API Reference

This section provides the complete API documentation for MacroEconometricModels.jl.

The API documentation is organized into the following pages:

Types: Core type definitions for models, results, and estimators
Functions: Function documentation organized by module

The quick reference tables below cover all modules: data management, time series, multivariate models, cross-sectional and panel models, DSGE, difference-in-differences, factor models, spectral analysis, volatility, nowcasting, hypothesis tests, and output utilities.

Quick Reference Tables

Typed data containers, built-in datasets (FRED-MD, FRED-QD, Penn World Table), and data cleaning utilities. See Data Management for theory and examples.

Data Management

Function	Description
`TimeSeriesData(data; varnames, frequency, tcode)`	Typed time series container with metadata
`PanelData` / `CrossSectionData`	Panel and cross-section containers
`diagnose(d)`	Scan for NaN, Inf, constant columns
`fix(d; method=:listwise)`	Clean data (`:listwise`, `:interpolate`, `:mean`)
`validate_for_model(d, :var)`	Check dimensionality for model type
`apply_tcode(y, tcode)`	FRED transformation codes 1–7
`inverse_tcode(y, tcode; x_prev)`	Undo FRED transformation
`apply_filter(d, :hp; component=:cycle)`	Apply time series filters per-variable
`describe_data(d)`	Per-variable summary statistics
`xtset(df, group_col, time_col)`	Stata-style panel construction
`group_data(pd, g)`	Extract single entity from panel
`to_matrix(d)` / `to_vector(d)`	Convert to raw matrix/vector
`desc(d)` / `vardesc(d, name)`	Dataset and per-variable descriptions
`set_desc!(d, text)` / `set_vardesc!(d, name, text)`	Set descriptions
`rename_vars!(d, old => new)`	Rename variables
`load_example(:fred_md)` / `load_example(:fred_qd)` / `load_example(:pwt)`	Load built-in datasets (FRED-MD, FRED-QD, PWT)

AR, MA, ARMA, and ARIMA model estimation with automatic order selection. See ARIMA Models for estimation methods, forecasting, and model selection.

ARIMA Estimation Functions

Function	Description
`estimate_ar(y, p; method=:ols)`	AR(p) via OLS or MLE
`estimate_ma(y, q; method=:css_mle)`	MA(q) via CSS, MLE, or CSS-MLE
`estimate_arma(y, p, q; method=:css_mle)`	ARMA(p,q) via CSS, MLE, or CSS-MLE
`estimate_arima(y, p, d, q; method=:css_mle)`	ARIMA(p,d,q) via differencing + ARMA
`forecast(model, h; conf_level=0.95)`	Multi-step forecasting with confidence intervals
`select_arima_order(y, max_p, max_q)`	Grid search for optimal ARMA order
`auto_arima(y)`	Automatic ARIMA order selection
`ic_table(y, max_p, max_q)`	Information criteria comparison table

Trend-cycle decomposition via HP, Hamilton, Beveridge-Nelson, Baxter-King, and boosted HP filters. See Time Series Filters for theory and comparisons.

Time Series Filters

Function	Description
`hp_filter(y; lambda=1600.0)`	Hodrick-Prescott trend-cycle decomposition
`hamilton_filter(y; h=8, p=4)`	Hamilton (2018) regression filter
`beveridge_nelson(y; p=:auto, q=:auto)`	Beveridge-Nelson permanent/transitory decomposition
`baxter_king(y; pl=6, pu=32, K=12)`	Baxter-King band-pass filter
`boosted_hp(y; stopping=:BIC, lambda=1600.0)`	Boosted HP filter (Phillips & Shi 2021)
`trend(result)`	Extract trend component from filter result
`cycle(result)`	Extract cyclical component from filter result

VAR, VECM, BVAR, Local Projections, Factor Models, and Panel VAR estimation. See VAR, VECM, BVAR, LP, Factor Models, and Panel VAR for theory and examples.

