nowcasting economic activity with secular trends, large ...nowcasting economic activity with secular...

Nowcasting Economic Activity with Secular

Trends, Large Shocks and Alternative Data∗

Juan Antolın-Dıaz

London Business School

Thomas Drechsel

University of Maryland

Ivan Petrella

Warwick Business School

CEPR

June 18, 2020

INCOMPLETE DRAFT, PLEASE DO NOT CIRCULATE

Abstract

The assessment of macroeconomic conditions in real time is challenging. Exploiting recentadvances in Bayesian computational methods, this paper contributes three methodologicalinnovations to the widely used dynamic factor model framework to nowcast economic activity.First, we model low-frequency movements in the long-run growth rate and the volatility ofthe variables. Second, we incorporate heterogeneous lead-lag patterns in the responses ofthe variables to the common factor. Third, we allow for fat tailed observations. We carryout a comprehensive out-of-sample evaluation exercise using fully real-time unrevised USdata. As the model is re-estimated each time new information arrives, the sheer scale ofthe exercise requires the use of cloud computing. We show not only that low frequencymovements, dynamic heterogeneity and fat tails are pervasive features of macroeconomicdata, but that explicitly modeling them advances the real-time assessment of macroeconomicconditions. In an application to the Covid-19 recession, we find that the model robustlytracks economic activity despite unprecedented variation in the data releases. We alsodemonstrate how our framework can be used to incorporate ‘alternative data’ which becomesavailable in real time but has a short history. Our model’s assessment about the recoveryof the US economy from the Great Lockdown is significantly more optimistic than the consensus.

Keywords: Nowcasting; Dynamic factor models; Real-time data; Bayesian Methods; Fat Tails.JEL Classification Numbers: E32, E23, O47, C32, E01.

∗We thank seminar participants at the Bank of England, the Bank of Spain, the Barcelona Summer Forum, the CFEin London, the DC Forecasting Seminar at George Washington University, Fulcrum Asset Management and the IHSin Vienna. Author details: Antolın-Dıaz: London Business School, 29 Sussex Place, London NW1 4SA, UK; E-Mail:[email protected]. Drechsel: Department of Economics, University of Maryland, Tydings Hall, College Park,MD 20742, USA; E-Mail: [email protected]. Petrella: Warwick Business School, University of Warwick, Coventry, CV47AL, UK. E-Mail: [email protected]. A previous version of this research project was presented under the title“Advances in Nowcasting Economic Activity”.

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Contents

1 Introduction 3

2 Econometric Framework 8

2.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Dealing with Mixed Frequencies and Missing Data . . . . . . . . . . . . . . . . . . . . 10

2.3 Priors and Model Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Real-Time Estimation and Forecasting 12

3.1 Estimation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Construction of the real-time database . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Real-time forecasting using cloud computing . . . . . . . . . . . . . . . . . . . . . . . 15

4 Main implications for nowcasting economic activity 17

4.1 Secular movements in macroeconomic data: trends and SV . . . . . . . . . . . . . . . 17

4.2 Heterogeneous dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.3 Interpreting the data flow in the presence of outliers . . . . . . . . . . . . . . . . . . . 22

4.4 Daily tracking of economic activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5 Out-of-sample evaluation and model comparison 25

5.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Point Forecast Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.3 Density Forecast Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.4 Forecasting monthly indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6 An application to the Covid-19 recession 31

6.1 Incorporating alternative data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.2 Real-time tracking in 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7 Conclusion 32

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1 Introduction

The real-time assessment of macroeconomic conditions is an important responsibility of economists,

but remains a non-trivial task due to the idiosyncrasies of the macroeconomic data flow: the most

important economic indicators, such as Gross Domestic Product (GDP), are published on a quarterly

basis and with considerable delay, whereas there is a vast amount of related but noisy indicators

of economic activity that are available in a more timely fashion. Moreover, most macroeconomic

series are revised over time and the typical data panel is plagued with missing observations at

various points in the sample. As a consequence, there is great interest in econometric techniques

that produce reliable “nowcasts” of the current state of real economic activity.

As surveyed by Stock and Watson (2017), two developments have revolutionized the practice

of nowcasting: the greater availability of real-time datasets containing hundreds of time series,

and the development of econometric methods tailored to the features of macroeconomic data.

This paper makes several methodological contributions to nowcasting real activity, which center

around a third development: recent advances in Bayesian computational methods enable exact

finite-sample inference in high-dimensional, non-linear and non-Gaussian settings. A Bayesian

approach allows us to give a prominent role to what Sims (2012) calls “recurrent phenomena” of

macroeconomic time series that the existing literature traditionally treats “nuisance parameters

to be worked around”: low-frequency changes in trends, sustained periods of persistently high

or low volatility and large outliers. We propose a framework that explicitly models these salient

features of macroeconomic data and significantly improves the ability to track real activity.

An illustration of the properties of macroeconomic data which are at the core of our approach is

provided in Figure 1. These are features of the data that are not typically explicitly modeled in a

standard nowcasting framework, but which we incorporate formally. Panel (a) the quarterly time

series of US GDP growth over the last few decades (blue line). To highlight secular lower frequency

changes, the figure highlights the mean (red line) as well as the standard deviation (red shaded

areas) for different subsamples. It is evident that both the average growth rate of GDP, as well as

it volatility, exhibits changes over different episodes of the last decades. Panel (b) displays two

representative monthly indicators typically used for the purpose of nowcasting activity, XXX and

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Figure 1: SALIENT FEATURES OF THE MACROECONOMIC DATA FLOW

(a) Time-Varying Long-Run Growth and Volatility in US GDP

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

-4

-2

0

2

4

6

8

10

(b) Heterogeneous Dynamics in US Macroeconomic Time Series

2000 2002 2004 2006 2008 2010 2012 2014-3

-2

-1

0

1

New Home Sales

2000 2002 2004 2006 2008 2010 2012 2014-4

-3

-2

-1

0

1Industrial Production Growth

2000 2002 2004 2006 2008 2010 2012 2014

-3

-2

-1

0

1Payroll Employment Growth

(c) Outliers in US Macroeconomic Time Series

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015-50

0

50Light Weight Vehicle Sales (% MoM change)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015-10

-5

0

5

10Real Personal Disposable Income (% 1 m change)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015-2

-1

0

1

2Civilian Employment (% 1 m change)

