Macroeconomic Forecasting using Low‐frequency Filters
| Author | Ana Pereira,João Valle e Azevedo |
| DOI | http://doi.org/10.1111/obes.12194 |
| Published date | 01 February 2018 |
| Date | 01 February 2018 |
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©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 1 (2018) 0305–9049
doi: 10.1111/obes.12194
Macroeconomic Forecasting using Low-frequency
Filters*
Jo ˜
ao Valle e Azevedo†,‡ and Ana Pereira†,§
†Banco de Portugal: Av. Almirante Reis 71, 6th floor, 1150-012, Lisbon, Portugal (e-mail:
azevedojv@gmail.com)
‡Nova School of Business and Economics, Campus de Campolide, 1099-032 Lisbon, Portugal
§Instituto Superior de Economia e Gest¨ao, Rua do Quelhas 6, 1200-781 Lisbon, Portugal
(e-mail: ana.regina.pereira@gmail.com)
Abstract
We consider univariate low-frequency filters applicable in real-time as a macroeconomic
forecasting method. This amounts to targeting only low frequency fluctuations of the time
series of interest. We show through simulations that such approach is warranted and, using
US data, weconfir m empiricallythat consistent gains in forecast accuracy can be obtained in
comparison with a variety of other methods. There is an inherent arbitrariness in the choice
of the cut-off defining low and high frequencies, which calls for a careful characterization
of the implied optimal (for forecasting) degree of smoothing of the key macroeconomic
indicators we analyse.We document interesting patterns that emerge: for most variables the
optimal choice amounts to disregarding fluctuations well belowthe standard business cycle
cut-off of 32 quarters while generally increasing with the forecast horizon; for inflation
and variables related to housing this cut-off lies around 32 quarters for all horizons, which
is below the optimal level for federal government spending.
I. Introduction
This paper considers univariate predictions of the low-frequencies of macroeconomic time
series as a forecasting method. The idea is to project only low frequencies of the time series
of interest onto past observations, or using a low-pass filter applicable in real time.We then
treat these projections as forecasts of the original time series. This may be more efficient
than targeting the original series, which contains (mostly) unpredictable high-frequency
components, especially at long horizons. Our approach follows the principle of decoupling
model/parameter estimation from forecasting or, more generally, signal extraction. This
means that forecasts are not computed as the model implied ‘optimal’ forecasts (under
correct specification and true parameter values) but, instead, they are the solution to a
general signal extraction problem that imposes little or no parametric structure to the
moments of the data (see Wildi, 2008 for an exhaustive analysis of this distinction). Here,
JEL Classification numbers: C14, C32, C51, C53
*We are grateful to Paulo Rodrigues and Ant´onio Rua for insightful comments. All errors are ours. The views
expressed are those of the authors and do not necessarily represent those of the Banco de Portugal or the Eurosystem.
40 Bulletin
we additionally reduce the problem of forecasting into one of predicting a smooth (or
filtered) version of the time series of interest.
An approach close to ours in spirit is that of new EuroCoin indicator of Altissimo et al.
(2010). We use a univariate approach while the new Eurocoin is multivariate but does not
include observations of the series of interest in the projections.1Additionally, we do not
prefilter the series of interest to construct the projection. We use instead the solution to
a generic signal extraction problem. Finally, we do not restrict ourselves to a particular
cut-off period or to very short horizons (Altissimo et al., 2010 concentrate on a cut-off of
12 months and on horizons up to two quarters, with a clear focus on nowcasting); we try
instead to characterize the optimal cut-off while looking at horizons up to three years.
Weperfor m a simple Monte Carlo simulation to show that even when the parameters of
a very parsimonious autoregression (AR) are efficiently estimated, the forecasts produced
by the typical AR forecast function are often outperformed by a low-frequency projection
(filter), using the same information. We also conduct a pseudo out-of-sample forecasting
exercise focusing on 13 key US macroeconomic indicators (all of them forecasted in
the Philadelphia Survey of Professional Forecasters, SPF henceforth). We show that our
method produces significant and consistent forecast accuracy gains in practice, even when
compared to methods that explore information from a large panel of predictors. The results
lend clear support to the use of this simple method as a benchmark in macroeconomic
forecasting studies. They also call for a careful theoretical analysis of these low-frequency
projections, one that elucidates the trade-off between the information loss due to filtering
and the forecast accuracy gains obtained by focusing on (the more) predictable fluctuations
of the time series.
A relevant choice when using this method is the cut-off defining low and high frequen-
cies. The optimal (for forecasting) cut-off mayvary across series and forecast horizons but
we show that clear patterns characterize groups of time series in terms of the implied opti-
mal degree of smoothing. For most variables, the optimal choice amounts to disregarding
fluctuations well below the standard business cycle cut-off of 32 quarters while generally
increasing (slowly) with the forecast horizon; for CPI inflation and variables related to
housing this cut-off lies around 32 quarters for all horizons. This is belowthe optimal level
for federal spending, which lies around 44–48 quarters. Importantly, the results are robust
to relevant deviations from this optimal degree of smoothing. A good compromise across
variables and forecast horizons is achieved by using a standard cut-off of 16 quarters.
The outline of the paper is as follows: in section II, we make clear how the low-
frequency projections are constructed. Section III presents some Monte Carlo results.
1The New Eurocoin indicator of Altissimo et al. (2010) targets a monthlymeasure of quar terlyGDP growth free
of fluctuations with period less than one year. New EuroCoin is obtained by projecting such medium to long run
component of output growth onto monthlyf actors estimated bygeneralized principal components. These factors span
the subspace of the factor space not containing fluctuations with period less than 12 months. The objective is to have
an indicator free of short-run oscillations, just as the target. Observations of GDP are not used as covariates in the
implicit filter. We project instead fluctuations of the series of interest below a specified (and not necessarily fixed)
cut-off onto unsmoothed availableobservations of that series of interest. Earlier work by Vallee Azevedo and Pereira
(2013) reveals that these are the single most important observations (taking into account the objective of minimizing
the prediction error) even in a multivariate setting.We should refer that the current paper was motivated by the desire
to extend those results to a wider range of macroeconomic time series while trying to characterize the optimal degree
of smoothing for forecasting across variables and horizons. What we found wasthat the gains relative to the simple
univariate filter (that we analysein this paper) were most often, if anything, very slim.
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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