Financial variables and the out-of-sample forecastability of the growth rate of Indian industrial production.
Gupta, Rangan ; Ye, Yuxiang ; Sako, Christopher M. 等
JEL Classification: C22, C53, E44, E32.
Introduction
There exists a large international literature dealing with the role
of financial variables in forecasting real output growth (1). However,
as far as India is concerned, there is virtually no studies dealing with
this issue. The four papers, distantly related to this topic that we
could come across are the recent works by Ray and Chatterjee (2001),
Biswas et al. (2010), Kar and Mandal (2011) and Bhattacharya et al.
(2011). Biswas et al. (2010), used a three-variable Bayesian vector
autoregressive (BVAR) model, comprising of industrial production, whole
sale price index and M1, to forecast inflation and industrial production
growth. They showed that the BVAR model outperformed its classical
counterpart in forecasting both inflation and output growth, but the
study did not emphasize the role M1 plays in the forecasting performance
of the two key macro variables. While Ray and Chatterjee (2001)
indicated financial variables (stock price inflation, broad money (M3)
growth rate, call money rate, gold price inflation and exchange rate)
did not Granger-cause gross domestic product (GDP) growth (2), Kar and
Mandal (2011) indicated that non-food credit and stock prices did
Granger-cause the growth rate of industrial production. Bhattacharya et
al. (2011) used financial variables, such as deposits, non-food credit
growth and the national stock exchange turnover, in their
bridge-equation (3) for now casting the GDP. In general, as can be seen,
the little evidence, at times conflicting, that exists regarding the
role of financial variables in forecasting Indian output growth is
mainly in-sample. And as is well-known, it is possible for a variable to
carry significant in-sample information even when it is not the case
out-of-sample (Rapach et al. 2005; Rapach, Wohar 2006). Also, Beck et
al. (2000, 2004) points out that, forecasting is at the root of
inference in time series analysis. Further, as argued by Clements and
Hendry (1998), in time series models, estimation and inference
essentially means minimizing of the one-step (or multi-step) forecast
errors. Hence, establishing a model superiority boils down to showing
that it produces smaller forecast errors than its competitors. In other
words, one needs to analyse whether adding financial variables over and
above the information already contained in the lagged output growth
improves predictability of the latter over an out-of-sample, besides
within-sample.
Against this backdrop, we consider the forecasting power of 11
financial variables with respect to the growth rate of Indian industrial
production over the monthly out-of-sample period of 2005:4-2011:4, using
an in-sample of 1994:1-2005:3. The length of our entire sample period is
governed by data availability, while, the starting point of the
out-of-sample period is motivated by the fact that the growth rate of
the Indian industrial production became more volatile ever since, as can
be seen from Figure 1. Note that, we use industrial production as a
measure of output rather than the GDP, simply because of the fact that
quarterly values of the latter are only available from the beginning of
1994. Given this, we felt that around seventy data points covering
eighteen years (1994-2011) or so, would be too small a sample to yield
statistically significant results, and hence, fail to yield credibility
to our analysis. Further, even in the current scenario where services
are undertaking an increasing weight in economies around the world,
forecasting the industrial production index is an important task for
short-term economic analysis. In fact, because some of the services
activities (such as business services) are closely linked to the
industrial ones, the industrial sector is still important in explaining
aggregate fluctuations. In addition, forecasts of industrial production
can be useful in more general forecasting models. For example,
Bhattacharya et al. (2011), use the industrial production index in the
bridge-equation for forecasting the quarterly Indian GDP. In this case,
reliable three-month ahead forecasts would be extremely helpful.
Furthermore, the industrial production index series could be used to
derive cyclical indicators of the manufacturing sectors, which, in turn,
requires signal extraction techniques, and, hence, accurate forecasts of
the industrial production that needs to be filtered are essential (4).
