Choosing a model

Start from the question, not the class list. The tables below map common research questions to the class that answers them and to the page that explains it. Run the Diagnostics and specification testing first: whether a series has a unit root, is cointegrated or behaves nonlinearly decides half of the choices below.

One series

You want to …	Use	Read
model the conditional mean of a stationary series	AR, ARMA	Univariate linear models
model an integrated or seasonal series	ARIMA, SARIMA (...X variants for regressors)	Univariate linear models
estimate long memory, \(d\) between 0 and 1/2	ARFIMA; semiparametric \(d\) in long_memory	Univariate linear models
decompose into trend, cycle and seasonal components	UnobservedComponents; filters in cultivars.spectral	Univariate linear models, Spectral analysis and filtering
model time-varying volatility of returns	GARCH, GJR, EGARCH, FIGARCH	Volatility models
treat volatility as a latent process	SV, UCSV	Volatility models
let dynamics switch at an observed threshold	SETAR	Nonlinear and regime-switching univariate models
let dynamics change smoothly with a transition variable	LSTAR, ESTAR	Nonlinear and regime-switching univariate models
let dynamics switch with an unobserved Markov state	MarkovSwitchingAR	Nonlinear and regime-switching univariate models
fit a flexible nonlinear mean	ARNN, TARNN	Nonlinear and regime-switching univariate models

Several series, reduced form

You want to …	Use	Read
model joint dynamics of a few stationary series	VAR	Vector autoregressions
condition on series you do not model (oil, foreign rates)	VARX	Vector autoregressions
model cointegrated series in levels	VECM	Beyond the basic VAR
allow moving-average terms	VARMA	Beyond the basic VAR
pool the same system across many units	PanelVAR	Beyond the basic VAR
link country models through trade weights	GVAR	Beyond the basic VAR
mix monthly and quarterly series	MFVAR, MIDASVAR	Beyond the basic VAR
model a whole curve each period (yields, distributions)	DynamicNelsonSiegel, FunctionalVAR	Beyond the basic VAR

Many series

You want to …	Use	Read
shrink a medium or large VAR toward a prior	BVAR, HierarchicalBVAR	Bayesian VARs
use a non-conjugate or global-local shrinkage prior	GibbsBVAR	Bayesian VARs
handle fat tails or time-varying volatility in a BVAR	StudentBVAR, BVARSV	Bayesian VARs
summarize a large panel with a few factors	DFM, FAVAR	Large and high-dimensional systems
select a sparse lag structure or a network	SparseVAR, GraphicalVAR	Large and high-dimensional systems
measure connectedness between markets	Spillover	Large and high-dimensional systems

Structural questions

Pick the scheme by the identifying information you are willing to assume. All of them take a fitted reduced form; see Structural identification.

Your identifying assumption	Use	Read
a timing order: some variables do not respond within the period	RecursiveSVAR	Structural identification
some shocks have no long-run effect on some variables	LongRunSVAR	Structural identification
a general pattern of zeros on impact (A/B model)	ShortRunSVAR, MixedSVAR	Structural identification
only the signs of responses	SignRestrictedSVAR, SetIdentifiedSVAR	Structural identification
signs plus facts about particular historical episodes	NarrativeSignRestrictedSVAR in sign_restrictions	Structural identification
an external instrument correlated with one shock	ProxySVAR	Structural identification
volatility regimes or non-Gaussian shocks do the identifying	HeteroskedasticSVAR, NonGaussianSVAR	Structural identification
shocks whose effects drift over time	TVPSVAR in time_varying	Nonlinear, time-varying and regime-switching VARs

Nonlinear and changing systems

You want to …	Use	Read
a VAR whose dynamics depend on a threshold variable	TVAR, STVAR	Nonlinear, time-varying and regime-switching VARs
coefficients that drift every period	TVPVAR, TVPVARSV	Nonlinear, time-varying and regime-switching VARs
regimes driven by a hidden Markov chain	MarkovSwitchingVAR	Nonlinear, time-varying and regime-switching VARs
responses at quantiles of the distribution	QVAR	Nonlinear, time-varying and regime-switching VARs

Frequency-domain questions

You want to …	Use	Read
estimate a spectrum from data	cultivars.spectral.periodogram	Spectral analysis and filtering
read the spectrum, coherence and phase a fitted system implies	SpectralDensity	Spectral analysis and filtering
test causality at business-cycle frequencies	SpectralCausality	Spectral analysis and filtering
extract a cycle (HP, band-pass, Butterworth)	cultivars.spectral.filters, cultivars.spectral.band_pass	Spectral analysis and filtering
localize co-movement in time and frequency	cultivars.spectral.wavelets	Spectral analysis and filtering

Point estimates or posteriors?

Most reduced forms come in a frequentist and a Bayesian version, and the choice changes what you get back:

	Frequentist (VAR, ARIMA, …)	Bayesian (BVAR, GibbsBVAR, SV, …)
Fit returns	point estimates, sampling covariance	posterior draws, credible intervals
Model choice	compare on information criteria, LR tests	marginal likelihood, model averaging (The Bayesian workflow)
Forecasts	forecast (point)	forecast_paths (predictive sample)
Identification	every scheme accepts the result	not yet: Bayesian results are not closed systems
Cost	milliseconds	seconds to minutes; set n_draws and seed

A prior= argument on VAR sits between the two. It shrinks the point estimate toward the prior mean but keeps a VAR result, which can still be identified; see Bayesian VARs.