Notes. Panel (a): The blue line is four-quarter real GDP growth in the United States. The red line and shaded areadisplay, respectively, the average and standard deviation of GDP growth over selected subsamples. The subsamples forthe average growth rate correspond to the periods considered by the growth literature: 1947-1974, the “productivityslowdown” period of 1974-1994 (Nordhaus, 2004), the “productivity boom” associated with information technologiesfrom 1995-2004 (Oliner and Sichel, 2000), and the period 2004-2015 where a subsequent productivity slowdown has beenreported by Fernald (2014) and Antolin-Diaz et al. (2017). The standard deviation is calculated over the subsamples1947-1984, the latter date being associated with the beginning of the Great Moderation (McConnell and Perez-Quiros,2000) and 1985-2015. Gadea et al. (2018) provide evidence that notwithstanding the large magnitude of the 2008-2009output drop the Great Moderation has persisted until the present time. Panel (b): twelve-month growth rate of selectedindicators of US real economic activity (blue) together with the four-quarter growth of real GDP (red) in the sample2000-2015. Shaded areas indicate NBER recessions. The figure illustrates how the business-cycle frequency comovementamong macroeconomic variables features heterogeneous patterns of leading and lagged dynamics. Panel (c): raw dataseries for light vehicle sales, real personal disposable income and civilian employment in the United States. The figure isintended to highlight the presence and different nature of outliers in macroeconomic time series.

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XXX, together with a common cyclical factor. It is visible that these series exhibit phase shifts. Some

series are leading the cycle, others are lagging the cycle. Panel (c) illustrates an example of fat-tailed

observations encountered in macroeconomic observations. It plots the light weight vehicle sales

and personal income series. In 2008 and 2013 the latter series was affected by tax changes that

created incentives to switch reported income from one period in the year to another. This creates

large movements around the period of the tax change, which are usually fully reverted the next

period. The impact of this outlier in the measurement of the volatility of the variable is typically so

large that no meaningful information can be extracted from this in real time. Another interesting

example of typical outliers’ pattern in monthly macroeconomic data. Here the series displays a

large one off movement in the level, which maps into a large spike of the growth rate.

This paper proposes a Bayesian dynamic factor model (DFM) that explicitly incorporates these

salient features of the data and shows that they are critical to improving our ability to track real-time

macroeconomic conditions. DFMs capture the idea that a small number of unobserved factors

drives the comovement of a large number of macroeconomic time series.1 We contribute three

methodological innovations to the DFM framework. First, we model low-frequency movements in

the long-run growth rate and the volatility of the variables. Second, we incorporate heterogeneous

lead-lag patterns in the responses of the variables to the common factor. Third, we allow for fat

tailed observations. The first innovation echoes Antolin-Diaz, Drechsel, and Petrella (2017), where

we presented evidence for the presence of low-frequency movements in macroeconomic variables,

such as secular trends in GDP and productivity growth. We argued that the Bayesian DFM provides

a natural way to incorporate them into the analysis. The second innovation is akin to D’Agostino

et al. (2015), who have studies heterogeneous dynamics in the context of a small-scale DFM for

US data. These authors show that the addition of lags in the measurement equation allows for a

rich variety of responses to the common shocks. We provide evidence in a larger model, and for a

panel of countries, that this modifies substantially the nowcasting process, as noisy but fast moving

hard data will receive more weight in real time relative to the standard model, in which highly

persistent soft (survey) data essentially dominate the results. Similar arguments lead us to the

third innovation. Large, transitory one-off innovations, usually caused by holidays, tax changes,1An extensive survey of the nowcasting literature is provided by Banbura et al. (2012), who also demonstrate, in a

real-time context, the good out-of-sample performance of DFM nowcasts.

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strikes or weather disruptions, are endemic to macroeconomic time series, especially at monthly

frequencies. In many cases practitioners simply substitute these outliers by missing data using

judgment or simple rules of thumb. Instead, we propose to augment the model with an additive

component which is distributed as a Student t. This does not completely discard the information

that they might contain, and recognizes the uncertainty surrounding whether an observation is an

outlier or not.

In order to deal with the increased complexity of the model, we develop a hierarchical Monte

Carlo Markov Chain (MCMC) algorithm that can harness the advantages of modern parallel

computing. We then put our modeling innovations to the test in a comprehensive out-of-sample

evaluation exercise. Using a new fully-real time database that covers the main advanced economies,

we mimic the exercise of a forecaster that updates her information set in real-time every day from

January 2000 to December 2019. The sheer scale of the exercise would have been infeasible just

a few years ago and is made possible thanks to the use of cloud computing. We compare the

forecasting performance of models that introduce each feature one by one, paying special attention

to the production of well-calibrated density forecasts that accurately characterize the uncertainty

around current economic activity. Contrary to the usual practice, which just focuses in evaluating

the performance in nowcasting GDP, we assess the performance in predicting each of the series

included in the panel. Therefore, we provide a comprehensive assessment of the importance of

these more complex model features for the nowcasting process.

We find that over the evaluation window 2000-2019 the model is at least as accurate at point

forecasting, and significantly better at density forecasting than the benchmark DFM. In terms of

point forecasts of GDP growth, XXX. In terms of density forecasts of GDP growth, we find that most

of the improvement in density forecasting comes from correctly assessing the center and the right

tail of the distribution, implying that the time-invariant DFM is assigning excessive probability to a

strong recovery. In terms of nowcasting monthly indicators, XXX. Overall, our assessment is that

the addition of the novel components not only provides a tool to asses our knowledge about the

state of long-run growth and volatility in real time. It also brings about a substantial improvement

in short-run forecasting performance. The proposed model therefore provides a robust and timely

methodology to track macroeconomic conditions.

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Figure 2: TRACKING ACTIVITY DURING THE GREAT LOCKDOWN OF 2020

Notes.

Finally, we provide an application of the model to the recent Covid-19 recession. This has been

an extremely challenging period for forecasters, because XXX. we find that the model robustly

tracks economic activity despite huge variation in the data releases. We also demonstrate how our

framework can be used to incorporate ‘alternative data’, that becomes available in real time but

has a short history. Our model’s assessment about the recovery of the US economy from the Great

Lockdown is significantly more optimistic than the consensus. Figure 2 shows...

The rest of this paper is organized as follows: Section 2 introduces the econometric framework.

