International Journal of Forecasting 16 (2000) 207–227 www.elsevier.com / locate / ijforecast
Forecasting OECD industrial turning points using unobserved components models with business survey data *, Marcos Bujosa-Brun ´ Antonio Garcıa-Ferrer ´ ´ ´ Cuantitativa, Ciudad Universitaria de Cantoblanco, , Economıa Departamento de Analisis Economico ´ Universidad Autonoma de Madrid, 28049 Madrid, Spain
Abstract The approach followed in this paper stresses the importance of timing in signalling turning points. This is done in two stages; first a signal that a turning point is likely to occur, and later a statement of when it will occur. We use Young’s trend derivative method, adding leading qualitative survey data. We find high coherence between its low frequency component and that of the corresponding economic variable. We study industrial production in six OECD countries with special emphasis on France and Spain. Inclusion of survey data improves forecast accuracy. 2000 Elsevier Science B.V. All rights reserved. Keywords: Turning point forecasting, Unobserved components and qualitative survey data
1. Introduction There is a long tradition in business cycle forecasting to focus on turning points. Gross National Product and Industrial Production are the most frequently used reference series. Earlier studies show that these series are not periodic but recurring. Neither are the sizes of the fluctuations stable over time, Westlund (1993). Second, given the difficulties in developing one simple theory that encompasses all the basic features of business cycles, there are *Corresponding author. Tel.: 134-91-3974811; fax: 134-91-3974091. ´ E-mail address:
[email protected] (A. GarcıaFerrer)
no simple reliable forecasting procedures, Gar´ cıa-Ferrer and Queralt (1998b). Third, turning point forecasting is often based on the use of leading indicators requiring special types of models, data and methodology, as well as an explicit definition of the turning point notion, Zellner et al. (1991). It is also well known that quantitative forecast evaluation becomes harder when we focus on the model’s ability to forecast turning points. This is a crucial issue, because business people and policy-makers are often less interested in GNP growth rates forecasts than in answers to simple questions like ‘‘Is consumption going to take off next quarter?’’ or, ‘‘Will present inflation rates remain low next year?’’ To address such questions a growing litera-
0169-2070 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0169-2070( 99 )00049-7
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ture has developed to estimate the probability that a turning point will occur at some future unspecified date. We follow an alternative that stresses the importance of timing when forecasting turning points. A turning point signal is considered as a two-stage decision process: a statement that a turning point is likely to occur (anticipation of the recession), and a statement of when it will occur (confirmation of the recession). To address this strategy we start ´ ´ from Garcıa-Ferrer et al. (1994) and GarcıaFerrer and Queralt (1998a) that use univariate unobserved components models with time varying parameters, developed by Young (1994) and Young et al. (1999). In particular, the first of these references uses the derivative of the unobserved trend component as a device for qualitative anticipation of peaks and troughs, as well as to provide alternative definitions of expansions and recessions in the economy. ´ More recently, Garcıa-Ferrer and Queralt (1998a) suggest a simple method for improving quantitative point forecasts for a large set of seasonal monthly time series of the Spanish economy. This paper shares the same methodological approach, but generalizes the results by introducing qualitative survey data. Business Tendency Surveys (BTS) in many countries are becoming increasingly popular as leading indicators (LI), given their prompt availability and lack of systematic revisions. If, additionally, we can find a high coherence between the LI low frequency component and the reference variable, we may be able to use this relationship to obtain improved forecasts of turning points. That question has been studied by many researchers over the years and the results are relatively mixed. While Hanssens and Vanden Abeele (1987) claim that BTS are not useful for this purpose, more recent studies by Madsen ¨ ¨ (1993); Kauppi and Terasvirta (1996); Oller and ¨ Tallbom (1996) and Rahiala and Terasvirta (1993) found predictive survey information useful in short-term forecasting. Our results confirm the latter finding.
This paper is organized as follows: the next section describes the theoretical framework. Section 3 proposes a turning point characterization, using monthly industrial production for six OECD countries. Section 4 analyses the behavior and forecasting performance of the model when the BTS-variable Industrial New Orders (INO) is used as a leading indicator for manufacturing in France and Spain. Finally, Section 5 discusses the implications of the results for existing and future empirical work.