[FIGURE 1 OMITTED]
The 11 financial variables used in this study, namely, M0, M1, M2,
M3, lending rate, 3-month Treasury bill rate, term spread, real
effective exchange rate, real stock prices, dividend yield and non-food
credit growth, are quite popular in the extant literature (Rapach, Weber
2004). For each financial variable, we construct recursive out-of-sample
forecasts of industrial production growth over the 2005:4-2011:4 period
based on an autoregressive distributed lag (ARDL) model that includes a
given financial variable as an explanatory variable. We use the Harvey
et al. (1998) and Clark and McCracken (2001) statistics to test the null
hypothesis that the out-of-sample forecasts of industrial production
growth from a benchmark autoregressive (AR) model encompass the
forecasts from the ARDL model that includes a given financial variable.
To understand better the idea of forecast encompassing, consider two
sets of out-of-sample forecasts of the industrial production: one from
an ARDL model that includes a financial variable and one from the
benchmark AR model, and consider forming an optimal composite forecast
as a convex combination of the forecasts from the two models. If the
optimal weight attached to the forecast from the ARDL model is greater
than zero (equal to zero), then the ARDL model does (does not) contain
information that is useful for forecasting the output growth apart from
the information already contained in the AR model. Clark and McCracken
(2001, 2005) indicates that there are a number of econometric issues
that arise when comparing forecasts from two nested models, as is
obviously the scenario in our applications. Hence, following the
recommendations of Clark and McCracken (2005), we base our inferences on
a bootstrap procedure similar to the one in Kilian (1999). Furthermore,
given that we consider a large number of financial variables, we check
the robustness of our results using a version of the Inoue and Kilian
(2005) bootstrap procedure that explicitly controls for data mining. The
rest of the article is organized as follows: We lay out the basics of
the approaches used to testing for forecasting ability in Section 1.
Section 2 presents that data, and discusses forecasting test results. In
this section, we also check whether the significant results can be
attributed to data mining. The final section contains concluding
remarks.
1. Econometric methodology
Let us define: [DELTA][y.sub.t] = [y.sub.t] - [y.sub.t-1], where
[y.sub.t] is the log-level of industrial production at time t. Also let
[z.sub.t+h] = [[summation].sup.h.sub.i-1] [DELTA][y.sub.t+i]. Given
this, the ARDL model can be defined as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
with h, the forecasting horizon; [x.sub.t], the financial variable
and [[epsilon].sub.t+h], the disturbance term. As the [z.sub.t+h]
observations will be overlapping in this case, the disturbance term is
serially correlated when h > 1. To account for the serial correlation
in the disturbance term, a Newey and West (1987)--type
heteroscedasticity and autocorrelation-consistent (HAC) covariance
matrix is be used. Although we are primarily interested in out-of-sample
tests, it is straightforward to conduct an in-sample test of the
forecasting ability of [x.sub.t] by using all of the available
observations to conduct a Wald test of the null hypothesis that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If we reject this
null hypothesis, this is evidence that the financial variable xt has
in-sample forecasting ability with respect to future output growth.
To assess the simulated out-of-sample forecasting ability of a
given financial variable with respect to output growth, we use a
recursive scheme. This allows us to simulate the situation of a
forecaster in real time. We divide the total sample of T observations
into an in-sample (first R observations) and an out-of-sample (remaining
P observations). We compute out of-sample forecasts from the
unrestricted version of equation (1) and also from a restricted version
that excludes the financial variable (Eq. (1) with y0 =... = yq2 -1 =
0). Our recursive scheme continuously updates the parameter estimates of
the models by adding one observation at a time from the out-of-sample to
the expanding in-sample, and forecasting h-steps ahead. This results in
two sets of T-R-h+1 recursive out-of-sample forecast errors, one each
for the unrestricted and restricted regression models ([{[[??].sub.1,t +
h]}.sup.T-h.sub.t=R] and errors, one each for the unrestricted and,
respectively) (5).
