Transcript 147 kB

Use of Business Tendency Survey
Results for Forecasting
Industry Production in Slovakia
Jana Juriová
INFOSTAT – Institute of Informatics and Statistics, Slovakia
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industry production indicators are very important for
construction of GDP flash estimates, because the share of
industrial production comprises more than 30% of GDP in
Slovakia
nowadays flash estimates of GDP are being prepared
within 45 days after the end of reference quarter (at the
time T+45), but perspectively it should be shortened up to
T+30 days
using results from business tendency surveys (BTS) can
help to obtain a very early estimate of industrial
production, as these qualitative data are known at the time
T-2 before the end of reference quarter
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monthly industrial production is represented by two
quantitative indicators:
 industrial production index (IPI) - finished production
 index of new orders in industry (INOI) - potential
production (which is expected to be realized in the near
future)
Similarity of development for
quarterly time series of GDP and
indices of industrial production for
the period from the 1st quarter 2000
to 2nd quarter 2009
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Correlation analysis has also
confirmed the strong dependence
between GDP and industrial
production; correlation coefficient
achieved:
• cca 0.91 between GDP and IPI
• cca 0.82 between GDP and INOI
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GDP index (constant prices, chain-linked), 2005=100
Industry production index, 2005=100
Industry new orders index, 2005=100
Methodology
2 different methodological approaches are used, but
explanatory variables of both are only qualitative data from
BTS:
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econometric model with error correction term
- explains separately the long-term and short-term influence of explanatory
variables on dependent variable
- solves the problem of so-called “spurious” regression (non-stationary time
series used in classical regression models can produce spurious results)
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ARIMA and ARIMAX models
- univariate ARIMA models are widely used in forecasting practice
- the basic concept of this type of models is stationarity
- ARIMAX are ARIMA models with input variables or regression models with
ARMA errors
Error Correction Model (ECM)
The short-term dynamics of variable Yt is joined with the long-term
equilibrium relationship in the form of ECM:
 Y t   0   1  X t   u t 1   t
where the parameter α represents the short-run effect that a change in
Xt will have on a change in Yt,
π or the parameter of so-called error correction term is the adjustment
effect and shows how much of disequilibrium from the previous period
is being corrected this period,
ut-1 is random variable from long-term relationship: Y t   0   1 X t  u t
(if ut is stationary, variables Xt and Yt are cointegrated and ut-1 can be
used in the ECM form)
and εt is random variable with attributes of white noise.
Error Correction Model (ECM)
the initial hypothesis:
industrial production in the form of fixed-base index (IP05) is growing
over time at more or less constant rate and fluctuations around the
trend (time) are changing in dependence on the balance statistics from
business tendency surveys (BBTS)
IP 05  a * e
b * time  c * BBTS
or
log( IP 05 )  a  b * time  c * BBTS
Residuals obtained from estimation of long-term relationship defined
this way are tested on stationarity by Augmented Dickey-Fuller (ADF)
test of unit root.
ARIMA and ARIMAX models
ARIMA combines three processes: AutoRegressive (AR), dIfferences
(I) and Moving Average (MA)
The resulting general linear model is in the following form:
Z t   1 Z t 1  ...   p Z t  p  a t   1 a t 1  ...   q a t  q
 i are autoregressive parameters (i=1,…,p), θj are moving average parameters
(j=1,…,q), Zt is obtained by differencing original time series d-times, at is
white noise component.
Very strong seasonality of both analyzed time series indicates the need of
seasonal ARIMA models (or SARIMA models) and they are denoted as
ARIMA(p,d,q)(P,D,Q)s
where (P,D,Q) are the parameters of seasonal part of the model based on the
same principles as the non-seasonal part and s represents the seasonality.
ARIMAX models are ARIMA models with eXogenous variables (X).
In this case ARIMA modelling identification is applied to residual series from
the regression model (these residuals should be stationary). Exogenous
variables in our case are balances from BTS.
Industry production index
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2001 2002 2003 2004 2005 2006 2007 2008
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Industry production index, 2005=100
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Industry production index, y-o-y change in %
Industrial confidence indicator, balance
The time series of industrial production index (IPI) was increasing almost all
the time regardless the trend break in the end of 2008. In the whole analyzed
period the average monthly growth rate was approximately 5.8% year-on-year.
The industrial confidence indicator (ICI) - composed of 3 balances: order
books, stocks of finished products and production expectations - was proved
as the main explanatory variable for models of industrial production index.
Industry production index – Error correction model
The long-term relation: LOG(IPI)=4.248+0.006*TIME+0.007*ICI(-1) explains almost
88% of variability for the dependent variable and its residuals are stationary.