2. The theoretical framework It is reasonable to assume that economic time series are particularly appropriate for a time varying parameters modeling approach. Since over a long period of time, the economic system may be nonlinear, it seems logical to allow for variation in model parameters. Following Young (1994) we can write the unobserved components model of a seasonal time series Yt as Yt 5 T t 1 St 1 et
(1)
where T t is a low frequency trend component, St 2 is a seasonal component; and et is i.i.d. (0,s e ). Eq. (1) may be appropriate for dealing with economic data, exhibiting pronounced trend and seasonality, as is the case with the monthly variables used in this paper. It is assumed that the trend can be represented by a local linear Integrated Random Walk (IRW) of the form, T t 5 T t 21 1 Dt 21 Dt 5 Dt 21 1 j t
(2)
where Dt denotes the local slope or derivative of the trend, and j t is i.i.d. (0,s 2j ). and et and j t are mutually independent. The IRW trend model is an interesting alternative to modeling low frequency components with a minimum number of unknown parameters. In Eq. (2) only j t is unknown and it can be defined by the Noise Variance Ratio (NVR):
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s 2j NVR 5 ]2 se
(3)
It is also assumed that the seasonal component can be adequately represented by a Dynamic Harmonic Regression (DHR),
O ha coss2pf td 1 b sins2pf tdj F
St 5
jt
j
jt
j
(4)
j51
where fj , j 5 1,2, . . . ,F are the frequencies in cycles per units of time, and the regression coefficients a jt , b jt , j 5 1,2, . . . ,F are time variable parameters that can handle nonstationary seasonality. It is assumed that parameter variation in a j and b j can be expressed as random-walks a jt a jt 21 mjt (5) b jt 5 b jt 21 1 h jt ,
F G F G F G
where again mjt and h jt are i.i.d. with expected values zero and variances s 2m and s 2h , respectively. Furthermore, m and h should be mutually independent. This assumption is useful for time series with growing amplitude seasonality, as is commonly found in many economic time series data. Young (1994) has shown that the DHR model is an extension of classical Fourier analysis, with the number of frequencies (2p f ) limited by the number of observations. In the DHR model, the number of frequencies is constrained by the requirement of spectral separation of the model components. Also, parameter variation should be chosen such that the components take on well defined shapes (Young et al. (1999)). Both the trend and the seasonal models can be formulated in state-space form and it is straightforward to assemble both structures into an aggregate state-space model (Ng and Young (1990)). On the other hand, expressions for the power spectra of the IRW/ DHR models are ´ derived in Garcıa-Ferrer and Queralt (1998a) and Young et al. (1999) that also provide the details of the Quasi-Fisher estimation algorithm.
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3. Turning point characterization with monthly seasonal data The problem of defining what constitutes a turning point has attracted considerable attention in the literature, because of its close relationship with business cycle dating. With the exception of annual data, where turning points are easily defined, the remaining data frequencies often present many situations where precise definitions of recessions and contractions are case dependent, cf. Hess and Iwata (1997). Even for seasonally-adjusted quarterly data, using the NBER rule for defining a recession as the first of at least two successive quarters of decline in seasonal differences of GNP, has had serious flaws in characterizing business cycle facts (McNees (1991)). Further modifications of ´ ´ this criterion (e.g. Garcıa-Ferrer and Sebastian (1996)) also indicate that no simple rule is sufficient to translate quarterly GNP changes into official cyclical turning points. Somehow, there seems to be a need for ad hoc rules that work with certain types of data and also may hold for future turning points in a large number of cases. When using seasonally unadjusted data these ad hoc criteria abound. In the case of Swedish ¨ quarterly data, Oller and Tallbom (1996) define a turning point where the seasonal logarithmic difference, =4 y t changes sign, and keeps it for at least four quarters. However, direct translation of this rule when using monthly data leads to an excessive number of turning points making it useless. An alternative solution is to propose a new set of definitions of recessions and expansions which, in our case, are directly linked to the IRW trend derivative, outlined in the previous section. The IRW trend model seems to have some advantages over other procedures. Although most of the alternatives may track the long term behavior in any time series equally well, when we look at their associated first difference transformations the picture changes dramatically. In some cases, estimated trends
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actually contain some higher frequency components related to the annual cycle, which are then amplified by the differencing operation, (cf. ´ Morales and Rojo (1992); Garcıa-Ferrer and Queralt (1998a)). Therefore, using the IRW trend derivative, our goal is simply to formalize and make transparent an alternative definition of turning points when using monthly seasonal data.
3.1. Definitions We first define the anticipation of a recession at time t as the point where the trend derivative reaches its maximum numerical value. We then define the confirmation of a recession as the point where the derivative becomes negative and remains so for at least six months. Analogously, we define the anticipation of an expansion at the derivative’s minimum; and the confirmation of an expansion when the derivative becomes positive and remains so for at least nine months. The empirical time differences for an expansion and a recession are somehow heuristic and based on empirical observations over a large set of monthly economic series. Additionally, the turning point characterization obtained following these rules must always agree with the information provided by annual growth rates of the reference variable. All the concepts just defined are illustrated in the following section for a set of Industrial Production Indexes (IPI).
3.2. Turning point dating for industrial production indexes In this subsection we consider series of monthly industrial production indexes in six OECD countries: France, Italy, Japan, Spain, United Kingdom and United States. With the exception of France, all series are from the period January 1975 to December 1998. Germany was excluded, because post-reunification
time-series were too short. In all countries in the sample, IPIs are high quality indicators of the country’s industrial activity. Because of accentuated seasonals, we use IRW/ DHR models. In this case, the trend’s NVR is updated during estimation, and the NVR values associated with the main seasonal frequency (and its harmonics) are also estimated recursively. The AR spectral estimates have peaks at 12, 6, 4, 3, 2.4 and 2 (6th harmonic) months, so the annual frequencies used in the subsequent analysis will be 0, 1 / 12, 1 / 6, 1 / 4, 1 / 3, 5 / 12 and 1 / 2. Industrial production indexes (in logs) and their estimated IRW trends for the period 1975.1 to 1998.12 are shown in Fig. 1 where both nonstationarity in the mean and strong seasonality are evident. In Table 1, annual growth rates of IPI for each country are presented. Two common recession periods can be identified: 1980–82, and 1990–1993. Furthermore, mild recessions affected individual countries: UK, in 1984; Italy in 1985, and Japan, in 1986. The 1996 recession hit both Italy and Spain and, to a lesser degree, France. Japan has a substantial drop in 1998, not shared by any of the remaining countries in the sample. In general, both the intensity and the duration of the recessions change from cycle to cycle. NVR estimates for all countries using the whole sample are shown in Table 2. There are large differences in the trend NVR estimates between the US and Japan, on the one hand, and the remaining countries on the other. This indicates less smooth trends than in the European countries. Differences are also large in the main seasonal frequency (H:12), while the remaining seasonal harmonics estimates vary much less. Using the trend estimates of Table 2, we have obtained and plotted the IRW trend derivatives for each country in Fig. 2. Shaded areas are recession periods according to the definitions stated in Section 3.1 and the complete IPI’s turning point characterization is summarized in Table 3. At this point, it is worth
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Fig. 1. OECD countries’ industrial production (in logs) and estimated IRW trends, 1975.1–1998.12.