The next step is to compare the simulated out-of-sample forecasts
from the unrestricted and restricted models. And we do this by using the
Theil's U metric, which, in turn, is defined as the ratio of the
root mean squared forecast error (RMSFE) for the unrestricted model
forecasts to the RMSFE for the restricted model forecasts. So, if the
RMSFE for the unrestricted model forecasts is less (more) than the RMSFE
for the restricted model forecasts, then U < (>)1. To test whether
the MSFE for the unrestricted model forecasts is statistically less than
the MSFE for the restricted model forecasts, we use the Diebold and
Mariano (1995) and West (1996) statistic, as well as a variant of this
statistic due to McCracken (2004). Both statistics are based on the loss
differential: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the
Diebold and Mariano (1995) and West (1996) statistic can be expressed
as:
MSE - T = [(T - R - h + 1).sup.0.5] x [bar.d] x
[[??].sup.-0-5.sub.dd]. (2)
Under the null hypothesis of equal forecasting ability,
[MSFE.sub.0] = MSFE, so that d and MSE-T are equal to zero. We test this
null hypothesis against the one-sided (upper-tail) alternative
hypothesis that the MSFE for the unrestricted model forecasts is less
than the MSFE for the restricted model forecasts ([MSFE.sub.0] >
MSFE), so that MSE-T > 0. We follow Clark and McCracken (2005) and
use the Bartlett kernel, K(j / J) = 1 - [j /(J +1)], and we set J =
[1.5h] for h > 1, where [*] is the nearest-integer function; for h =
1, we use = f dd (0). The McCracken(2004) variant of the MSE-T statistic
is given by:
MSE-F = (T-R -k +1) x [bar.d] / [??]. (3)
An alternative way to judge forecasting ability is based on the
notion of forecast encompassing. Consider forming an optimal composite
out-of-sample forecast of [z.sub.t+h] as a convex combination of the
out-of-sample forecasts from the unrestricted and restricted models:
[[??].sub.c,t+h] = [gamma][[??].sub.1,t+h] + (1 - [gamma])
[[??].sub.0,t+h], (4)
where 0 [less than or equal to] [lambda] [less than or equal to] 1.
If [lambda] = 0([lambda] > 0), the restricted model forecasts are
said to encompass (not encompass) the unrestricted model forecasts,
because the latter model does not contribute any valuable information,
over and above that is already contained in the restricted model. Harvey
et al. (1998) develop a statistic that can be used to test the null
hypothesis that [lambda] = 0 in Eq. (4) against the one-sided
(upper-tail) alternative hypothesis that [lambda] > 0:
ENC - T = [(T - R - h + 1).sup.0.5] x [bar.c] x
[[??].sup.-0-5.sub.cc], (5)
where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Clark and McCracken (2001) propose a variant of the ENC-T
statistic:
ENC - NEW = (T - R - k + 1) x [bar.c] / [??]. (6)
Clark and McCracken (2001) showed that these four forecast
comparison statistics have a non-standard asymptotic distribution forh
=1. Furthermore, Clark and McCracken (2004) also showed that these
statistics have a nonstandard asymptotic distribution and is not
asymptotically pivotal for h > 1, when comparing forecasts from
nested models, as is our case. Hence, Clark and McCracken (2004)
recommend basing inferences for the MSE-T, MSE-F, ENC-T and ENC-NEW
statistics on a bootstrap procedure, given that the statistics are not
in general asymptotically pivotal. The bootstrap procedure we employ is
similar to the one in Clark and McCracken (2004), which is a version of
the Kilian (1999) bootstrap procedure, and is discussed in detail in
Rapach and Weber (2004). Based on Monte Carlo simulations, Clark and
McCracken (2001, 2004) indicate that ENC-NEW is the most powerful
statistic, followed by the ENC-T, the MSE-F and the MSE-T. These
rankings suggest that the forecast encompassing statistics, especially
ENC-NEW, can have important power advantages over test statistics based
on relative MSFE. (6)
2. Data description and empirical results
2.1. Data description
The monthly data used in this study, covering the period of
1994:1-2011:4, are obtained from the Handbook of Statistics on the
Indian economy provided by the Reserve Bank of India (RBI),Global
Financial Database (GFD) and International Monetary Fund's (IMF)
International Financial Statistics (IFS). As discussed before, we use
the industrial production index as a proxy for Indian output, while, 11
financial variables are used as possible predictors of the growth rate
of industrial production. Besides, the real non-food credit growth, the