Section 3 describes the estimation algorithm and the real-time evaluation exercise. Section 4

illustrates how major challenges in nowcasting economic activity are addressed with the novel

components of the model. The results for the out-of-sample evaluation exercise are presented in

Section 5. Section 6 presents to application to the Covid-19 recession. Section 7 concludes.

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2 Econometric Framework

2.1 The model

The model follows closely the Dynamic Factor Model with time-varying long-run growth and

stochastic volatility of Antolin-Diaz, Drechsel, and Petrella (2017), extended to allow for endogenous

treatment of outliers, as well as heterogeneous responses to the common factors.

Much of the existing DFM literature employs frequentist approaches to estimation and inference.

Principal components approaches and quasi-maximum likelihood estimation based on the EM

algorithm (Doz et al. 2012) have been shown to be robust to non-Gaussianity and other sources of

misspecification when the number of time series, N , is large. For the purposes of nowcasting in

real time, however, the asynchronous release of macroeconomic indicators −the so-called “ragged

edge” problem− implies that N is very small at the beginning of the nowcasting period, precisely

when accuracy is most important. By taking instead a Bayesian perspective, we avoid relying on

asymptotic results and explicitly model previously overlooked features of the data.

Let yt be an n× 1 vector of observable macroeconomic time series. A small number of latent

common factors, ft is assumed to capture the bulk of the comovement between the growth rates of

the series. Moreover, the raw data also displays outliers, denoted ot. Formally,

∆(yt − ot) = ct + Λ(L)ft + ut, (1)

where Λ(L) is a matrix polynomial of order m in the lag operator containing the loadings on the

contemporaneous and lagged common factors, and ut is a vector of idiosyncratic components.

The notation above makes use of the first difference operator, ∆, to make clear that it is the level

of the variables displays that displays outliers, but the factor structure is present in the growth

rate of the series. The former choice mimics the standard practice, where typically the statistical

agency adjusts for outliers on the level of the series, and the data is differenced when appropriate

to achieve stationarity before estimating the DFM. It is also convenient because, as we will see,

many time series related to real economic activity feature large one-off innovations to the level,

such as strikes and weather related disturbances, that are purely transitory in nature and the series

8

returns to its original level once their effect dissipates.

Following Antolin-Diaz et al. (2017), low frequency shifts in the long-run growth rate of yt are

captured by time-variation in ct. In principle one could allow time-varying intercepts in all or a

subset of the variables in the system. Moreover, time variation in the mean of a given series could

be shared by other series. For instance, one might want to make the long-run growth component to

be the same for GDP and consumption. ct is therefore flexibly specified as

ct =

B 0

0 c

at

1

, (2)

where at is an r × 1 vector of time-varying means, B is an m× r matrix which governs how the

time-variation affects the corresponding observables, and c is an (n−m)× 1 vector of constants.

Equations (1) and (2) therefore allow for stochastic trends in the mean of all or a subset of selected

observables in yt, and for these trends to be common or idiosyncratic across variables.

The laws of motion of the various components are specified as

(I2 −Φ(L))ft = Σεtεt, (3)

(1− ρi(L))ui,t = σηi,tηi,t, i = 1, . . . , n (4)

oi,tiid∼ t(vo,i), i = 1, . . . , n (5)

where Φ(L) and ρi(L) denote polynomials in the lag operator of order p and q, respectively, and

I2 is the 2× 2 identity matrix. The idiosyncratic components are cross-sectionally orthogonal and

are assumed to be uncorrelated with the common factor at all leads and lags, i.e. εtiid∼ N(02×2, I2)

and ηi,tiid∼ N(0, 1).

Finally, the dynamics of the model’s time-varying parameters are specified to follow driftless

random walks:

aj,t = aj,t−1 + vaj,t , vaj,tiid∼ N(0, ω2

a,j) j = 1, . . . , r (6)

log σεt = log σεt−1 + vε,t, vε,tiid∼ N(0, ω2

ε) (7)

log σηi,t = log σηi,t−1 + vηi,t , vηi,tiid∼ N(0, ω2

η,i) i = 1, . . . , n (8)

9

where aj,t are the r time-varying elements in at, and σεt and σηi,t capture the SV of the innovations

to factor and idiosyncratic components. Our motivation for specifying the time-varying parameters

as random walks is similar to Primiceri (2005).2 Finally, the outliers are modeled as independent

additive Student-t innovations, with the degrees of freedom, vo,i, to be estimated jointly with the

other parameters of the model.

2.2 Dealing with Mixed Frequencies and Missing Data

Tracking activity in real time requires a model that can efficiently incorporate information from

series measured at different frequencies. In particular, it must include both quarterly variables,

such as the growth rate of real GDP, as well as more timely monthly indicators of real activity.

Therefore, the model is specified at monthly frequency, and following Mariano and Murasawa

(2003), the (observed) quarterly growth rates of a generic quarterly variable, xqt , can be related to

the (unobserved) monthly growth rate xmt and its lags using a weighted mean. Specifically,

xqt =1

3xmt +

2

3xmt−1 + xmt−2 +

2

3xmt−3 +

1

3xmt−4, (9)

and only every third observation of xqt is actually observed. Substituting the corresponding line of

(1) into (9) yields a representation in which the quarterly variable depends on the factor and its

lags. The presence of mixed frequencies is thus reduced to a problem of missing data in a monthly

model.

Besides mixed frequencies, additional sources of missing data in the panel include: the “ragged

edge” at the end of the sample, which stems from the non-synchronicity of data releases; missing

data at the beginning of the sample, since some data series have been created or collected more

recently than others; and missing observations due to outliers and data collection errors. Our

Bayesian estimation method exploits the state space representation of the DFM and jointly estimates

the latent factors, the parameters, and the missing data points using the Kalman filter (see Durbin

and Koopman, 2012, for a textbook treatment).

2For the case of more than one factor, following Primiceri (2005), the covariance matrix of ft, denoted by Σε,t, canbe factorised without loss of generality as AtΣε,tA′t = ΩtΩ

′t, where At is a lower triangular matrix with ones in the

diagonal and covariances aij,t in the lower off-diagonal elements, and Ωt is a diagonal matrix of standard deviationsσεi,t . Furthermore, for k > 1, Qε would be an unrestricted (k × k) matrix.

