Terence C. Mills and Kerry Patterson xviidistinction between, for example, a variable being empiricallyI(d)rather than
structurallyI(d); a leading example here is theI( 2 )case which, unlike theI( 1 )
case, has attracted some “suspicion” when applied in an absolute sense to empiri-
cal series. The challenging empirical case considered by Juselius is the relationship
between German and US prices and nominal exchange rates within a sample that
includes the period of German reunification. The methodology lies firmly within
the framework of general-to-specific modeling, in which a general unrestricted
model is tested down (see also Hendry, Chapter 1) to gain as much information
without empirical distortion. A key distinction in the methodological and empir-
ical analysis is between pushing and pulling forces: in the current context, prices
push whereas the exchange rate pulls. PPP implies that there should be just a sin-
gle stochastic trend in the data, but the empirical analysis suggests that there are
two, with the additional source of permanent shocks being related to speculative
behaviour in the foreign exchange market.
In an analysis of trends and cycles, economists often characterize the state of
the economy in terms of indirect or latent variables, such as the output gap, core
inflation and the non-accelerating rate of inflation (NAIRU). These are variables
that cannot be measured directly, but are nevertheless critical to policy analysis.
For example, the need to take action to curb inflationary pressures is informed by
the expansionary potential in the economy; whether or not a public sector bud-
get deficit is a matter for concern is judged by reference to the cyclically adjusted
deficit. These concepts are at the heart of Chapter 9 by Tommaso Proietti, entitled
“Structural Time Series Models for Business Cycle Analysis,” which links with the
earlier chapters by Pollock and Cardinale and Taylor. Proietti focuses on the mea-
surement of the output gap, which he illustrates throughout using US GDP. In the
simplest case, what is needed is a framework for decomposing a time series into a
trend and cycle and Proietti critically reviews a number of methods to achieve such
a decomposition, including the random walk plus noise (RWpN) model, the local
linear trend model (LLTM), methods based on filtering out frequencies associated
with the cycle, multivariate models that bring together related macroeconomic
variables, and the production function approach. The estimation and analysis of a
number of models enables the reader to see how the theoretical analysis is applied
and what kind of questions can be answered. Included here are a bivariate model
of output and inflation for the US and a model of mixed data frequency, with quar-
terly observations for GDP and monthly observations for industrial production, the
unemployment rate and CPI inflation. The basic underlying concepts, such as the
output gap and core inflation, are latent variables and, hence, not directly observ-
able: to complete the chapter, Proietti also considers how to judge the validity of
the corresponding empirical measures of these concepts.
To complete the part of theHandbookon Times Series Applications, in Chapter
10 Luis Gil-Alana and Javier Hualde provide an overview of fractional integration
and cointegration, with an empirical application in the context of the PPP debate.
A time series is said to be integrated of orderd, wheredis an integer, ifdis the min-
imum number of differences necessary to produce a stationary time series. This is
a particular form of non-stationarity and one which dominated the econometrics