financial variables used include four monetary aggregates, three
interest rate variables, two stock market variables and the real
effective exchange rate. The monetary variables are the monetary base
(M0), M1, M2 and M3. The interest rate variables comprise of the lending
rate, 3-month Treasury bill rate and the term spread, with the latter
calculated as the difference between annualized returns on the long-term
government bonds (average maturity of 10 years) and 3-month Treasury
bills. The two stock market variables are real stock prices and dividend
yield. Note, the real values of the non-food credit and stock prices are
obtained by dividing the respective nominal values by the Consumer Price
Index (CPI) (7). Data on industrial production, M0, M3, lending rate,
3-month Treasury bill yield, 10-year government bond yield, dividend
yield and real effective exchange rate are drawn from GFD, and M1, M2,
and the CPI data are from the IFS, with the non-food credit coming from
the RBI. To work with stationary variables, industrial production, the
four monetary aggregates, real share price, the real effective exchange
rate and the real non-food credit is transformed into growth rates.
While the dividend yields, lending rate and the 3-month Treasury bill
rate are measured in first differences (8). We consider horizons h = 1,
3, 6, 9 and 12 months over a volatile out-of-sample period of
2005:4-2011:4, using an in-sample of 1994:1-2005:3. Tables 1 and 2
report the results of the forecasting exercise with the growth rate of
industrial production appearing as the dependant variable in Eq. (1).
For the out-of-sample period, we use the Schwarz Information Criterion
(SIC) and in-sample data to determine the lag structure of Eq. (1). We
consider values of [q.sub.1] from zero to twelve, while, we considered
values of [q.sub.2] from one to twelve to ensure that the financial
variable appears in the unrestricted model.
2.2. Empirical results
Table 1 presents forecasting test results for the four
out-of-sample test statistics for Indian industrial production growth
corresponding to the 11 financial variables at horizons 1, 3, 6, 9 and12
months over the 2005:4-2011:4 out-of-sample period. Table 1 further
presents values of [q.sub.1] and [q.sub.2] determined by the SIC
criterion, the in-sample Wald statistic and Theil's U. Following
Rapach and Weber (2004), a bootstrap procedure is used to generate the
p-values given in parentheses for the Wald and four out-of-sample
statistics. We find evidence of in-sample forecasting power for M0, M1,
M2, M3, the lending rate and real share price growth rate for at least
one of the 5horizon-lengths considered. The strongest evidence is
obtained for M0. Further, when compared to the existing literature,
unlike Ray and Chatterjee (2001), we find that stock price, M3 and an
interest rate variable (lending rate) do have in-sample predictability
for output growth. Our results corroborate the findings for Ray and
Chatterjee (2001) regarding the exchange rate, but fail to find
in-sample predictability of non-food credit growth, unlike Kar and
Mandal (2011).
When we move to the relative MSFE metric, we find that barring few
cases (six-months, nine-months and twelve-months ahead forecast horizons
for M1 and one-month ahead forecast horizon for the first-differenced
lending rate), the value of the Theil's U is less than one for all
the cases where we found in-sample predictability. However, there are
also three cases (six-months and nine-months ahead for the term-spread
and nine-months ahead for the dividend yield), where the Theil's U
is less than one even when there is no in-sample predictability. Now,
when we turn to the significance of the four out-of-sample statistics
for the cases where in-sample and out-of-sample predictabilities
coincide, we find that at least one of MSE-T, MSE-F, ENC-T and ENC-NEW
statistics are significant. In fact, barring the nine-months ahead
horizon of the lending rate, for which the MSE-F statistic is
significant at the 10 percent level, the most powerful of the
out-of-sample statistics, namely ENC-NEW, is significant at least at the
ten percent level for all the cases where the Theil's U less than
one, and there exists in-sample predictability. However, in the case of
the nine-month ahead forecast resulting from the term-spread, where
there is no in-sample predictability, but the Theil's U is less
than one, none of the forecast comparison statistics are significant.