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2.3 Priors and Model Settings

The number of lags in the polynomials Λ(L), φ(L), and ρ(L) is set to m = 1, p = 2, and q = 2,

respectively. As we will see below, the choice of m = 1 is enough to allow for rich heterogeneity in

the dynamics of the variables, and increasing m does not improve in-sample fit in a meaningful

way. In turn, by setting p = q = 2, which follows Stock and Watson (1989), the model allows for the

hump-shaped responses to aggregate shocks commonly thought to characterize macroeconomic

time series. Despite these parsimonious choices, the model features many parameters. One of

the advantages of the Bayesian approach is that an a-priori preference for simpler models can be

naturally encoded by shrinking the parameters towards a more parsimonious specification. In

particular, we follow the long tradition in economics of applying stronger shrinkage to more distant

lags initiated by Doan et al. (1986). More specifically, “Minnesota”-style priors are applied to the

coefficients in Λ(L), φ(L) and ρi(L):

• For the autoregressive coefficients of the factor dynamics, φ(L), the prior mean is set to 0.9

for the first lag, and to zero in subsequent lags. This reflects a belief that the common factor

captures a highly persistent but stationary business cycle process.

• For the factor loadings, Λ(L), the prior mean is set to 1 for the first lag, and to zero in

subsequent lags. This shrinks the model towards the factor being the cross sectional average

of the variables, see D’Agostino et al. (2015).

• For the autoregressive coefficients of the idiosyncratic components, ρi(L) the prior is set to

zero for all lags, thus shrinking the model towards a model with no serial correlation in ui,t.

In all cases, the variance on the priors is set to τh2 , where τ is a parameter governing the tightness of

the prior, and h is equal to the lag number of each coefficent, ranging 1 : p, 1 : q and 1 : s+ 1. We

set τ = 0.2, the reference value used in the Bayesian VAR literature.

The variances of the innovations to the time-varying parameters, namely ω2a, ω2

ε and ω2η,i in

equations (6)-(8) are difficult to identify from the information contained in the likelihood alone.

As the literature on Bayesian VARs documents, attempts to use non-informative priors for these

parameters will in many cases produce posterior estimates which imply a relatively large amount

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of time-variation. While this will tend to improve the in-sample fit of the model it is also likely

to worsen out-of-sample forecast performance. We therefore use priors to shrink these variances

towards zero, i.e. towards the standard DFM which excludes time-varying long-run GDP growth

and SV. In particular, for ω2a we set an inverse gamma prior with one degree of freedom and scale

equal to 0.001.3 For ω2ε and ω2

η,i we set an inverse gamma prior with one degree of freedom and

scale equal to 0.0001, closely following Cogley and Sargent (2005) and Primiceri (2005).

3 Real-Time Estimation and Forecasting

3.1 Estimation Algorithm

Our fully-Bayesian approach allows us to estimate the joint posterior distribution of the parameters

of the model and the latent objects. We present a Gibbs sampler algorithm that allows us to sample

from this posterior. Many of the individual steps are adapted from ideas in Kim and Nelson (1999),

Bai and Wang (2015), and Moench et al. (2013). In particular, the stochastic volatility step is adapted

from Kim et al. (1998), and we draw the Student-t distributed innovations following Jacquier

et al. (2004). Our main contribution here is a hierarchical re-writing of the algorithm that avoids

drawing from large state-spaces. Together with additional computational gains already proposed

by Antolin-Diaz et al. (2017), the estimation is made feasible and extremely fast. A sketch of the

algorithm is provided below, and full details are provided in Appendix A.

Algorithm 1. This algorithm draws from the posterior distribution of the unobserved components and

parameters of the model described in section 2.1

1. Initialize the parameters of the model as well as the stochastic volatility processes at their prior means;

The latent components ct, st,ot, and ft, are initialized by running the Kalman filter and smoother once

conditional on the initialized parameters.

2. For each variable, i = 1, . . . , N :

2.1. Compute ∆yi,t − ci,t − λi(L)ft = ui,t + ∆si,t + ∆oi,t.3To gain an intuition about this prior, note that over a period of ten years, this would imply that the random walk

process of the long-run growth rate is expected to vary with a standard deviation of around 0.4 percentage points inannualized terms, which is a fairly conservative prior.

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2.2. Use the Kalman filter and simulation smoother to independently draw the outlier components.

Draw the associated parameters σεs,t, vo,i.

2.3. Compute the outlier adjusted variable, ∆ySAi,t = ∆(yi,t − si,t − oi,t) = ci,t + λi(L)ft + ui,t.

3. Conditional on the outlier adjusted variables:

3.1. Use the Kalman filter and simulation smoother to draw the common factors and long run trends,

ct, ft.

3.2. Conditional on the factors and long-run trends, draw the remaining parameters of the model,

Λ(L), φ(L) and ρi(L), as well as the stochastic volatility processes, the innovations to the

time-varying parameters, ω2a, ω2

ε and ω2η,i.

4. Go back to Step 2 until convergence has been achieved.

Several points are worth noting. First, the algorithm iterates between two state spaces: a

univariate one in Step 2, which performs outlier adjustment, and a multivariate one in Step 3,

which estimates a DFM on the outlier adjusted variables. It therefore mimics the usual practice of

using independently outlier adjusted data in the factor model, but incorporates the uncertainty

inherent in the outlier adjustment process, which is typically disregarded. Second, the univariate

state space in Step 2 is independent across variables, which means that it can be run in parallel

using multi-core processors.4 Finally, by incorporating the mixed-frequency measurement into

Step 2 only, the maximum size of the state-space in Step 3 is limited if, following Antolin-Diaz et al.

(2017), the system is re-written in terms of quasi-differences, avoiding the inclusion of idiosyncratic

components as state variables.

3.2 Construction of the real-time database

As variables included in the model, we consider indicators of real economic activity for the US,

Germany, France, Italy, Canada, United Kingdom and Japan. Our choice of variables is quite

parsimonious and reflects the consensus reached in the nowcasting literature. First, a choice is

made of which broad categories of data (e.g., production, sales, employment, prices, etc.) to

4Additional computational gains can be obtained if the univariate Kalman Filter is compiled in a fast language suchas C++.

