Nowcasting

Central banks and forecasters need current-quarter GDP estimates weeks before official release. Nowcasting bridges this gap by extracting signal from timely high-frequency indicators –- monthly industrial production, employment, and financial data –- to produce real-time estimates of quarterly aggregates. MacroEconometricModels.jl implements three complementary approaches:

Dynamic Factor Model (DFM): EM + Kalman smoother on latent factors with Mariano-Murasawa temporal aggregation; native news decomposition; see DFM Nowcasting
Large Bayesian VAR: GLP-style Normal-Inverse-Wishart prior with hyperparameter optimization via marginal likelihood; see BVAR Nowcasting
Bridge Equations: OLS regressions on quarterly-aggregated monthly indicators, combined via median; see Bridge Equations
News Decomposition: attribute nowcast revisions to individual data releases (Banbura and Modugno 2014); see News Decomposition

using MacroEconometricModels, Random
Random.seed!(42)

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Quick Start

All recipes use the following FRED-MD mixed-frequency setup:

fred = load_example(:fred_md)
nc_md = fred[:, ["INDPRO", "UNRATE", "CPIAUCSL", "M2SL", "FEDFUNDS"]]
Y = to_matrix(apply_tcode(nc_md))
Y = Y[all.(isfinite, eachrow(Y)), :]
Y = Y[end-99:end, :]
nM, nQ = 4, 1
for t in 1:size(Y, 1)
    if mod(t, 3) != 0
        Y[t, end] = NaN
    end
end
Y[end, end] = NaN       # simulate ragged edge
nothing # hide

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Recipe 1: DFM nowcasting

dfm = nowcast_dfm(Y, nM, nQ; r=2, p=1, idio=:ar1)
report(dfm)

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Recipe 2: BVAR nowcasting

bvar = nowcast_bvar(Y, nM, nQ; lags=5)
report(bvar)

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Recipe 3: Bridge equation nowcasting

bridge = nowcast_bridge(Y, nM, nQ; lagM=1, lagQ=1)
report(bridge)

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Recipe 4: Nowcast extraction and comparison

r_dfm = nowcast(dfm)
r_bvar = nowcast(bvar)
r_bridge = nowcast(bridge)
report(r_dfm)

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Recipe 5: News decomposition

X_old = copy(Y)
X_new = copy(Y)
X_old[end, 1:3] .= NaN   # simulate 3 releases arriving

news = nowcast_news(X_new, X_old, dfm, size(Y, 1); target_var=size(Y, 2))
report(news)

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The Nowcasting Problem

Quarterly aggregates like GDP are released with a 4–8 week delay, while dozens of monthly indicators are available in real time. Nowcasting produces current-quarter estimates by exploiting this timely high-frequency information:

\[\underbrace{Y_t}_{\text{target (quarterly)}} = f\big(\underbrace{X_{1,t}, \ldots, X_{N,t}}_{\text{monthly indicators}}\big) + \varepsilon_t\]

where:

$Y_t$ is the quarterly target variable (e.g., GDP growth)
$X_{j,t}$ are monthly indicator variables
$\varepsilon_t$ is the forecast error

Three challenges define the problem:

Mixed frequencies –- monthly indicators and quarterly targets coexist in the same model
Ragged edges –- not all series update simultaneously; the most recent months have missing observations for slower-release variables
Large cross-sections –- dozens to hundreds of indicators provide complementary information

Data Layout Convention

All nowcasting functions expect a $T \times N$ matrix where the first nM columns are monthly variables and the last nQ columns are quarterly variables. Quarterly observations appear every 3rd row (months 3, 6, 9, 12) with NaN for non-quarter-end months. The ragged edge is represented by trailing NaN values in the most recent rows.