Multivariate Estimation Functions

Function	Description
`estimate_var(Y, p)`	Estimate VAR(p) via OLS
`estimate_bvar(Y, p; ...)`	Estimate Bayesian VAR (conjugate NIW)
`estimate_lp(Y, shock_var, H; ...)`	Standard Local Projection
`estimate_lp_iv(Y, shock_var, Z, H; ...)`	LP with instrumental variables
`estimate_smooth_lp(Y, shock_var, H; ...)`	Smooth LP with B-splines
`estimate_state_lp(Y, shock_var, state_var, H; ...)`	State-dependent LP
`estimate_propensity_lp(Y, treatment, covariates, H; ...)`	LP with propensity scores
`doubly_robust_lp(Y, treatment, covariates, H; ...)`	Doubly robust LP estimator
`estimate_factors(X, r; ...)`	Static factor model via PCA
`estimate_dynamic_factors(X, r, p; ...)`	Dynamic factor model
`estimate_gdfm(X, q; ...)`	Generalized dynamic factor model
`estimate_pvar(pd, p; ...)`	Panel VAR via GMM (FD or System)
`estimate_pvar_feols(pd, p; ...)`	Panel VAR via Fixed-Effects OLS
`estimate_gmm(moment_fn, theta0, data; ...)`	GMM estimation
`structural_lp(Y, H; method=:cholesky, ...)`	Structural LP with multi-shock IRFs
`estimate_vecm(Y, p; rank=:auto, ...)`	Estimate VECM via Johansen MLE or Engle-Granger
`to_var(vecm)`	Convert VECM to VAR in levels
`select_vecm_rank(Y, p; ...)`	Select cointegrating rank
`granger_causality_vecm(vecm, cause, effect)`	VECM Granger causality test
`forecast(vecm, h; ci_method=:none, ...)`	VECM forecast preserving cointegration

Impulse response functions, forecast error variance decomposition, historical decomposition, and 18+ structural identification methods. See Innovation Accounting and Non-Gaussian Identification.

Structural Analysis Functions

Function	Description
`irf(model, H; ...)`	Compute impulse response functions
`fevd(model, H; ...)`	Forecast error variance decomposition
`identify_cholesky(model)`	Cholesky identification
`identify_sign(model; ...)`	Sign restriction identification
`identify_long_run(model)`	Blanchard-Quah identification
`identify_narrative(model; ...)`	Narrative sign restrictions
`identify_arias(model, restrictions, H; ...)`	Arias et al. (2018) sign + zero restrictions
`identify_uhlig(model, restrictions, H; ...)`	Mountford-Uhlig (2009) penalty function sign + zero restrictions
`identify_fastica(model; ...)`	FastICA SVAR identification
`identify_jade(model; ...)`	JADE SVAR identification
`identify_sobi(model; ...)`	SOBI SVAR identification
`identify_dcov(model; ...)`	Distance covariance SVAR identification
`identify_hsic(model; ...)`	HSIC SVAR identification
`identify_student_t(model; ...)`	Student-t ML SVAR identification
`identify_mixture_normal(model; ...)`	Mixture-normal ML SVAR identification
`identify_pml(model; ...)`	Pseudo-ML SVAR identification
`identify_skew_normal(model; ...)`	Skew-normal ML SVAR identification
`identify_nongaussian_ml(model; ...)`	Unified non-Gaussian ML dispatcher
`identify_markov_switching(model; ...)`	Markov-switching SVAR identification
`identify_garch(model; ...)`	GARCH SVAR identification
`identify_smooth_transition(model, s; ...)`	Smooth-transition SVAR identification
`identify_external_volatility(model, regime)`	External volatility SVAR identification
`pvar_oirf(model, H)`	Panel VAR orthogonalized IRF (Cholesky)
`pvar_girf(model, H)`	Panel VAR generalized IRF (Pesaran & Shin 1998)
`pvar_fevd(model, H)`	Panel VAR forecast error variance decomposition
`pvar_stability(model)`	Panel VAR eigenvalue stability check
`pvar_bootstrap_irf(model, H; ...)`	Panel VAR bootstrap IRF confidence intervals
`lp_fevd(slp, H; method=:r2, ...)`	LP-FEVD (Gorodnichenko & Lee 2019)
`cumulative_irf(lp_irfs)`	Cumulative IRF from LP impulse response
`historical_decomposition(slp)`	Historical decomposition from structural LP

Direct multi-step forecasting from Local Projection models. See Local Projections for estimation details.