13

consider. Giannone et al. (2008) conclude that that prices and monetary indicators do not contribute

to the precision of GDP nowcasts, whereas Banbura et al. (2012), Forni et al. (2003) and Stock and

Watson (2003) find at best mixed results for financial variables. Therefore, we include only variables

measuring real activity, excluding prices, monetary and financial indicators, and extract a single

common factor that captures real economic activity. Importantly, we include all of the available

surveys of consumer and business sentiment, known as soft data, given that the literature has found

that their timeliness makes them very valuable for nowcasting. Second, with respect to what level

of disaggregation to reach within each category, Boivin and Ng (2006), Alvarez et al. (2012), and

Banbura et al. (2010, 2012) all argue that the presence of strong correlation in the idiosyncratic

components of disaggregated series of the same category will be a source of misspecification that

does not improve, and can worsen, the performance of the model in terms of in-sample fit and

out-of-sample forecasting of key series. Therefore, we exclude disaggregated data (e.g., sector-level

production measures or labor market data broken down in demographic groups) and include only

the headline indicators for each category. This leaves us with models that include, depending on

the country, between 15 and 30 series. The exact series used for each country in the estimation are

detailed in Appendix B.

Macroeconomic data series are revised over time by statistical agencies, incorporating additional

information that might not be available during the initial releases. In order to mimic the exercise of

a real-time forecaster using our model, it is therefore crucial to use vintages of unrevised data as

they were available at each point in time. Real-time vintages spanning the period January 2000

to December 2016 are collected from the (1) the Archival Federal Reserve Economic Database

(ALFRED) and (2) the OECD Original Release Data and Revisions Database. For each vintage, the

start of the sample is set to January 1960, appending missing observations to any series which starts

after that date.

For several series vintages are available in nominal terms. In those cases, we separately obtain

the appropriate deflators, which are not subject to revisions, from Haver Analytics, and deflate

the series in real time. Additionally, in several occasions the series are subject to methodological

changes and part of their history is deleted by the statistical agency. In this case, given our interest

in using long samples for all series, we use older vintages to splice the growth rates back to the

14

earliest possible date. For soft variables real-time data is not as readily available. The literature on

real-time forecasting has generally assumed that these series are unrevised, and therefore used the

latest available vintage. However while the underlying survey responses are indeed not revised,

the seasonal adjustment procedures applied to them do lead to important differences between

the series as was available at the time and the latest vintage. For this reason we use seasonally

unadjusted data. For the version of the model which endogenously incorporates seasonality, this

component will be estimated with the rest of the parameters. For the benchmark version which

treats seasonality outside the model, we apply the Census-X12 procedure in real time to obtain

a real-time seasonally adjusted version of the surveys. We follow the same procedure for the

initial unemployment claims series. We then use Bloomberg to obtain the exact date in which each

monthly data point was first published.

3.3 Real-time forecasting using cloud computing

Using our real-time vintage database, we re-estimate the following five models each day in which

new data is released: a benchmark with constant long-run GDP growth and constant volatility

(Model 0, similar to Banbura and Modugno (2014)), a version with constant long-run growth but

with stochastic volatility (Model 1, similar to Marcellino et al. (2014)), the baseline model put

forward in Antolin-Diaz et al. (2017) with both time-variation in the long-run growth of real GDP

and SV (Model 2), an extension to Model 2 which also allows for heterogenous dynamics, i.e. m = 5

(Model 3), and a version of Model 3 which treats outliers endogenously within the estimation

(Model 4). As can be seen, Models 0 to 4 are increasing in complexity, so we introduce the various

features one at a time in order to assess their marginal impact on performance.

In the construction of the real time dataset above, a vintage is constructed for each day in which

a new observation or a revision to any of the series is released. On average, this occurs 12-13 days

every month. Given that we have 17 years of real-time vintages, this leaves us with approximately

2,500 vintages per country, totaling almost 20,000 vintages across all countries. 10,000 iterations

of the Gibbs sampler presented in section 3.1 are run, discarding the first 2,000 as burn-in draws.

one of these runs of the algorithm takes approximately 3 hours in a modern computer. Therefore,

the entire exercise across all vintages, countries and models would take more than twenty years if

15

done in a single computer! In order to make it feasible, we leverage the possibilities of massively

parallelized cloud computation. We have integrated our MATLAB code with the Amazon Elastic

Compute Cloud (Amazon EC2), which allows us to compute up to 2,500 runs of the algorithm

simultaneously.5 This reduces the total computation time to just a few hours per country and

model. All of the relevant outputs are then downloaded back into local servers for subsequent

analysis.

5We are especially grateful to Jago Westmacott and the technology team at Fulcrum Asset Management for developingand implementing a customized interface for seamlessly interacting with the cloud computing platform.

16

4 Main implications for nowcasting economic activity

This section shows how the models’ novel components work in sample. We focus on trend and SV,

heterogeneous dynamics, and outliers in turn. We also focus on daily

4.1 Secular movements in macroeconomic data: trends and SV

Figure 3 displays the posterior estimate of the time-varying long-run growth rate of GDP as well

as the SV of the common factor. These estimates are conditional on the full sample and account

for both filtering and parameter uncertainty. These results reflect the first of our three modeling

innovations and can be seen as an updated version of the main results in Antolin-Diaz et al. (2017).

Panel (a) presents the posterior median, together with the 68% and 90% posterior credible intervals

of the long-run growth rate of real GDP. As dicussed in Antolin-Diaz et al. (2017), this estimate

conforms with some of the major anecdotes about US postwar growth, including the “productivity

slowdown” of the 1970’s (Nordhaus, 2004) or the 1990s’ productivity boom in the IT sector (Oliner

and Sichel, 2000). Importantly, it reveals the gradual slowdown since the start of the 2000’s, with

most of the decline having occurred before the Great Recession. Interestingly, at the end of the

sample, XXX.

Panel (b) presents posterior estimate of the SV of the common factor. It is evident that volatility

declines over the sample, with the Great Moderation clearly visible and still in place, confirming the

insights of Gadea-Rivas et al. (2014). The plot also shows that volatility spikes during recessions, a

feature that brings our estimates close to the recent findings of Jurado et al. (2014) and Bloom (2014)

relating to business-cycle uncertainty. It appears that the random walk specification is flexible

enough to capture cyclical changes in volatility as well as permanent phenomena such as the Great

Moderation.

Index of uncertainty

1

N

N∑i=1

√λiσ2

ελ′i + σ2

u,i

SCALE2i

(10)

17

Figure 3: LONG-RUN COMPONENTS OF US GDP GROWTH

(a) Real GDP Growth and Estimated Long-Run Growth Rate

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

-4

-2

0

2

4

6

8

10

(b) Estimated Time-Varying Volatility of the Common Activity Factor

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 20150

1

2

3

4

5

6

7

Note: .