Also note that, for the two cases (six-months ahead for the term-spread
and nine-months ahead for the dividend yield), where the Theil's U
value is less than one without any evidence of in-sample predictability,
at least one of the weaker (MSE-T and MSE-F) out-of-sample test
statistics are significant.
There are four interesting cases, namely, three-months, six-months
and nine-months ahead forecast horizons for M1, and one-month ahead
forecast horizon for the first-differenced lend ingrate, where the
Theil's U is greater than one, but out-of-sample predictability is
obtained based on the ENC-NEW test statistic. Note that, for the case of
three-months ahead forecast for M1, there is no evidence of in-sample
predictability. At this stage, it is important to highlight what the ENC
statistics mean, since it might seem counterintuitive to have
out-of-sample forecasting ability from a specific variable, even when
the Theil's U exceeds one. Intuitively, the significance of the ENC
statistics reflects the fact that the AR (restricted) model forecasts
have little explanatory power for the ARDL (unrestricted) model forecast
errors, so that the ARDL model forecasts must contain information not
found in the AR model forecasts. That is, if the AR model forecast
errors contain little information for predicting the ARDL errors, the AR
model does not forecast encompass the ARDL model, even if the two model
yield forecast errors with very similar variances. In addition, the ENC
statistics are also likely to be significant when the AR and ARDL model
forecast errors have strong negative correlation. In this case, AR model
forecast errors of a given sign are associated with ARDL model forecast
errors of the opposite sign, so that the optimal composite forecast
should incorporate information from both the AR and ARDL models. In
general, we find relatively strong evidence (based on the ENC-NEW
statistics) of out-of-sample predictability for at least one of the
horizons considered for M0, M1, M2, M3, the lending rate and real share
price growth rate. The term-spread and dividend yield are added to the
list when weaker versions of the out-of-sample test statistics are
considered as well. Overall, eight out of the eleven financial variables
considered contain some form of out-of-sample predictability for the
Indian industrial production growth rate.
Our results point to at least six financial variables, where, for
at least one of the five out-of-sample horizons considered, we can
reject the null hypothesis that forecasts of industrial production
growth generated by a benchmark AR model encompass forecasts generated
by a more general ARDL model that includes a financial variable.
However, such tests of statistical significance fail to provide us
information about by how much these financial variables improve
forecasts, i.e. these tests do not inform us of economic significance of
our results. Given this, Table 2 reports the estimated weight, [lambda],
attached to the ARDL model forecast in forming the optimal composite
forecast. We only consider the cases in Table 1, for which the ENC-T
and/or the ENC-NEW statistics are significant at the 10 percent level.
Following Granger and Ramanathan (1984), we report the estimates of
[lambda] that are obtained with an intercept term included in Eq. (4).
Note that, as [lambda] increases the unrestricted model forecast is
relatively more important in generating the optimal composite forecast.
Though all the estimates of [lambda] are significant at the 10 percent
level, as is known from Table [lambda], its estimates vary considerably
in Table 2. Barring the equations involving M1 growth, the
first-difference of the lending rate, and longer horizons of M0 growth,
where the values of [lambda] lie between 0.1044 to 0.2614, the other
estimated values of [lambda] are exceptionally high and all over 0.9056.
In the latter cases, forecasts formed from using the ARDL model, i.e.
including financial variables, play a quantitatively important role in
generating the optimal composite of the growth rate of the Indian
industrial production. Also in number of cases, as can be seen from the
U measures reported in Table 2, there is considerable reduction in the
relative MSFE for the optimal composite forecasts relative to the
benchmark AR forecasts.