LP Forecasting Functions

Function	Description
`forecast(lp, shock_path; ...)`	Direct multi-step LP forecast
`forecast(slp, shock_idx, shock_path; ...)`	Structural LP conditional forecast

Augmented Dickey-Fuller, KPSS, Phillips-Perron, Zivot-Andrews, Ng-Perron, and Johansen cointegration tests. See Hypothesis Tests for interpretation and examples.

Unit Root Test Functions

Function	Description
`adf_test(y; ...)`	Augmented Dickey-Fuller unit root test
`kpss_test(y; ...)`	KPSS stationarity test
`pp_test(y; ...)`	Phillips-Perron unit root test
`za_test(y; ...)`	Zivot-Andrews structural break test
`ngperron_test(y; ...)`	Ng-Perron unit root tests (MZα, MZt, MSB, MPT)
`johansen_test(Y, p; ...)`	Johansen cointegration test
`is_stationary(model)`	Check VAR model stationarity
`unit_root_summary(y; ...)`	Run multiple tests with summary
`test_all_variables(Y; ...)`	Apply test to all columns

Likelihood ratio (LR) and Lagrange multiplier (LM/score) tests for comparing nested models across ARIMA, VAR, and GARCH families. See Hypothesis Tests.

Model Comparison Tests

Function	Description
`lr_test(m1, m2)`	Likelihood ratio test for nested models
`lm_test(m1, m2)`	Lagrange multiplier (score) test for nested models

Pairwise and block Wald tests for Granger causality in VAR models. See Hypothesis Tests for details.

Granger Causality Tests

Function	Description
`granger_test(model, cause, effect)`	Pairwise or block Granger causality test
`granger_test_all(model)`	All-pairs pairwise Granger causality matrix

Convenience functions for extracting impulse responses from fitted LP models. See Local Projections.

LP IRF Extraction

Function	Description
`lp_irf(model; ...)`	Extract IRF from LPModel
`lp_iv_irf(model; ...)`	Extract IRF from LPIVModel
`smooth_lp_irf(model; ...)`	Extract smoothed IRF
`state_irf(model; ...)`	Extract state-dependent IRFs
`propensity_irf(model; ...)`	Extract ATE impulse response

Static PCA, Dynamic Factor, and Generalized Dynamic Factor model estimation, forecasting, and selection criteria. See Factor Models.

Factor Model Functions

Function	Description
`estimate_factors(X, r; ...)`	Estimate r-factor model
`estimate_dynamic_factors(X, r, p; ...)`	Dynamic factor model
`estimate_gdfm(X, q; ...)`	Generalized dynamic factor model
`forecast(fm, h; p=1, ci_method=:none)`	Static FM forecast (fits VAR(p) on factors)
`forecast(dfm, h; ci_method=:none)`	DFM forecast (`:none/:theoretical/:bootstrap/:simulation`)
`forecast(gdfm, h; ci_method=:none)`	GDFM forecast (`:none/:theoretical/:bootstrap`)
`ic_criteria(X, r_max)`	Bai-Ng information criteria
`ic_criteria_dynamic(X, max_r, max_p)`	DFM factor/lag selection
`ic_criteria_gdfm(X, max_q)`	GDFM dynamic factor selection
`scree_plot_data(model)`	Data for scree plot
`is_stationary(dfm)`	Check DFM factor VAR stationarity
`common_variance_share(gdfm)`	GDFM common variance share per variable
`predict(fm)`	Fitted values (all factor model types)
`residuals(fm)`	Idiosyncratic residuals (all factor model types)
`r2(fm)`	Per-variable $R^2$ (all factor model types)
`nobs(fm)`	Number of observations
`dof(fm)`	Degrees of freedom
`loglikelihood(dfm)`	Log-likelihood (DFM only)
`aic(dfm)` / `bic(dfm)`	Information criteria (DFM only)

Bayesian prior optimization, instrument strength tests, and Panel VAR specification tests. See BVAR and Panel VAR.

