n_2 = \max(2, \mathrm{round}(n / \mathrm{imb})) are generated. The innovations are drawn from rnorm, scaled Student-t_{(5)}, scaled Student-t_{(3)} or scaled Student-t_{(2.1)} so that the nominal innovation variance is one when the law has a finite second moment. Group one has mean zero; group two has mean \Delta\cdot\sigma_\infty where \sigma_\infty = 1/\sqrt{1 - \phi^2}.

Inferential layers

• HAR-Wald ("har"). Welch-style two-sample statistic z = (\bar x_1 - \bar x_2) / \sqrt{\hat\sigma_1^2/n_1 + \hat\sigma_2^2/n_2} with long-run variances estimated via htdv_lrv (QS kernel, Andrews bandwidth) on each group's demeaned series. Rejection at asymptotic \chi^2_1 critical value.

• Stationary block bootstrap ("boot"). Each group resampled independently using htdv_boot with block_length = "auto" (Patton- Politis-White). Percentile interval on \bar x_1^* - \bar x_2^*.

• Hierarchical Bayesian ("bayes"). Two-sample AR(1) Stan model (simstudy_two_sample.stan); posterior interval on \delta = \alpha_2 - \alpha_1. A run is flagged diag_pass = TRUE only if \hat R < 1.01, bulk and tail ESS above 200, and zero divergences.

References

Kiefer, N.M., & Vogelsang, T.J. (2005). Econometric Theory 21(6): 1130-1164. Patton, A., Politis, D.N., & White, H. (2009). Econometric Reviews 28(4): 372-375. Kruschke, J.K. (2018). Advances in Methods and Practices in Psychological Science 1(2): 270-280.

Examples

res <- htdv_simstudy(n_grid = c(40, 80),
                     phi_grid = c(0, 0.6),
                     tail_grid = c("normal"),
                     imb_grid = c(1, 3),
                     delta_grid = c(0, 0.25),
                     R = 5L, n_cores = 1L,
                     layers = c("har", "boot"))
head(htdv_simstudy_summary(res))

Aggregate a Simulation-Study Output

Description

Computes empirical size (or rejection rate), coverage, and mean interval length per (cell x layer) from the raw output of htdv_simstudy.

Usage

htdv_simstudy_summary(res, alpha = 0.05)

Arguments

Value

A data frame with one row per (cell, layer) and columns n, phi, tail, imb, delta, layer, n_reps, reject_rate, coverage, mean_ci_length, mean_runtime, diag_pass_rate.

Examples

res <- htdv_simstudy(n_grid = c(40), phi_grid = c(0.3),
                     tail_grid = "normal", imb_grid = 1,
                     delta_grid = c(0, 0.3), R = 5,
                     layers = c("har"))
htdv_simstudy_summary(res)

Flag Simulation-Study Cells in the Limit-of-Identification Zone

Description

Reads an aggregated htdv_simstudy_summary output and returns the subset of cells where the Bayesian diagnostic-pass rate falls below a user-set threshold. Such cells are typically located in the corner of the design where strong autocorrelation meets a small sample (high \phi and low n); the AR(1) likelihood there approaches its limit of identification, MCMC diagnostics flag the resulting posterior, and practitioners should treat the cell with extra caution—either by increasing HMC iterations, tightening the priors on \phi, or falling back to the conformal anchor whose validity does not require identifiability.

Usage

htdv_simstudy_warnings(summ, threshold = 0.7)

Arguments

Value

A data frame with the columns n, phi, tail, imb, delta, layer, diag_pass_rate, restricted to Bayesian rows whose pass rate is below threshold, plus an integer column flag_index (sequential identifier of flagged cells, useful for cross-referencing in reports and in vignettes).

Examples

res <- htdv_simstudy(n_grid = c(40, 200),
                     phi_grid = c(0, 0.85),
                     tail_grid = "normal",
                     imb_grid = c(1, 6),
                     delta_grid = c(0, 0.25),
                     R = 50L)
summ <- htdv_simstudy_summary(res)
htdv_simstudy_warnings(summ, threshold = 0.7)

Predictive Stacking of Bayesian Models

Description

Computes stacking weights (Yao, Vehtari, Simpson, Gelman 2018) across a list of fitted models by LOO-log-score maximization.

Usage

htdv_stack(fits, method = c("log_score"))

Arguments

Value

A list with weights, model_names, and elpd_per_model.

Examples

if (requireNamespace("loo", quietly = TRUE)) {
  x <- rnorm(50)
  f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 1)
  f2 <- htdv_fit(x, model = "wsc", chains = 2, iter = 500,
                 refresh = 0, seed = 2)
  htdv_stack(list(tac = f1, wsc = f2))$weights
}

Print-Friendly Summary for an HTDV Fit

Description

Print-Friendly Summary for an HTDV Fit

Usage

htdv_summary(fit, rope = NULL, target = "theta")

Arguments

Value

A data frame with posterior mean, sd, 2.5%, 50%, 97.5%, Rhat, bulk and tail ESS for target, plus the ROPE decision if requested.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_summary(fit, target = "theta")

WAIC and Leave-Future-Out Cross-Validation

Description

Computes the Widely Applicable Information Criterion (Watanabe 2010) and leave-future-out expected log predictive density (Buerkner-Gabry-Vehtari 2020) from a fitted htdv_fit object.

Usage

htdv_waic_lfo(fit, L = NULL, k_threshold = 0.7)

Arguments

Value

A list with waic, elpd_lfo, elpd_se, pareto_k, and refresh_times.

References

Watanabe, S. (2010). Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion. JMLR 11: 3571-3594. Buerkner, P.-C., Gabry, J., & Vehtari, A. (2020). Approximate Leave-Future-Out Cross-Validation for Bayesian Time Series Models. Journal of Statistical Computation and Simulation 90(14): 2499-2523.

Examples

if (requireNamespace("loo", quietly = TRUE)) {
  x <- rnorm(50)
  fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                  refresh = 0, seed = 1)
  htdv_waic_lfo(fit)$waic
}

Whittle Likelihood for Stationary Series

Description

Computes the Whittle pseudo-log-likelihood at Fourier frequencies for a user-supplied spectral density.

Usage

htdv_whittle(x, spec_fun, theta, taper = FALSE)

Arguments

Value

A list with loglik (scalar), frequencies, periodogram, and fitted_spectrum.

References

Whittle, P. (1953). Estimation and Information in Stationary Time Series. Arkiv foer Matematik, 2(5), 423-434. Dzhaparidze, K. (1986). Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series. Springer.

Examples

x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
ar1_spec <- function(lambda, theta) {
  phi <- theta[1]; sigma2 <- theta[2]
  sigma2 / (2 * pi * (1 - 2 * phi * cos(lambda) + phi^2))
}
htdv_whittle(as.numeric(x), ar1_spec, c(0.5, 1))$loglik