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Table 1 Annual growth rates: 1976–1998 Year
France
Italy
Japan
1976 1977 1978 1979 1980
9.03 1.79 2.20 4.49 21.00
11.7 1.19 1.85 6.46 4.80
10.5 4.13 6.11 7.09 4.62
1981 1982 1983 1984 1985
21.06 20.88 0.14 1.77 1.49
22.98 23.06 22.08 3.58 20.23
1986 1987 1988 1989 1990
0.56 1.23 4.57 3.66 1.57
1991 1992 1993 1994 1995 1996 1997 1998
UK
US
4.94 5.04 2.31 0.78 1.00
3.26 5.09 2.91 3.69 26.83
8.80 7.86 5.69 3.31 22.82
0.98 0.34 3.13 8.92 3.63
21.11 21.17 2.77 1.02 1.81
23.09 1.94 3.56 20.03 5.45
1.63 25.52 3.60 8.64 1.63
3.86 2.48 7.11 3.97 6.11
20.18 3.31 9.97 4.71 4.12
2.83 4.51 3.12 4.45 20.02
1.45 4.02 5.06 2.12 0.03
1.17 4.51 4.45 1.79 20.22
21.19 21.25 23.89 3.93 2.06
20.66 21.58 21.97 6.43 6.19
1.92 25.95 24.51 1.23 3.24
20.66 22.89 24.67 7.19 4.53
23.32 0.40 2.07 5.29 1.80
22.02 3.10 3.40 5.26 4.82
0.25 3.04 4.60
23.19 2.80 1.30
2.34 3.48 26.68
20.70 6.61 5.50
1.04 0.79 0.90
4.35 5.85 3.64
checking whether the length and timing of the recessions are in agreement with the results shown by the annual growth rates in Table 1. The fourth column in Table 3 indicates the
Spain
duration of contractions (in months) and ‘‘asterisks’’ (*) denote periods where estimated recessions do not seem agree with annual growth rates. This happens twice for France and Japan,
Table 2 Dynamic harmonic regression estimation results for IPI Country
France c Italy Japan Spain UK US a
Noise variance ratios a Trend
H:12 b
H:6
H:4
H:3
H:2.4.
H:2
s2
7.22 6.97 21.9 3.23 5.53 87.9
6.50 20.7 3.08 6.90 31.5 49.8
3.50 7.66 2.80 4.13 4.69 4.05
2.04 9.56 3.00 7.78 4.74 2.59
2.29 8.28 12.6 19.5 23.4 1.19
6.89 4.74 5.91 8.15 5.59 1.95
3.80 5.46 1.62 4.45 2.46 0.50
0.0142 0.0208 0.0112 0.0209 0.0158 0.0053
All NVR estimated coefficients are multiplied by 10 3 . H:X stands for harmonic and X is the annual frequency. c Estimation period: 1976.1–1998.11. b
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Fig. 2. Estimated trend derivatives of IPI and recession periods.
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Table 3 Turning points and the length of expansions and contractions 1975.1–1998.12 Recession
Expansion
Ratio
Begins
Ends
Length
Begins
Ends
Length
Expansion ]] Recession
Italy
1977.02 1980.05 1984.11 1990.10 1995.09
1977.12 1983.03 1985.04 1993.06 1996.10
10* 34 6 32 13
1978.01 1983.04 1985.05 1993.07 1996.11
1980.04 1984.10 1990.09 11995.08 –
28 18 64 25 –
2.8 0.5 10.7 0.8 –
Japan
1980.05 1982.01 1985.08 1991.03 1997.06
1980.11 1982.10 1986.09 1993.12 1998.12 ?
6* 9* 13 32 18 ?