In Figure 2, we analysed the ability of the 11 financial variables
in predicting the turning points of the growth rate of industrial
production over the seventy-three months out-of-sample period of 2005:4
to 2011:4. In this regard, we plot the one-step-ahead forecasts obtained
from the recursive estimation of the AR and the 11 individual ARDL
models over the out-of-sample period. The recursive scheme allows us to
simulate the situation of a forecaster in real time. As can be seen from
Figure 2, all the financial variables tend to behave similarly in
predicting the turning points of the growth rate of industrial
production. And, in general, barring the end of the sample where the AR
and ARDL models predicted a slowdown in the growth rate of the
industrial production when the same actually witnessed an increase in
the growth rate, all the models perform equally well for the other
turning points. In sum, it is difficult to differentiate between the
role played by the individual financial variables relative to each other
and also the AR model based on the turning point exercise.
[FIGURE 2 OMITTED]
We have indicated that majority of the 11 financial variables
considered evince ability to forecast and predict the turning points of
industrial production growth over the out-of-sample period of
2005:4-2011:4. But, given that we consider a large number of financial
variables, it is fair to wonder, as suggested by Gupta and Modise
(2012), if our significant results reported in Table 1 are due to data
mining across the 11 financial variables, even though it is believed
that out-of-sample tests are, in general, immune to data mining. Inoue
and Kilian (2005), however, suggest that both in-sample and
out-of-sample tests are equally susceptible to data mining. For this
reason, we implement a version of the data-mining bootstrap procedure
developed by Inoue and Kilian (2005). In our case, the null hypothesis
posits that none of the 11 financial variables considered has
out-of-sample predictive ability over the out-of-sample period, with the
alternative hypothesis being that at least one of the financial
variables has forecasting power over the out-of-sample. Inoue and Kilian
(2005) recommend using the maximal out-of-sample test statistic to
implement this test, whereby we test the null hypothesis that the
largest specific out-of-sample test statistic (MSE-T, MSE-F, ENC-T or
ENC-NEW) concerned for the 11 financial variables is equal to zero
against the alternative that the same is greater than zero. Table 3
reports the data-mining-robust critical values corresponding to Table 1
for the out-of-sample period forecasting exercise of the industrial
production growth rate. Given the ranking of the out-of-sample test
statistics, we are most interested in checking whether the significant
ENC-T and ENC-NEW tests reported in Table 1, continue to remain
significant after we use data-mining-robust critical values. Comparing
the results in Table 1 with that of Table 3, it is clear that a majority
of our positive out-of-sample results suffer from data mining. As can
now be seen, only M0 (one-month, three-months, six-months and
nine-months), M1 (six-months) and M2 (one-month) retain some of its
predictive ability with respect to industrial production. Three-months
ahead forecasts from M2 and M3 is added to this list, if we consider the
relatively
weaker MSE-T statistic. Interestingly, the forecasting ability of the
real stock price growth rate completely disappears. Our results, thus,
highlight the importance of accounting for data mining, since if
ignored, one could be led to falsely over emphasizing the ability of
financial variables in predicting the growth rate of Indian industrial
production.