Method Comparison

Criterion	DFM	BVAR	Bridge
Cross-section size	Large (50–200)	Medium (10–50)	Small (5–20)
Interpretability	Latent factors	Direct coefficients	Simple OLS
News decomposition	Native	–-	–-
Computational cost	Moderate (EM)	Moderate (optimization)	Fast (OLS)
Best for	Large mixed-frequency panels	Medium panels with priors	Quick baseline

Nowcast Extraction

The nowcast() function extracts the current-quarter estimate and a one-quarter-ahead forecast from any AbstractNowcastModel:

result = nowcast(dfm)
result.nowcast    # current-quarter value
result.forecast   # next-quarter forecast
result.method     # :dfm, :bvar, or :bridge

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Each method computes the forecast differently: DFM projects the state vector 3 months forward, BVAR iterates the VAR one step, and Bridge uses the median of individual equation nowcasts. Multi-step forecasts are available via forecast(model, h) for DFM and BVAR models.

StatsAPI Interface

Function	DFM	BVAR	Bridge
`loglikelihood(m)`	Log-likelihood at convergence	Marginal log-likelihood	–-
`predict(m)`	Smoothed data `X_sm`	Smoothed data `X_sm`	Smoothed data `X_sm`
`nobs(m)`	Number of time periods	Number of time periods	Number of time periods

Visualization

Sub-Page Guide

For detailed treatment of each method –- theory, model specification, keyword tables, return value tables, and advanced usage:

DFM Nowcasting –- EM algorithm, Kalman smoother, Mariano-Murasawa temporal aggregation, block structure, idiosyncratic dynamics
BVAR Nowcasting –- GLP prior, dummy observations, hyperparameter optimization, Kalman smoothing
Bridge Equations –- quarterly aggregation, pairwise OLS, median combination, interpolation
News Decomposition –- revision attribution, per-release impact, group aggregation, data vintage comparison

Common Pitfalls

NaN placement determines quarterly alignment. Quarterly values must appear at rows divisible by 3 (months 3, 6, 9, 12). Placing quarterly observations at other rows produces silently incorrect temporal aggregation weights.
Column ordering matters. Monthly variables occupy columns 1:nM and quarterly variables occupy columns nM+1:nM+nQ. Swapping this order causes the Mariano-Murasawa weights to apply to the wrong variables.
Standardize before estimation. The DFM internally standardizes data, but raw data with vastly different scales can slow EM convergence. Apply apply_tcode() to FRED-MD data to obtain stationary, comparable-scale series.
News decomposition requires two vintages. The nowcast_news function compares two data matrices (X_new and X_old) that differ only in newly released observations. Both matrices must have the same dimensions; the old vintage has NaN where the new vintage has observed values.
Bridge equations need sufficient quarterly observations. With lagM, lagQ, and lagY lags, the effective sample shrinks. Ensure at least 20 quarterly observations remain after lag truncation to avoid overfitting.

References

Banbura, Marta, and Michele Modugno. 2014. "Maximum Likelihood Estimation of Factor Models on Datasets with Arbitrary Pattern of Missing Data." Journal of Applied Econometrics 29 (1): 133–160. DOI: 10.1002/jae.2306
Banbura, Marta, Irina Belousova, Katalin Bodnar, and Mate Barnabas Toth. 2023. "Nowcasting Employment in the Euro Area." ECB Working Paper No. 2815.
Cimadomo, Jacopo, Domenico Giannone, Michele Lenza, Francesca Monti, and Andrej Sokol. 2022. "Nowcasting with Large Bayesian Vector Autoregressions." ECB Working Paper No. 2696.
Giannone, Domenico, Michele Lenza, and Giorgio E. Primiceri. 2015. "Prior Selection for Vector Autoregressions." Review of Economics and Statistics 97 (2): 436–451. DOI: 10.1162/REST_a_00483
Mariano, Roberto S., and Yasutomo Murasawa. 2003. "A New Coincident Index of Business Cycles Based on Monthly and Quarterly Series." Journal of Applied Econometrics 18 (4): 427–443. DOI: 10.1002/jae.695