Diagnostic Functions

Function	Description
`optimize_hyperparameters(Y, p; ...)`	Optimize Minnesota prior (τ only)
`optimize_hyperparameters_full(Y, p; ...)`	Joint optimization over (τ, λ, μ) (BGR 2010)
`posterior_mean_model(post; ...)`	VARModel from posterior mean
`posterior_median_model(post; ...)`	VARModel from posterior median
`weak_instrument_test(model; ...)`	Test for weak instruments
`sargan_test(model, h)`	Overidentification test
`test_regime_difference(model; ...)`	Test regime differences
`propensity_diagnostics(model)`	Propensity score diagnostics
`pvar_hansen_j(model)`	Hansen J-test for Panel VAR
`pvar_mmsc(model)`	Andrews-Lu MMSC for Panel VAR
`pvar_lag_selection(pd, max_p; ...)`	Panel VAR lag order selection
`j_test(model)`	Hansen J-test for GMM
`gmm_summary(model)`	Summary statistics for GMM

Multivariate normality tests for VAR residuals. See Non-Gaussian Identification for using these as pre-tests for ICA/ML identification.

Normality Test Functions

Function	Description
`jarque_bera_test(model; method=:multivariate)`	Multivariate Jarque-Bera test
`mardia_test(model; type=:both)`	Mardia skewness/kurtosis tests
`doornik_hansen_test(model)`	Doornik-Hansen omnibus test
`henze_zirkler_test(model)`	Henze-Zirkler characteristic function test
`normality_test_suite(model)`	Run all normality tests

Diagnostic tests for non-Gaussian SVAR identification validity. See Non-Gaussian Identification.

Identifiability Test Functions

Function	Description
`test_shock_gaussianity(result)`	Test non-Gaussianity of recovered shocks
`test_gaussian_vs_nongaussian(model; ...)`	LR test: Gaussian vs non-Gaussian
`test_shock_independence(result; ...)`	Test independence of recovered shocks
`test_identification_strength(model; ...)`	Bootstrap identification strength test
`test_overidentification(model, result; ...)`	Overidentification test

ARCH, GARCH, EGARCH, GJR-GARCH, and Stochastic Volatility estimation, forecasting, and diagnostics. See Volatility Models.

Volatility Model Functions

Function	Description
`estimate_arch(y, q)`	ARCH(q) via MLE
`estimate_garch(y, p, q)`	GARCH(p,q) via MLE
`estimate_egarch(y, p, q)`	EGARCH(p,q) via MLE
`estimate_gjr_garch(y, p, q)`	GJR-GARCH(p,q) via MLE
`estimate_sv(y; variant, ...)`	Stochastic Volatility via KSC Gibbs
`forecast(vol_model, h)`	Volatility forecast with simulation CIs
`arch_lm_test(y_or_model, q)`	ARCH-LM test for conditional heteroskedasticity
`ljung_box_squared(z_or_model, K)`	Ljung-Box test on squared residuals
`news_impact_curve(model)`	News impact curve (GARCH family)
`persistence(model)`	Persistence measure
`halflife(model)`	Volatility half-life
`unconditional_variance(model)`	Unconditional variance
`arch_order(model)`	ARCH order $q$
`garch_order(model)`	GARCH order $p$
`predict(m)`	Conditional variance series $\hat{\sigma}^2_t$
`residuals(m)`	Raw residuals (ARCH/GARCH) or standardized (SV)
`coef(m)`	Coefficient vector
`nobs(m)`	Number of observations
`loglikelihood(m)`	Maximized log-likelihood (ARCH/GARCH)
`aic(m)` / `bic(m)`	Information criteria (ARCH/GARCH)
`dof(m)`	Number of estimated parameters

Mixed-frequency nowcasting via DFM, BVAR, and bridge equations with news decomposition. See Nowcasting for theory and examples.