Conclusions
The little evidence, at times conflicting, that exists regarding
the role of financial variables in forecasting Indian output growth is
mainly in-sample. Against this backdrop, we consider the forecasting
power, both in- and out-of-sample, of 11 financial variables with
respect to Indian industrial production growth rate over the monthly
out-of-sample period of 2005:4-2011:4, using an in-sample of
1994:1-2005:3. The financial variables used in this study, namely, M0,
M1, M2, M3, lending rate, 3-month Treasury bill rate, term spread, real
effective exchange rate, real stock prices, dividend yield and non-food
credit growth, are quite popular in the extant literature. We observe
strong evidence of out-of-sample predictability for at least one of the
horizons for M0, M1, M2, M3, the lending rate and real share price
growth rate. The term-spread and dividend yield are added to the list
when weaker versions of the out-of-sample test statistics are considered
as well. We also observe that, at times, in-sample and out-of-sample
predictive ability of the financial variables tend to coincide. Given
that we consider a large number of financial variables, when we checked
the significant results by accounting for data mining across the 11
financial variables, majority of these results are found not to be
robust to data mining. Once, we control for data mining only M0, M1 and
M2 retain some of its predictive ability. In light of this result of
limited predictability of the Indian output growth based on financial
variables in a linear framework, future research would aim to analyse
the same in a non-linear framework along the lines of Peel and Paya
(2004).
Caption: Fig. 1. Industrial production in levels and growth rates
Caption: Fig. 2. Out-of-sample one-step-ahead recursive forecast
plots (2005:4-2011:4)
doi: 10.3846/20294913.2013.879544
Acknowledgements
We would like to thank three anonymous referees for many helpful
comments. Any remaining errors are, however, solely ours. We are also
indebted to the Editor, Professor Saparauskas, for extending our
deadline to revise the paper.
References
Beck, N.; King, G.; Zeng, L. 2000. Improving quantitative studies
of international conflict: a conjecture, American Political Science
Review 94(1): 21-26. http://dx.doi.org/10.2307/2586378
Beck, N.; King, G.; Zeng, L. 2004. Theory and evidence in
international conflict: a response to de Marchi, Gelpi, and Grynaviski,
American Political Science Review 98(2): 379-389.
http://dx.doi.org/10.1017/S0003055404001212
Bhattacharya, R.; Pandey, R.; Veronese, G. 2011. Tracking India
growth in real time, Working paper, National Institute of Public Finance
and Policy, New Delhi.
Biswas, D.; Singh, S.; Sinha, A. 2010. Forecasting inflation and
IIP growth: Bayesian vector autoregressive model, Reserve Bank of India
Occasional Papers 31(2): 31-48.
Bruno, G.; Lupi, C. 2004. Forecasting industrial production and the
early detection of turning points, Empirical Economics 29(3): 647-671.
http://dx.doi.org/10.1007/s00181-004-0203-y
Clark, T. E.; McCracken, M. W. 2001. Tests of equal forecast
accuracy and forecast encompassing for nested models, Journal of
Econometrics 105(1): 85-110.
http://dx.doi.org/10.1016/S0304-4076(01)00071-9
Clark, T. E.; McCracken, M. W. 2004. Evaluating long-horizon
forecasts. University of Missouri-Columbia Manuscript.
Clark, T. E.; McCracken, M. W. 2005. Evaluating direct multistep
forecasts. Econometric Reviews 24(4): 369-404.
http://dx.doi.org/10.1080/07474930500405683
Clements, M.; Hendry, D. 1998. Forecasting economic time series.
New York: Cambridge University Press. 368 p.
http://dx.doi.org/10.1017/CBO9780511599286
Diebold, F.; Mariano, R. 1995. Comparing predictive accuracy,
Journal of Business and Economic Statistics 13(2): 253-265.
http://dx.doi.org/10.2307/1392185
Espinoza, R.; Fornari, F.; Lombardi, M. J. 2012. The role of
financial variables in predicting economic activity, Journal of
Forecasting 31(1): 15-46. http://dx.doi.org/10.1002/for.1212
Granger, C. W. J.; Ramanathan, R. 1984. Improved methods of
forecasting, Journal of Forecasting 3(2): 197-204.
http://dx.doi.org/10.1002/for.3980030207
Gupta, R.; Modise, M. P. 2012. South African stock return
predictability in the context data mining: the role of financial
variables and international stock returns, Economic Modelling 29(3):
908-916. http://dx.doi.org/10.1016/j.econmod.2011.12.013
Harvey, D.; Leybourne, S.; Newbold, P. 1998. Tests for forecast
encompassing, Journal of Business and Economic Statistics 16(2):
254-259. http://dx.doi.org/10.2307/1392581
Inoue, A.; Kilian, L. 2005. In-sample or out-of-sample tests of
predictability: which one should we use?, Econometric Reviews 23(4):
371-402. http://dx.doi.org/10.1081/ETC-200040785
Kar, S.; Mandal, K.; 2011. Banks, stock markets and output:
interactions in the Indian economy, in GDN 12th Annual Global
Development Conference, 13-15 January, 2011, Colombia.