1978.01 1983.04 1985.05 1993.07 1996.11
1980.12 1982.11 1986.10 1994.01 –
12 32 52 41 –
2.0 3.5 4.0 1.3
1977.03 1979.11 1990.06 1995.04
1977.09 1982.12 1993.07 1996.01
6* 36 37 7*
1977.10 1983.01 11993.08 1996.02
1979.11 1990.05 1995.03 –
25 89 19 –
1980.02 1989.12 1995.07
1982.03 1993.04 1996.03
25 40 8
1982.04 1993.05 1996.04
1989.11 1995.06 –
99 25 –
–
UK
1979.08 1984.01 1990.02
1981.03 1984.07 1991.11
19 6 21
1981.04 1984.08 1992.12
1983.12 1990.01 –
32 65 –
1.7 10.8 –
US
1979.08 1981.08 1989.05
1980.07 1982.11 1991.04
12 15 23
1980.08 1982.12 1991.05
1981.07 1989.04 –
11 76 –
0.9 5.1
France
Spain
and once for Italy. The 1977 recession period in France and Italy is the result of a tremendous drop in IPI from a 10% growth rate in 1976 to levels around 1% the following year. Similar causes can be found for the 1980 and 1982 recessions in the case of Japan, where annual growth rates were below 1% after periods of high growth. Finally, the short 1996 French recession, where the trend derivative became negative for only six months, is a good approximation of the low value of the growth rate during that year (0.25%). In spite of these minor failures, the definitions proposed earlier seem to work well, properly characterizing most of the turning points in the data, as compared to methodologies such as the
– 4.2 2.5 0.5 – 4.0 0.6
–
´ Hodrick and Prescott filter (cf. Garcıa-Ferrer ´ and Sebastian, 1996), or even more recent alternatives. Just for illustration in the Spanish case, we have plotted in Fig. 3a and b the trend derivatives obtained by using two standard signal extraction procedures: the Basic Structural Model (BSM) of Harvey (1989) estimated by STAMP 5.0, and by the SEATS / TRAMO software developed by Gomez and Maravall (1996). The IRW model seems particularly useful for describing large and smooth changes in the trend, while the other methods provide less smooth variations, and their associated trend derivatives are too volatile and irregular to be useful for dating turning points in monthly data. In general, the Quasi-Fisher estimation results in
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Fig. 3. Estimated trend derivatives of Spanish IPI: (a) STAMP, (b) SEATS / TRAMO and (c) IRW model.
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Table 4 Noise variance ratio a estimates for different subperiods Estimation period
Trend
H:12
H:6
France 1976.01–1990.07 1975.01–1993.12 1975.01–1995.07
3.16 3.88 4.39
21.5 24.1 23.2
6.70 5.22 4.71
Spain 1975.01–1989.12 1975.01–1993.10 1975.01–1995.09 1975.01–1996.10
0.71 1.81 2.71 2.46
13.5 12.9 7.3 9.3
3.98 2.34 2.82 2.19
a
H:2.4
H:2
sˆ 2
6.40 5.36 5.87
11.4 15.6 14.0
7.03 7.32 6.94
3.18 2.34 1.37
0.0142 0.0136 0.0138
12.2 10.9 8.46 7.91
20.6 17.8 17.7 20.5
11.0 10.0 8.65 8.09
6.36 5.97 6.16 5.37
0.0195 0.0202 0.0207 0.0208
All NVR estimated coefficients are multiplied by 10 3 .
smooth changes in all the component’s amplitude and the smoothly varying trend. This seems to be a typical feature of this method repeating itself in a large number of data sets, e.g. Pedregal (1995). The maximum likelihood estimator applied by Harvey and Gomez and Maravall appears to produce higher NVR values explaining the higher volatility in the components. In the case of Spain, the estimated trend NVR in Table 2 is 0.00323 which implies retaining trend cycles longer than 27 months. The other trend alternatives seem to allow for shorter cycles.1 For the spectral properties of the IRW filter, see Young (1988); Pedregal (1995).
1
H:3
H:4
These contrasting results are directly related to the key issue of smoothness and, the ability of alternative detrending methods to broadly replicate asymmetric business cycles. Although a detailed treatment of this issue is outside the scope of this paper, a consensus is emerging that the choice of the signal extraction method should depend both on the purpose of the research (Wickens (1995)) and on initial judgements on either the length of the cycle or the required degree of smoothness of the trend (Canova (1994)).
4. Forecasting turning points using survey data So far, we have shown that the univariate decomposition and forecasting method is easy to apply on any manufacturing time series. IPI of six countries has been included to show this. This section also shows that you can take one further step and include leading information, but that requires a lot of work and knowledge of the economy proper. Hence only two countries are presented as examples of how much forecast accuracy improvement can be achieved by doing so. Therefore, we have split the French and Spanish data into subsamples in order to generate forecasts for the last two turning points of our data, the first turning points are too close to the beginning of the series and therefore dropped from the comparison. Table 4 presents estimates of the univariate IRW/ DHR model for alternative sample periods in both countries. The estimated NVR for the trend has large changes after 1990, reflecting different industrial growth rates over the estimation period. As in Table 3, the main seasonal frequency (H:12) indicates variation in the
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seasonal weights, while the remaining seasonal harmonics are less variable. In assessing the ability of the IRW/ DHR model in anticipating trend reversals, we will compare its turning point forecasts to that of two univariate methods: (Box and Jenkins (1970)) multiplicative seasonal ARIMA, and (Harvey (1989)) BSM model which had an excellent forecasting record for the 111 seasonal time series in Andrews (1994). Accuracy in turning point forecasting is presented in Tables 5–7 and discussed in Section 4.2.