Nowcasting Functions

Function	Description
`nowcast_dfm(Y, nM, nQ; r=2, p=1, ...)`	DFM nowcasting via EM + Kalman smoother (Banbura & Modugno 2014)
`nowcast_bvar(Y, nM, nQ; lags=5, ...)`	Large BVAR nowcasting with GLP priors (Cimadomo et al. 2022)
`nowcast_bridge(Y, nM, nQ; lagM=1, ...)`	Bridge equation combination nowcasting (Banbura et al. 2023)
`nowcast(model)`	Extract current-quarter nowcast and next-quarter forecast
`forecast(dfm_or_bvar, h; ...)`	Multi-step ahead forecast from nowcasting model
`nowcast_news(X_new, X_old, dfm, t; ...)`	News decomposition: attribute revision to data releases
`balance_panel(d; r=2, method=:dfm)`	Fill NaN in TimeSeriesData/PanelData via DFM

Publication-quality tables, display backend switching, and bibliographic references. See individual section pages for usage examples.

Display and Output Functions

Function	Description
`set_display_backend(sym)`	Switch output format (`:text`/`:latex`/`:html`)
`get_display_backend()`	Current display backend
`report(result)`	Print comprehensive summary
`table(result, ...)`	Extract results as matrix
`print_table([io], result, ...)`	Print formatted table
`refs(model; format=...)`	Bibliographic references
`refs(io, :method; format=...)`	References by method name

HAC (Newey-West), heteroskedasticity-robust (White), and panel-robust (Driscoll-Kraay) covariance estimators.

Covariance Functions

Function	Description
`newey_west(X, residuals; ...)`	Newey-West HAC estimator
`white_vcov(X, residuals; ...)`	White heteroskedasticity-robust
`driscoll_kraay(X, residuals; ...)`	Driscoll-Kraay panel-robust
`long_run_variance(x; ...)`	Long-run variance estimate
`long_run_covariance(X; ...)`	Long-run covariance matrix
`optimal_bandwidth_nw(residuals)`	Automatic bandwidth selection

Low-level matrix construction and numerical utilities used internally.

Utility Functions

Function	Description
`construct_var_matrices(Y, p)`	Build VAR design matrices
`companion_matrix(B, n, p)`	VAR companion form
`robust_inv(A)`	Robust matrix inverse
`safe_cholesky(A; ...)`	Stable Cholesky decomposition

Specify, solve, simulate, and estimate Dynamic Stochastic General Equilibrium models. See DSGE Models for the full guide.

DSGE Specification and Solution

Function	Description
`@dsge begin ... end`	Parse DSGE model specification
`compute_steady_state(spec)`	Compute deterministic steady state
`linearize(spec)`	Linearize around steady state (Sims canonical form)
`solve(spec; method=:gensys)`	Solve rational expectations model
`gensys(Γ₀, Γ₁, C, Ψ, Π)`	Sims (2002) QZ decomposition solver
`blanchard_kahn(ld, spec)`	Blanchard-Kahn (1980) eigenvalue counting
`klein(ld, spec)`	Klein (2000) generalized Schur solver
`perturbation_solver(spec; order=2)`	Higher-order perturbation solver
`collocation_solver(spec; ...)`	Chebyshev collocation projection
`pfi_solver(spec; ...)`	Policy function iteration
`vfi_solver(spec; ...)`	Value function iteration
`is_determined(sol)`	Check existence and uniqueness
`is_stable(sol)`	Check stability of solution

DSGE Simulation and Analysis

Function	Description
`simulate(sol, T)`	Stochastic simulation
`irf(sol, H)`	Analytical impulse responses
`fevd(sol, H)`	Forecast error variance decomposition
`historical_decomposition(sol, data, obs)`	DSGE historical decomposition
`solve_lyapunov(G1, impact)`	Unconditional covariance (Lyapunov equation)
`analytical_moments(sol; lags)`	Analytical variance and autocovariances
`perfect_foresight(spec; T_periods, shock_path)`	Deterministic transition path

DSGE Estimation

Function	Description
`estimate_dsge(spec, data, params; method)`	GMM estimation (IRF matching, Euler, SMM, analytical)
`estimate_dsge_bayes(spec, data, θ0; ...)`	Bayesian estimation (SMC/SMC²/MH)

Occasionally Binding Constraints (OccBin)