18

Figure 4: UNCERTAINTY INDEX

Notes.

19

4.2 Heterogeneous dynamics

Remember Figure 1, Panel (b). The fit is very similar for the survey variables, but can be very

different for the hard data. The heterogeneous model estimates that a meaningful part of the

variation in this series is due to common activity shocks, but which are propagated in a different

manner.

Inspection of the estimated impulse responses to a common shock (Figure 5) reveals that

certain variables, like GDP, industrial production, or lightweight vehicle sales, respond to common

shocks with a rapidly decaying pattern, whereas others, like surveys, respond with a hump shaped

pattern. Given that the surveys are very persistent, and have a common hump-shaped pattern,

they essentially dominate the results whenever a homogeneous model is used. This justifies the

practice of Camacho and Perez-Quiros (2010) of treating the soft data as a distributed lag of the

activity factor, but generalizes it to all variables and estimates, rather than fixes, the pattern of lags.

The addition of heterogeneous dynamics allows to increase the weight given to hard variables

while retaining the parsimonious one-factor structure.

Figure 5: IRFS OF SELECTED VARIABLES TO A COMMON SHOCK

0 5 10 15 20

Months

0

0.2

0.4

0.6

0.8

1Monotonic

GDPINDPROCONSUMPTION

0 5 10 15 20

Months

-1

0

1

2

3Reversing

CARSALESHOUSINGSTARTSNEWHOMESALES

0 5 10 15 20

Months

0

0.5

1

1.5

2

2.5Hump Shaped

ISMMANUFPHILLYFEDCHICAGO

Note: This figure displays the impulse response functions (IRFs) of different variables to an innovation in the processof the dynamic factor. The blue dotted lines show IRFs to a contemporaneous factor (which are all proportional to theIRF of the factor itself) while the red lines represent IRFs from a model that allows for heterogeneous dynamics. Thethree panels of the figure group these IRFs into categories based on the different shapes of the responses (‘monotonic’,‘reversing’ and ‘hump-shaped’), that arise from the possibility of lead-lag responses.

20

Figure 6: UNPACKING HETEROGENEOUS DYNAMICS

(a) Cross Correlogram

-6 -4 -2 0 2 4 6

lag (months)

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

corr

elat

ion

Without lags With lags

(b) Static vs. dynamic factors

Notes.

21

4.3 Interpreting the data flow in the presence of outliers

Assuming Normally distributed innovations, as is commonly done in the literature, is such that

the impact of the information from these variables in the nowcasting process is downplayed.

Moreover, since outliers are typically more common in the hard data as opposed to the soft data,

the presence of the outliers tends to push the model toward overemphasizing the importance of

the soft indicators.

Banbura and Modugno (2014) show in a Gaussian model that the impact of a new release on

the nowcasts can be written as a linear function of the news:

E(yk,tk|Ω2)− E(yk,tk|Ω1) = wj (yj,tj − E(yj,tj |Ω)) (11)

wj =ΛkE

((ftk − ftk|Ω)(ftj − ftjΩ)

)Λ′j

ΛjE(

(ftj − ftj |Ω)(ftj − ftjΩ))

Λ′j + σ2ηj,tj

(12)

We show that with the Student-t distribution the weights are no longer linear, but depend on

the value of the forecast error itself:

E(yk,tk|Ω2)− E(yk,tk|Ω1) = wj(yj,tj) (yj,tj − E(yj,tj |Ω)) (13)

wj(yj,tj) =ΛkE

((ftk−ftk|Ω)(ftj−ftjΩ)

)Λ′j

ΛjE(

(ftj−ftj |Ω)(ftj−ftjΩ))

Λ′j+σ2ηj,tj

δj,tj(14)

δj,tj = (((yj,tj − E(yj,tj |Ω))2/σ2ηj,tj + vo,j)/(vo,i + 1) (15)

Large errors are discounted as outlier observations containing less information. This is reflected in

the so-called “influence functions”, which measure the expected update of the common factor to

news of a given standard deviation. Figure 7 displays the influence functions. For a model with

Gaussian innovations, the update of the factor is a line with slope equal to wi,j . These are displayed

as the blue lines in Figure 7. As can be seen, noisy variables such as car sales have very low weights,

meaning that surprises to this variable lead to small updates to the current factor. With t-distributed

outliers, the influence functions are now the S-shaped red lines of Figure 7. Around the origin, i.e.,

22

for a small surprise, the function is close to linear, but as the surprise increases in size the update of

the factor tapers off, and eventually can decrease in size. The intuition is clear: if one observes a

three- or four standard deviation surprise, it is increasingly likely that that observation represents

a one-off outlier in the data, and therefore our estimate of underlying economic activity should

respond less to those “news”.

Figure 7: INFLUENCE FUNCTIONS

-5 0 5Forecast Error (standard deviations)

-0.5

0

0.5

Now

cast

Upd

ate

(per

cent

age

poin

ts a

nn.) Industrial Production


-0.5

0

0.5Initial Unemployment Claims


-0.5

0

0.5Personal Income

Note: The panels of the figure plot the influence functions for different variables, that is, by how much the estimate of thedynamic factor is updated when the release in the variable is different from its forecast and thus contains “news”. Theblue lines plot these influence functions in the Gaussian case while the red lines represent the student-t case. As shownin equations (11) - (15) the model with fat tails allows these functions to be nonlinear and nonmonotonic.

4.4 Daily tracking of economic activity

23

Figure 8: DAILY TRACKING OF ECONOMIC ACTIVITY

Notes.

24

5 Out-of-sample evaluation and model comparison

5.1 Setup

We evaluate the point and density forecast accuracy relative to the third release of all the indicators.