The short-term relation: DLOG(IPI)=0.002*D(ICI(-1))-0.382*RESID_LT-
1)+0.048*D(SD3)+0.031*D(SD6)-0.04*D(SD8)+0.056*D(SD10)+0.067*D(SD11)
where RESID_LT are residuals from the long-term relation and SDi are seasonal
variables.
The estimated EC model explains about 60% of variability for the dependent variable.
The parameter of error correction term represents how much of the imbalance
from the previous month is being corrected this month, so it is 38% of imbalance in
this case. The Durbin-Watson statistic (2.26) confirms that there is no
autocorrelation in the model.
Conclusions:
- industrial confidence indicator is statistically significant for explaining of
deviations of industrial production index from its long-term trend being
approximated by linear trend;
- industrial confidence indicator is statistically significant from short-term
view as well.
Industry production index –ARIMAX model
Transformation of non-stationary time series of IPI:
logarithmic transformation, 1st unseasonal and 1st seasonal differences;
transformed time series:
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IPI
IPI
Z t   log
IPI
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t
t  12
 log
t 1
IPI
t  13
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The final seasonal model ARIMA(0,1,1)(0,1,1)12 explains about 34.8% of variability
for dependent variable.
The most suitable balance from business tendency surveys that has improved the
model is production expectations (EXPROD) over the next 3 months. The final
ARIMAX model explains a greater part of variability for dependent variable; it
increased almost up to 40%.
Z t  0 . 000416 D ( EXPROD
t
)  a t  0 . 38 a t 1  0 . 844603 a t 12
Variable EXPROD was transformed by means of first differences:
D(EXPROD)=EXPRODt-EXPRODt-1
Industry production index – Compared forecasts
Static simulation ex post for the period from January 2008 to June 2009:
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The lower RMSE (8.67%) was
achieved by ECM model,
because RMSE for ARIMAX
model is 9.65%.
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(RMSE – Root Means Square
Error or standard deviation
of forecasts’ errors)
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08M01
08M04
08M07
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Industry production index, 2005=100
Predictions of IPI05 from ECM model
Predictions of IPI05 from ARIMAX model
The conclusion is that ECM
model achieves better
forecasts for industrial
production index than
ARIMAX model.
Industrial new orders index
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Industry new orders index, 2005=100
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Industry new orders index, y-o-y changes, %
Order books in industry, balance
The time series of index of new orders in industry (INOI) has an
increasing trend (like in the case of IPI), but its variability and slope is
more distinct. The break in trend appeared a little earlier than for the time
series of IPI; INOI (y-o-y) has been continuously achieving minus
numbers from August 2008. Average growth rate was almost 12% during all
analyzed period.
The main explanatory variable for the error correction model of industrial
new orders index is the balance of order books.
Industrial new orders index - Error correction model
The long-term relation: LOG(INOI)=4.008+0.009*TIME+0.010*ORDERBOOKS explains
almost 80% of variability for dependent variable and its residuals are stationary.
The short-term relation:
DLOG(INOI05)=0.001*D(ORDERBOOKS)-0.206*RESID_LT(-1)+0.058*D(SD3)0.059*D(SD7)-0.134*D(SD8)-0.108*D(SD12)
The estimated EC model explains about 44% of variability for the dependent variable. The
Durbin-Watson statistic (2.22) confirms that there is no autocorrelation in the model.
Conclusions:
- balance of order books is statistically significant for explaining of deviations of
industrial new orders index from its long-term trend being approximated by linear trend;
- industrial confidence indicator is statistically significant from short-term view as
well.
Industrial new orders index –ARIMAX model
The same transformation of non-stationary time series of INOI was used like for IPI.
The final seasonal model ARIMA(3,1,)(0,1,1)12 explains almost 50% of variability for
dependent variable.
The final ARIMAX model with balance of order books as input variable explains a greater
part of variability for dependent variable; it increased to about 55.5%.
Z t  0 . 004 D ( ORDERBOOKS
t
)  0 . 288 Z t 1  0 . 207 Z t  3  a t  0 . 894 a t 12
Industrial new orders index – Compared forecasts
Static simulation ex post for the period from January 2008 to June 2009:
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The lower RMSE was
achieved by ARIMAX
model - 8.57% (10.12% for
ECM model).
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The conclusion is that
ARIMAX model has better
forecasting accuracy than
ECM model for index of
new orders in industry; the
opposite result like for IPI.
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08M01
08M04
08M07
08M10
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09M04
Industry new orders index, 2005=100
Predictions of INOI05 from ECM model
Predictions of INOI05 from ARIMAX model
Both model approaches are
useful for forecasting
industrial production using
results from BTS.
Thank you for attention.
[email protected]