Function	Description
`parse_constraint(expr, spec)`	Parse constraint expression
`occbin_solve(spec, constraint; ...)`	Piecewise-linear OccBin solution (1 or 2 constraints)
`occbin_irf(spec, constraint, shock_idx, H; ...)`	OccBin impulse responses

DSGE Smoothers and Diagnostics

Function	Description
`dsge_smoother(ss, data)`	RTS Kalman smoother for linear DSGE
`dsge_particle_smoother(nss, data)`	FFBSi particle smoother for nonlinear DSGE
`evaluate_policy(sol, grid)`	Evaluate policy function on grid
`max_euler_error(sol, grid)`	Maximum Euler equation error

OLS, WLS, IV/2SLS, logit, probit, ordered, and multinomial estimation for cross-sectional data. See Regression and Binary Choice for theory and examples.

Cross-Sectional Models

Function	Description
`estimate_reg(y, X; ...)`	OLS/WLS regression (HC0–HC3, cluster-robust SEs)
`estimate_iv(y, X, Z; ...)`	IV/2SLS estimation
`estimate_logit(y, X)`	Logit MLE via IRLS
`estimate_probit(y, X)`	Probit MLE via IRLS
`estimate_ologit(y, X)`	Ordered logit MLE
`estimate_oprobit(y, X)`	Ordered probit MLE
`estimate_mlogit(y, X)`	Multinomial logit MLE
`marginal_effects(m; ...)`	AME/MEM/MER with delta-method SEs
`odds_ratio(m)`	Odds ratios for logit models
`classification_table(m)`	Classification accuracy table
`vif(m)`	Variance inflation factors
`brant_test(m)`	Brant test for parallel regression
`hausman_iia(m)`	Hausman test for IIA assumption

FE, RE, FD, Between, CRE, Arellano-Bond, and Blundell-Bond panel estimators. See Panel Models for theory and examples.

Panel Regression

Function	Description
`estimate_xtreg(pd, :y, :x1, :x2; ...)`	Panel FE/RE/FD/Between/CRE/AB/BB
`estimate_xtiv(pd, :y, :x; ...)`	Panel IV (FE-IV/RE-IV/FD-IV/Hausman-Taylor)
`estimate_xtlogit(pd, :y, :x; ...)`	Panel logit (pooled/FE/RE/CRE)
`estimate_xtprobit(pd, :y, :x; ...)`	Panel probit (pooled/FE/RE/CRE)
`hausman_test(m_fe, m_re)`	Hausman FE vs RE specification test
`breusch_pagan_test(m)`	Breusch-Pagan LM test
`pesaran_cd_test(m)`	Pesaran CD cross-sectional dependence test
`wooldridge_ar_test(m)`	Wooldridge AR(1) test
`modified_wald_test(m)`	Modified Wald heteroskedasticity test
`f_test_fe(m)`	F-test for fixed effects

TWFE, Callaway-Sant'Anna, Sun-Abraham, BJS, and didmultiplegt estimators plus LP-DiD and diagnostics. See DiD and [Event Study](eventstudy.md) for theory and examples.

Difference-in-Differences

Function	Description
`estimate_did(pd, :y, :treat; ...)`	DiD estimation (5 methods: twfe/cs/sa/bjs/did_multiplegt)
`estimate_event_study_lp(pd, :y, :treat; ...)`	Event study LP for panel data
`estimate_lp_did(pd, :y, :treat; ...)`	LP-DiD (Dube et al. 2025)
`bacon_decomposition(pd, :y, :treat)`	Goodman-Bacon (2021) decomposition
`pretrend_test(result)`	Pre-trend parallel trends test
`negative_weight_check(pd, :y, :treat)`	Negative weight diagnostic
`honest_did(result; ...)`	HonestDiD sensitivity analysis

Two-step or Bayesian Gibbs FAVAR with factor-to-observable IRF mapping. See FAVAR for theory and examples.