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4.1. Industrial new orders ( INO) This survey variable, both for France and Spain, offers several advantages over its competitors. Apart from its prompt availability and lack of systematic revisions, the INO is based on realized industrial orders rather than on expectations. However, as usually happens with survey data, the main problem with INO is the scale of measurement. Questions on recent economic performance and on a firm’s shortterm plans are designed to be easily answered,
Table 5 RMSE of turning points (h-steps ahead) Estimation period
Forecast period
ARIMA
BSM
IRW/ DHR
LI
France 1976.1–1990.7 1976.1–1993.12 1976.1–1995.7
1990.8–1991.12 1994.1–1994.12 1995.8–1996.12
0.049 0.053 0.035
0.041 0.056 0.33
0.039 0.051 0.034
0.018 0.029 0.024
Spain 1975.1–1989.12 1975.1–1993.10 1975.1–1995.9 1975.1–1996.10
1990.1–1990.12 1993.11–1994.12 1995.10–1996.12 1996.11–1997.12
0.041 0.110 0.050 0.055
0.047 0.120 0.059 0.056
0.044 0.119 0.052 0.059
0.021 0.055 0.031 0.041
Table 6 Observed and forecasted annual growth rates for IPI Year France 1991 1994 1996 Spain a 1990 1994 1996 1997 a
Observed G.R.
ARIMA
BSM
IRW/ DHR
LI
21.19 3.03 0.25
3.76 20.67 2.65
2.15 20.98 1.79
2.05 20.92 2.73
20.03 1.59 0.81
20.01 7.2 20.7 6.8
2.8 23.1 3.6 3.2
3.8 24.7 4.3 2.7
3.1 23.3 3.9 2.0
1.1 2.0 1.2 5.1
a
Forecasted growth rates for alternative models.
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Table 7 Forecasted annual growth rates of spanish IPI, the recovery 1994 a Forecast origin 9.93 10.93 11.93 12.93 1.94 2.94 3.94 a
Models ARIMA
BSM
IRW/ DHR
LI
22.7 22.8 23.1 0.0 1.0 1.8 3.0
23.8 24.3 24.7 22.6 20.6 21.0 0.6
22.7 22.6 23.3 0.3 1.2 2.0 3.5
21.5 0.3 2.0 2.1 2.9 5.3 7.3
Note: Bold numbers correspond to the date when a model successfully forecast a turning point in the annual growth rate.
but they lack quantitative precision. Respondents are asked just to choose one of the three alternatives, ‘‘higher’’ (H), ‘‘normal’’ (N) or ‘‘lower’’ (L) orders. The INO figures are the balances, i.e. the differences between the percentages of H and L answers. Plots of the INO data and their corresponding IRW trends for the whole sample are depicted in Fig. 4. Note, however, that the NVR values for the trends are not estimated here but fixed, using the same smoothing values as for IPI. This ‘‘prefiltering’’ produces the same smoothness as for the reference series. In both series, the variance in the same low frequency band remains. The Spanish INO trend derivative plotted in Fig. 5b shows how the last two turning points are correctly anticipated by the LI. In the case of the 1990 recession the lead (point 1 in Fig. 5) is 9 months while in the case of the 1996 recession, the lead (point 3) is 5 months. Recoveries are also correctly reproduced (points 2 and 4) by the LI variable. The differences between recession and recovery leads are related to the different historical lengths shown by the two components of the Spanish industrial cycles. The much shorter recession periods do not fully allow the algorithm to incorporate the most recent information and, consequently, lead signals of recovery are much weaker than those of recession. Similar results hold for the French data, as Fig. 5a shows. In the 1991 recession,
the lead (point 1) is 10 months, while for the 1996 recession, the lead (point 3) is 5 months. Recoveries (points 2 and 4) are also correctly reproduced by the LI trend derivative. The evidence presented, so far, only proves one thing: from a historical point of view the LI trend correctly anticipates the turning points. Although this result is encouraging, we should not forget that both trends are smoothed estimates, that at each data point use information pertaining to the whole sample. In terms of forecasting, however, the real test implies confirmation of the evidence presented in Fig. 5 when using only the information available at the beginning of each forecast period. This is done in Figs. 6 and 7 that show the results for each one of the recession / recovery cases in both countries.
4.1.1. France Fig. 6 presents the IPI and INO trend derivatives for France. The forecast of the 1991 – 1993 recession in Fig. 6a is based on data that end in 1990.07. At that time, while the IPI trend derivative was already decreasing but still positive, the INO trend derivative had crossed the zero line as early as 1989.06. For the forecasts regarding the 1994 recovery, presented in Fig. 6b, estimation ends in 1993.12. At that moment, information related to future trend reversal is already obvious in the IPI trend derivative, that
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Fig. 4. Industrial New Orders (INO) and estimated IRW Trend: (a) France, (b) Spain.
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Fig. 5. INO Trend Derivatives and IPI recessions: (a) France, (b) Spain.
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Fig. 6. (a) Estimated Trend Derivatives for IPI and INO for the start of the 1991–93 recession. (b) Estimated Trend Derivatives for IPI and INO for the recovery from the 1991–93 recession. (c) Estimated Trend Derivatives for IPI and INO for the start of the 1996 recession.