As is common in the literature, we pay particular attention to evaluating the “advance” estimate of

GDP, which is released between 25 and 30 days after the end of the reference quarter.6

When comparing the five different models, we test the significance of any improvement of

Models 1-4 relative to Model 0. This raises some important econometric complications given that

(i) the five models are nested, (ii) the forecasts are produced using an expanding window, and (iii)

the data used is subject to revision. These three issues imply that commonly used test statistics for

forecasting accuracy, such as the one proposed by Diebold and Mariano (1995) and Giacomini and

White (2006) will have a non-standard limiting distribution. However, rather than not reporting

any test, we follow the “pragmatic approach” of Faust and Wright (2013) and Groen et al. (2013),

who build on Monte Carlo results in Clark and McCracken (2012). Their results indicate that the

Harvey et al. (1997) small sample correction of the Diebold and Mariano (1995) statistic results in

a good sized test of the null hypothesis of equal finite sample forecast precision for both nested

and non-nested models, including cases with expanded window-based model updating. Overall,

the results of the tests should be interpreted more as a rough gauge of the significance of the

improvement than a definitive answer to the question. We compute various point and density

forecast accuracy measures at different moments in the release calendar, to assess how the arrival

of information improves the performance of the model. In particular, the computations are carried

out starting 180 days before the end of the reference quarter, and every subsequent day up to 25

days after its end, when the GDP figure for the quarter is usually released. This means that we

will evaluate the forecasts of the next quarter, current quarter (nowcast), and the previous quarter

(backcast). We consider two different samples for the evaluation: the full sample (2000:Q1-2016:Q4)

and the sample covering the recovery since the Great Recession (2009:Q2-2016:Q4).

6We have explored the alternative of evaluating the forecasts against subsequent releases, or the latest availablevintages. The relative performance of the five models is broadly unchanged, but all models do better at forecasting theinitial release. If the objective is to improve the performance of the model relative to the first official release, then ideallyan explicit model of the revision process would be desirable. The results are available upon request.

25

5.2 Point Forecast Evaluation

Figure 9 shows the results of evaluating the posterior mean as point forecast. We use two criteria,

the root mean squared error (RMSE) and the mean absolute error (MAE). As expected, both of these

decline as the quarters advance and more information on monthly indicators becomes available,

see e.g. Banbura et al. (2012). Both the RMSE and the MAE of Model 2 are lower than that of Model

0, particularly so from the start of the nowcasting period, while Model 1 is somewhat worse overall.

Our gauge of significance indicates that these differences in nowcasting performance are significant

at the 10% level for the overall sample in the case of the MAE, but not the RMSE. The improvement

in performance is much clearer in the recovery sample. In fact, the inclusion of the time varying

long run component of GDP helps anchor GDP predictions at a level consistent with the weak

recovery experienced in the past few years and produces nowcasts that are ‘significantly’ superior

to those of the reference model from around 30 days before the end of the reference quarter. In

essence, ignoring the variation in long-run GDP growth would have resulted in being on average

around 1 percentage point too optimistic from 2009 to 2015. TO DO: Need to add description of

results from evaluation of Model 4.

26

Figure 9: POINT FORECAST EVALUATION: RMSE

(a) Evolution of RMSE as the data flow arrives

-180 -150 -120 -90 -60 -30 0

NowcastForecast Backcast

1.4

1.6

1.8

2

2.2

2.4

2.6

Model 0 Model 1 Model 2 Model 3

(b) Evolution of RMSE through time

Notes. Panel(a): The horizontal axis indicates the forecast horizon, expressed as the number of days to the end of thereference quarter. Thus, from the point of view of the forecaster, forecasts produced 180 to 90 days before the end ofa given quarter are a forecast of next quarter; forecasts 90-0 days are nowcasts of current quarter, and the forecastsproduced 0-25 days after the end of the quarter are backcasts of last quarter. The boxes below each panel display, with avertical tick mark, a gauge of statistical significance at the 10% level of any difference with Model 0, for each forecasthorizon, as explained in the main text. Panel (b): .

27

Figure 10: US GDP NOWCASTS WITH AND WITHOUT TIME-VARYING LR GROWTH

GDP: Model forecasts vs realizations, day before release

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

-8

-6

-4

-2

0

2

4

6

Actual Model 0 Model 1

Note: The black line represents the time series of actual real GDP growth in the United States. The blue line plots thenowcasts for real GDP growth based on information up to this point using a model without time-varying long-rungrowth (Model 0). The red line plots the nowcasts when time variation in long run growth is added (Model 1). The blueand red shaded areas indicate the corresponding density around the nowcasts. It is visible that the nowcasts form Model0 exhibit an upward bias in the later part of the sample.

28

5.3 Density Forecast Evaluation

Density forecasts can be used to assess the ability of a model to predict unusual developments,

such as the likelihood of a recession or a strong recovery given current information. The adoption

of a Bayesian framework allows us to produce density forecasts from the DFM that consistently

incorporate both filtering and estimation uncertainty.

There are several measures available for density forecast evaluation. The (average) log score,

i.e. the logarithm of the predictive density evaluated at the realization, is one of the most popular,

rewarding the model that assigns the highest probability to the realized events. Gneiting and Raftery

(2007), however, caution against using the log score, emphasizing that it does not appropriately

reward values from the predictive density that are close but not equal to the realization, and

that it is very sensitive to outliers. They therefore propose the use of the (average) continuous

rank probability score (CRPS) in order to address these drawbacks of the log-score. Figures C.3

and 11 show that by both measures our model outperforms its counterparts. Interestingly, the

comparison of Model 1 and Model 2 suggests that failing to properly account for the long-run

growth component might give a misrepresentation of the GDP densities, resulting in poorer density

forecasts. TO DO: Need to add description of results from evaluation of Models 3 and 4.

5.4 Forecasting monthly indicators

Table 1: NOWCASTING MONTHLY INDICATORS

RMSE

CRPS

Notes:

29

Figure 11: DENSITY FORECAST EVALUATION: CRPS

(a) Evolution of CRPS as the data flow arrives

-180 -150 -120 -90 -60 -30 0


0.5

1

1.5


(b) Evolution of CRPS through time


30

6 An application to the Covid-19 recession

The Covid-19 episode has been posing a dramatic challenge to the monitoring of macroeconomic

conditions.

6.1 Incorporating alternative data

Bla

6.2 Real-time tracking in 2020

Figure 12: FIGURE TO BE DISCUSSED

Notes.

31

7 Conclusion

In this paper we have proposed a bayesian DFM, which incorporates low-frequency variation

in the mean and variance of the variables, heterogeneous responses to common shocks, outlier

observations and fat tails. In a comprehensive evaluation exercise based on fully real-time unrevised

data from various countries, we have demonstrated that the real-time nowcasting performance is

substantially improved across a variety of metrics.