FAVAR

Function	Description
`estimate_favar(Y_slow, Y_fast, r, p; ...)`	FAVAR (two-step or Bayesian Gibbs)
`favar_panel_irf(favar, H)`	Map factor IRFs to N observables
`favar_panel_forecast(favar, h)`	FAVAR multi-step forecasting

Structural DFM combining GDFM spectral estimation with structural VAR identification. See Factor Models for theory and examples.

Structural DFM

Function	Description
`estimate_structural_dfm(X, q; ...)`	Structural DFM (GDFM + VAR)
`sdfm_panel_irf(sdfm, H)`	Map structural factor IRFs to observables

Periodogram, Welch/Daniell/AR spectral density, cross-spectrum, coherence, and autocorrelation functions. See Hypothesis Tests for serial correlation tests.

Spectral Analysis

Function	Description
`periodogram(y; ...)`	Raw periodogram
`spectral_density(y; ...)`	Smoothed spectral density (Welch/Daniell/AR)
`cross_spectrum(x, y; ...)`	Cross-spectral analysis
`acf(y, maxlag)`	Sample autocorrelation function
`pacf(y, maxlag)`	Partial autocorrelation function
`ccf(x, y, maxlag)`	Cross-correlation function
`coherence(cs)`	Coherence from cross-spectrum
`phase(cs)`	Phase spectrum
`gain(cs)`	Gain function
`ideal_bandpass(y; pl, pu)`	Ideal bandpass filter
`transfer_function(b, a; ...)`	Filter transfer function

Ljung-Box, Box-Pierce, and Durbin-Watson tests for autocorrelation and serial correlation. See Hypothesis Tests for details.

Portmanteau and Serial Correlation Tests

Function	Description
`ljung_box_test(y, K)`	Ljung-Box autocorrelation test
`box_pierce_test(y, K)`	Box-Pierce autocorrelation test
`durbin_watson_test(m)`	Durbin-Watson serial correlation test
`bartlett_white_noise_test(y)`	Bartlett white noise test
`fisher_test(y)`	Fisher exact periodogram test

Fourier ADF/KPSS, DF-GLS, LM unit root, two-break ADF, and Gregory-Hansen cointegration tests. See Advanced Unit Root Tests for details.

Advanced Unit Root Tests

Function	Description
`fourier_adf_test(y; ...)`	Fourier ADF test (Enders & Lee 2012)
`fourier_kpss_test(y; ...)`	Fourier KPSS test
`dfgls_test(y; ...)`	DF-GLS/ERS unit root test
`lm_unitroot_test(y; ...)`	LM unit root test with breaks
`adf_2break_test(y; ...)`	Two-break ADF test (Narayan & Popp 2010)
`gregory_hansen_test(Y; ...)`	Gregory-Hansen cointegration test with break

Andrews SupWald/SupLM/SupLR, Bai-Perron multiple break detection, and factor structural break tests. See Structural Break Tests for details.

Structural Break Tests

Function	Description
`andrews_test(y, X; ...)`	Andrews (1993) SupWald/SupLM/SupLR
`bai_perron_test(y, X; ...)`	Bai-Perron (1998) multiple break detection
`factor_break_test(X; ...)`	Factor structural break test

PANIC, Pesaran CIPS, and Moon-Perron panel unit root tests. See Panel Unit Root Tests for details.

Panel Unit Root Tests

Function	Description
`panic_test(pd; ...)`	Bai-Ng (2004) PANIC test
`pesaran_cips_test(pd; ...)`	Pesaran (2007) CIPS test
`moon_perron_test(pd; ...)`	Moon-Perron (2004) test
`panel_unit_root_summary(pd; ...)`	Run all panel unit root tests

Within-group lag, lead, and differencing utilities for panel data construction. See Data Management for details.

Panel Data Utilities

Function	Description
`panel_lag(pd, :var, k)`	Within-group lagged variable
`panel_lead(pd, :var, k)`	Within-group lead variable
`panel_diff(pd, :var)`	Within-group first difference
`add_panel_lag(pd, :var, k)`	Add lagged column to panel
`add_panel_lead(pd, :var, k)`	Add lead column to panel
`add_panel_diff(pd, :var)`	Add differenced column to panel
`balance_panel(d; ...)`	Fill NaN via DFM imputation