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Fig. 7. (a) Estimated Trend Derivatives for IPI and INO for the start of the 1991–93 recession. (b) Estimated Trend Derivatives for IPI and INO for the recovery from the 1991–3 recession. (c) Estimated Trend Derivatives for IPI and INO for the start of the 1996 recession. (d) Estimated Trend Derivatives for IPI and INO for the recovery from the 1996 recession.
shows signs of potential recovery, but is still negative. The INO trend derivative became positive in 1993.08; leading the future recovery.
Finally, the results for the short 1996 recession are shown in Fig. 6c. Estimation ends in 1995.07. While the IPI trend derivative was
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already slowing down, it is still positive, while the INO trend derivative is signalling the incoming recession in 1995.05.
4.1.2. Spain Fig. 7a presents estimates of the IPI and INO trend derivatives (NVR 5 0.00071). In order to forecast the long 1990 – 1993 recession, we ended estimation at 1989.12. At that time, while the IPI trend was not showing any sign of trend reversal, the INO trend had already started to turn down nine months earlier. On the other hand, while the IPI trend derivative was already slowing down, but still positive, the INO trend derivative had crossed the zero line (confirmation of a recession) by 1989.03. As regards the 1994 recovery, results are presented in Fig. 7b. In this case, estimation ends at 1993.10. At that time, information regarding a future trend reversal is already evident in the IPI trend derivative, but the INO trend derivative became positive in 1993.06, leading the subsequent industrial recovery. Similar results hold for the short 1996 recession and the post-1997 recovery. For the first case, results are shown in Fig. 7c, where estimation ends at 1995.9. As before, while the IPI trend shows a healthy growth at the end of the sample, the one corresponding to INO had already turned negative in 1995.6. Similarly, the INO trend derivative signals the incoming recession as early as 1995.4. In the second case (Fig. 7d) both derivatives confirm the end of the short and mild 1996 recession although, in this case, the lead is very short.
for all the trend characterizations proposed in the unobserved components model literature, and hence, for their reduced form, ARIMA. As an example, take the IRW trend of the IRW/ DHR model. The prediction is a straight line with constant slope equal to the last value of the derivative. This is a rather restrictive and conservative assumption, given the evolution of the derivative in the vicinity of turning points, as Figs. 6 and 7 have shown.2 Specification and estimation of the transfer function LI model are associated with some difficulties. One is the asymmetry of recessions and expansions. In a truly ex-ante forecast experiment, the lead is unknown and has to be estimated. In the Spanish case, INO leads vary considerably between recessions and expansions from a maximum of six (in the 1990 recession) to a minimum of one month (in the case of the 1997 recovery). Since our goal is longer forecast horizons we have to rely on univariate forecasts of the input (cf. Ashley, 1983). Doing that we found only minor forecasting gains in the short-term (and none in the long-term) in comparison with the approach developed by ´ Garcıa-Ferrer and Queralt (1998a) where the IPI trend derivatives were forecasted directly from their univariate ARIMA representations. In all cases, the resulting AR(3) models indicate the presence of one real and two complex roots outside, but close to the unit circle. To construct the forecasts of our LI model we proceed as follows:
2
4.2. Comparing model forecast accuracy at turning points LI model forecasts will now be compared with those of the alternative univariate models mentioned earlier. A well known shortcoming of univariate models is their limited ability to anticipate turning points. This seems to be true
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Proposals of different (more flexible) trend characterizations that adequately represent long term variations in the trend derivative already exist in the unobserved components literature. A promising alternative is the Smoothed Random Walk trend, proposed by Young (1994), where smoothing constants can be included in the optimization process. Another one is the Double Integrated Autorregre´ sive model developed by Garcıa-Ferrer et al. (1996) for estimation of locally smooth trends in annual economic data.
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1. forecasts of trend values T t 1h of IPI are derived directly from Eq. (2) where future values are obtained using its trend derivative forecasts Dt 1h , obtained earlier. Note, however, that here the direction of change is known, given the information provided by the INO derivative at the time of the forecast. 2. forecasts of the seasonal component St 1h are obtained directly from the Quasi-Fisher algorithm of the DHR model. 3. final forecasts of the output Yt 1h are obtained by adding the trend and seasonal components directly from Eq. (1). Turning points forecasting performance will be compared to that of ARIMA, BSM and the default IRW/ DHR models. In all cases, predictive results are referred to as h-steps ahead forecasts. Three accuracy criteria are used: aggregate RMSE, forecasted annual growth rates and adaptability of forecasts to shifts in the forecast origins. The use of a variety of error measures has been recommended in the literature, c.f. Armstrong and Collopy (1992); Fildes (1992), to avoid that evaluation of different forecasting techniques may depend upon the choice of a particular accuracy measure. Forecast RMSE is presented in Table 5. The univariate models, in general, have large RMSE (in particular for the Spanish 1994 recovery). As could be expected, their forecasting behavior in the vicinity of turning points left much to be desired. The LI model behaves much better, showing a remarkable reduction in RMSE.3 However, for longer horizons, the use of 3
Spanish IPI has two well known irregularities: (1) the number of working days, and (2) the moving Easter holiday. To make forecasting comparisons easier we have explicitly decided not to do any intervention in any of the modeling approaches followed here. While their absence will undoubtedly increase RMSE considerably (specially the 1997 recovery when Easter falls in March), the increase will be proportionally equal for all alternatives and, hence, will not bias individual results.