Capturing trends and SV improves nowcasting performance significantly across countries.

Heterogeneous dynamics deliver substantial additional improvement. Fat tails successfully capture

outlier observations in an automated way, help in extracting a well-behaved factor, and improve

density forecasts of the monthly variables.

Overall, we provide a thorough assessment of novel model features for the nowcasting process

across many countries and variables, and demonstrate how they contribute to improving point and

density nowcasts in real time.

32

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36

Online Appendix to“Nowcasting Economic Activity with Secular Trends, Large Shocks and

Alternative Data”

by Juan Antolin-Diaz, Thomas Drechsel and Ivan Petrella

Contents

A Treatment of the missing observations in the vectorized Kalman Smoother 2

B Details on model and algorithm 2

B.1 Details of the Gibbs Sampler Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 2

B.2 Procedure to Set the Scale of the Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

B.3 Data Series Included in the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

C Additional results 4

1

A Treatment of the missing observations in the vectorized Kalman

Smoother

B Details on model and algorithm

B.1 Details of the Gibbs Sampler Algorithm

B.2 Procedure to Set the Scale of the Priors

We follow the following procedure to set the scale of the priors.

• The variables are divided into groups.

2

B.3 Data Series Included in the Analysis

Table B.1: DATA SERIES USED FOR US EMPIRICAL ANALYSIS

Type Start Date Transform. Lag

QUARTERLY TIME SERIES

Real GDP Expenditure & Inc. Q2:1947 % QoQ Ann 26Real GDI Expenditure & Inc. Q2:1947 % QoQ Ann 26Real Consumption (excl. durables) Expenditure & Inc. Q2:1947 % QoQ Ann 26Real Investment (incl. durable cons.) Expenditure & Inc. Q2:1947 % QoQ Ann 26Total Hours Worked Labor Market Q2:1948 % QoQ Ann 28

MONTHLY INDICATORS

Real Personal Income less Transfers Expenditure & Inc. Feb 59 % MoM 27Industrial Production Production & Sales Jan 47 % MoM 15New Orders of Capital Goods Production & Sales Mar 68 % MoM 25Real Retail Sales & Food Services Production & Sales Feb 47 % MoM 15Light Weight Vehicle Sales Production & Sales Feb 67 % MoM 1Real Exports of Goods Foreign Trade Feb 68 % MoM 35Real Imports of Goods Foreign Trade Feb 69 % MoM 35Building Permits Housing Feb 60 % MoM 19Housing Starts Housing Feb 59 % MoM 26New Home Sales Housing Feb 63 % MoM 26Payroll Empl. (Establishment Survey) Labor Market Jan 47 % MoM 5Civilian Empl. (Household Survey) Labor Market Feb 48 % MoM 5Unemployed Labor Market Feb 48 % MoM 5Initial Claims for Unempl. Insurance Labor Market Feb 48 % MoM 4

MONTHLY INDICATORS (SOFT)Markit Manufacturing PMI Business Confidence May 07 - -7ISM Manufacturing PMI Business Confidence Jan 48 - 1ISM Non-manufacturing PMI Business Confidence Jul 97 - 3NFIB Small Business Optimism Index Business Confidence Oct 75 Diff 12 M. 15U. of Michigan: Consumer Sentiment Consumer Confid. May 60 Diff 12 M. -15Conf. Board: Consumer Confidence Consumer Confid. Feb 68 Diff 12 M. -5Empire State Manufacturing Survey Business (Regional) Jul 01 - -15Richmond Fed Mfg Survey Business (Regional) Nov 93 - -5Chicago PMI Business (Regional) Feb 67 - 0Philadelphia Fed Business Outlook Business (Regional) May 68 - 0

Notes: % QoQ Ann refers to the quarter on quarter annualized growth rate, % MoM refers to(yt− yt−1)/yt−1 while Diff 12 M. refers to yt− yt−12. The last column shows the average publicationlag, i.e. the number of days elapsed from the end of the period that the data point refers to until itspublication by the statistical agency. All series were obtained from the Haver Analytics database.

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C Additional results

Figure C.1: INFLUENCE FUNCTIONS FOR ALL VARIABLES

-5 0 5-0.5

0

0.5INDPRO

-5 0 5-0.5

0

0.5NEWORDERS

-5 0 5-0.5

0

0.5CARSALES

-5 0 5-0.5

0

0.5INCOME

-5 0 5-0.5

0

0.5RETAILSALES

-5 0 5-0.5

0

0.5EXPORTS

-5 0 5-0.5

0

0.5IMPORTS

-5 0 5-0.5

0

0.5PERMIT

-5 0 5-0.5

0

0.5HOUSINGSTARTS

-5 0 5-0.5

0

0.5NEWHOMESALES

-5 0 5-0.5

0

0.5PAYROLL

-5 0 5-0.5

0

0.5EMPLOYMENT

-5 0 5-0.5

0

0.5UNEMPLOYMENT

-5 0 5-0.5

0

0.5CLAIMS

-5 0 5-0.5

0

0.5MARKITPMI

-5 0 5-0.5

0

0.5ISMMANUF

-5 0 5-0.5

0

0.5ISMNONMAN

-5 0 5-0.5

0

0.5CONSCONF

-5 0 5-0.5

0

0.5CONSSENT

-5 0 5-0.5

0

0.5RICHMOND

-5 0 5-0.5

0

0.5PHILLYFED

-5 0 5-0.5

0

0.5CHICAGO

-5 0 5-0.5

0

0.5NFIB

-5 0 5-0.5

0

0.5EMPIRE

Note: The panels of the figure plot the influence functions for different variables, that is, by how much the estimate of thedynamic factor is updated when the release in the variable is different from its forecast and thus contains “news”. Theblue lines plot these influence functions in the Gaussian case while the red lines represent the student-t case. As shownin equations (11) - (15) the model with fat tails allows these functions to be nonlinear and nonmonotonic.

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Figure C.2: POINT FORECAST EVALUATION: MAE

(a) Evolution of MAE as the data flow arrives

(b) Evolution of MAE through time


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Figure C.3: DENSITY FORECAST EVALUATION: LOG SCORE

(a) Evolution of Log Score as the data flow arrives

-180 -150 -120 -90 -60 -30 0


-2.5

-2

-1.5


(b) Evolution of Log Score through time


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nowcasting economic activity with secular trends, large ...nowcasting economic activity with secular...

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