RMSE or MAPE may be, not only dangerous ´ but misleading (Garcıa-Ferrer and Queralt, 1997). Comparing turning points forecast accuracy, we contend that forecasted annual growth rates become a more relevant criterion. Table 6 presents observed and forecasted annual growth rates for both countries. Again, univariate models results are similar and, in general, do not signal trend reversals, with the exception of the 1997 recovery anticipation for Spain. On the contrary, and also for the Spanish case, the LI models successfully anticipate the 1994 and 1997 recoveries and have much lower growth rates than univariate alternatives in the cases of the 1990 and 1996 recessions. Similar results hold for France. The LI model successfully forecasts the 1991 recession, the 1994 recovery and shows much lower growth rates than the other alternatives for the 1996 recession. Users of economic forecasts often complain about the inconsistency of monthly forecast reports due to the excessive volatility in the monthly published forecasts. With this in mind, we define a turning point anticipation signal as the first, of at least two consecutive announcements of a positive (negative) annual growth rate for the forecast period, thus avoiding the pitfalls associated with the presence of outliers at an end point of the sample that might change the expected growth rate at that point, only to return to the previous growth rate as soon as next month’s data is available. For the Spanish case, Table 7 shows the forecast performance of the models when forecasting the 1994 recovery, starting in 1993.09. Already by 1993.10 the LI model was forecasting a positive growth rate for 1994. Two months later, the IRW/ DHR model announces the same, to be followed by the ARIMA (1994.1) and BSM (1994.3) models. By 1994.2 the LI model was already forecasting a considerable positive growth rate, much closer to the outcome than what its competitors announced.
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5. Conclusions We propose an alternative approach to anticipating and confirming turning points in monthly time series. A turning point signal is considered as a two-stage decision process: a statement that a turning point is likely to occur (anticipation), and a statement of when it will occur (confirmation). The starting point is a univariate unobserved components model using time variable parameters developed by Young (1994). The derivative of the estimated trend component is used as a device for qualitative anticipation of peaks and troughs, as well as for providing alternative definitions of expansions and recessions. A complete turning point characterization, providing information about all the industrial business cycle features, is obtained for six OECD countries. With minor failures, the length and timing of the recessions are consistent with annual growth rates. Our approach, also contrasts with other, less smooth, alternatives that seem to contain shorter cycles than the ones implied by the IRW trend model. For both France and Spain, ex-ante turning point forecasts are improved by introducing survey data. In particular, Industrial New Orders (INO) is systematically leading IPI. The resulting leading indicator (LI) model is compared to well known modeling strategies in order to asses how accurately it forecasts the last seven turning points in the sample. Using different forecasting accuracy measures, LI compares favorably with the competing alternatives. While the empirical results presented here only concern industrial production, similar results have been found for a large number of seasonal economic time series in several countries. However, while the univariate modeling results are already well established, the leading indicator approach requires an input series that systematically leads the output. Business tendency surveys, that are promptly available and
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lack systematic revisions, should become an important area for future research. Also, the similarities between some of the national cycles suggest alternative multivariate approaches, e.g. dynamic factor models, where common trends and common cycles could be fully exploited. Acknowledgements We are grateful to Alfonso Novales, Pilar Poncela and Gerald Sweeney whose suggestions have led to significant improvements. We also thank Jan G. de Gooijer and an Associate Editor for helpful comments and corrections. Any errors are entirely ours. An early version of this paper was presented at the 17th International Symposium on Forecasting in Edinburgh, Scotland. The preparation of this paper and the research that it describes have been supported ´ Interministerial de Ciencia y by the Comision ´ programs P94-0180 and PB98Tecnologıa, 0075. Appendix. Data definitions and sources All IPI data are in seasonally unadjusted form and are obtained from the OECD database, with the exception of the Spanish data that have been obtained from the Instituto Nacional de Estad´ıstica. In all cases, the base year is 19905100. The INO data for the France also comes from the OECD data base, while the Spanish data have been obtained from the Ministerio de ´ database. Industria y Energıa References Andrews, R. L. (1994). Forecasting performance of structural time series models. Journal of Business and Economic Statistics 12, 129–133. Armstrong, J., & Collopy, F. (1992). Error measures for generalizing about forecasting methods: empirical comparisons. International Journal of Forecasting 8, 69– 90.
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Ashley, R. (1983). On the usefulnes of macroeconomic forecasts as inputs to forecasting models. Journal of Forecasting 2, 211–223. Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control, Holden Day, San Francisco. Canova, F. (1994). Detrending and turning points. European Economic Review 38, 614–623. Fildes, R. (1992). The evaluation of extrapolative forecasting methods. International Journal of Forecasting 8, 81–98. ´ ´ Garcıa-Ferrer, A., del Hoyo, J., Novales, A., & Sebastian, C. (1994). The use of economic indicators to forecast the Spanish economy: preliminary results from the ERISTE project, Tech. Rep. WP 9412, U.A.M. Dept. De ´ ´ Analisis Economico. ´ Garcıa-Ferrer, A., del Hoyo, J., Novales, A., & Young, P. C. (1996). Recursive identification estimation and forecasting of nonstationary time series with applications to GNP international data. In: Berry, D. A., Chaloner, K. M., & Geweke, J. K. (Eds.), Bayesian Analysis in Statistics and Econometrics: Essays in Honor of Arnold Zellnerm, John Wiley, New York, pp. 15–27. ´ Garcıa-Ferrer, A., & Queralt, R. (1997). A note on forecasting international tourist demand in Spain. International Journal of Forecasting 13, 539–549. ´ Garcıa-Ferrer, A., & Queralt, R. (1998a). Can univariate models forecast turning points in seasonal economic time series? International Journal of Forecasting 14, 433–446. ´ Garcıa-Ferrer, A., & Queralt, R. (1998b). Using long-, medium-, and short-term trends to forecast turning points in the business cycle: Some international evidence. Studies in Nonlinear Dynamics and Econometrics 3 (2), 79–105. ´ ´ C. (1996). A business Garcıa-Ferrer, A., & Sebastian, cycle characterization of the Spanish economy: 1970– 1994, Tech. Rep. WP 9606, ICAE, Universidad Complutense de Madrid. Gomez, V., & Maravall, A. (1996). Programas TRAMO and SEATS instructions for the user (BETA Version: Sept. 1996), Tech. Rep. WP 9628, Bank of Spain, Madrid. Hanssens, D. M., & Vanden Abeele, P. M. (1987). A time series study of the formation and predictive performance of EEC production survey expectations. Journal of Business and Economic Statistics 5, 507–519. Harvey, A. (1989). Forecasting Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge. Hess, G. D., & Iwata, S. (1997). Measuring and comparing business-cycle features. Journal of Business and Economic Statistics 15, 432–444.
¨ Kauppi, E. J. L., & Terasvirta, T. (1996). Short-term forecasting of industrial production with business survey data: experience from Finland’s great depression 1990– 1993. International Journal of Forecasting 12, 373– 381. ¨ Oller, L., & Tallbom, C. (1996). Smooth and timely business cycle indicators for noisy Swedish data. International Journal of Forecasting 3, 389–402. Madsen, J. B. (1993). The predictive value of production expectations in manufacturing industry. Journal of Forecasting 12, 273–289. McNees, S. (1991). Forecasting cyclical turning points: The record in past three recessions. In: Lahiri, K., & Moore, G. H. (Eds.), Leading Economic Indicators: New Approach and Forecasting Records, Cambridge University Press, Cambridge, pp. 149–168. Morales, E. E. A., & Rojo, M. L. (1992). Univariate methods for the analysis of the industrial sector in ´ Spain. Investigaciones Economicas 16 (1), 127–149. Ng, C. N., & Young, P. C. (1990). Recursive estimation and forecasting of nonstationary time series. Journal of Forecasting 9, 173–204. ´ teorica ´ Pedregal, D. (1995). Comparacion estructural y predictiva de modelos de componentes no observables y extensiones del modelo de Young, Ph.D. thesis, Facultad ´ de C.C. Economicas y Empresariales, Universidad ´ Autonoma de Madrid. ¨ Rahiala, M., & Terasvirta, T. (1993). Business survey data in forecasting the output of Swedish and Finnish metal and engineering industries: a Kalman filter approach. International Journal of Forecasting 2, 191–200. Westlund, A. H. (1993). Busines Cycle Forecasting. Journal of Forecasting 12 (3 and 4), 187–196. Wickens, M. (1995). Trend extraction: A practitioner’s guide. In: Technical report, Government Economic Service. Young, P. C. (1988). Recursive extrapolation interpolation and smoothing of non-stationary time series. In: Identification and System Parameter Estimation, Pergamon Press, Oxford, pp. 33–44. Young, P. C. (1994). Time variable parameters and trend estimation in non-stationary economic time series. Journal of Forecasting 13, 179–210. Young, P. C., Pedregal, D., & Tych, W. (1999). Dynamic Harmonic Regression. Journal of Forecasting 18, 369– 394. Zellner, A., Hong, C., & Min, C. (1991). Forecasting turning points in international output growth rates using Bayesian exponentially weighted autoregression time varying parameters and pooling techniques. Journal of Econometrics 49, 275–304.
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´ Biographies: Antonio GARCIA-FERRER is Professor of ´ ´ Econometrics in the Departamento de Analisis Economico: ´ Cuantitativa, Universidad Autonoma ´ Economıa de Madrid. From 1977 to 1980 he was Assistant Professor at the Universidad de Alcala´ de Henares and Fulbright Visiting Professor at the Graduate School of Business of the University of Chicago in 1984–85. He obtained his PhD in Economics at UC Berkeley in 1977, and is Associate Editor of the International Journal of Forecasting. His research interests include modelling and forecasting seasonal economic time series. On this topic, he has
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published in various journals and edited the special Issue on Time Series Advances in Economic Forecasting (Journal of Forecasting 13 (2) 1994).
Marcos BUJOSA-BRUN is a PhD student at Departamento ´ ´ ´ Cuantitativa, Univerde Analisis Economico: Economıa ´ sidad Autonoma de Madrid, and an economist at Facultad ´ de C.C. Economicas y Empresariales, Universidad Au´ tonoma de Madrid. He is currently involved in developing optimization algorithms in the frequency domain.