Kilian, L. 1999. Exchange rates and monetary fundamentals: what do
we learn from long-horizon regressions?, Journal of Applied Econometrics
14(5): 491-510.
http://dx.doi.org/10.1002/(SICI)1099-1255(199909/10)14:5<491::AID-JAE527>3.0.CO; 2-D
McCracken, M. 2004. Asymptotics for out-of-sample tests of granger
causality, Manuscript, University of Missouri at Columbia.
Newey, W.; West, K. 1987. A simple, positive semi-definite,
heteroskedasticity and autocorrelation consistent convariance matrix,
Econometrica 55(3): 703-708. http://dx.doi.org/10.2307/1913610
Peel, D.; Paya, I. 2004. Asymmetry in the link between the yield
spread and industrial production: threshold effects and forecasting,
Journal of Forecasting 23(5): 373-384. http://dx.doi.org/10.1002/for.921
Rapach, D. E.; Weber, C. E. 2004. Financial variables and the
simulated out-of-sample forecastability of U.S. output growth since
1985: an encompassing approach, Economic Inquiry 42(4): 717-738.
http://dx.doi.org/10.1093/ei/cbh092
Rapach, D. E.; Wohar, M. E.; Rangvid, J. 2005. Macro variables and
international stock return predictability, International Journal of
Forecasting 21(1): 137-166.
http://dx.doi.org/10.1016/j.ijforecast.2004.05.004
Rapach, D. E.; Wohar, M. E. 2006. In-sample vs. out-of-sample tests
of stock return predictability in the context of data mining, Journal of
Empirical Finance 13(2): 231-247.
http://dx.doi.org/10.1016/j.jempfin.2005.08.001
Rapach, D. E.; Strauss, J. K.; Zhou, G. 2009. Differences in
housing price forecastability across U.S. states, International Journal
of Forecasting 25(2): 351-372.
http://dx.doi.org/10.1016/j.ijforecast.2009.01.009
Rapach, D. E.; Strauss, J. K. 2010. Bagging or combining (or both)?
An analysis based on forecasting U.S. employment growth, Econometric
Reviews 29(5): 511-533. http://dx.doi.org/10.1080/07474938.2010.481550
Rapach, D. E.; Strauss, J. K.; Zhou, G. 2010. Out-of-sample equity
premium prediction: combination forecasts and links to the real economy,
Review of Financial Studies 23(2): 821-862.
http://dx.doi.org/10.1093/rfs/hhp063
Rapach, D. E.; Strauss, J. K. 2012. Forecasting U.S. state-level
employment growth: an amalgamation approach, International Journal of
Forecasting 28(2): 315-327.
http://dx.doi.org/10.1016/j.ijforecast.2011.08.004
Ray, P.; Chatterjee, J. S. 2001. The role of asset prices in Indian
inflation in recent years: some conjectures, Modelling Aspects of the
Inflation Process and the Monetary Transmission Mechanism in Emerging
Market Countries 8: 131-150.
Rossi, B.; Sekhposyan, T. 2010. Have economic models forecasting
performance for US output growth and inflation changed over time, and
when?, International Journal of Forecasting 26(4): 808-835.
http://dx.doi.org/10.1016/j.ijforecast.2009.08.004
Stock, J.; Watson, M. 2003. Forecasting output and inflation: the
role of asset prices, Journal of Economic Literature 41(3): 788-829.
http://dx.doi.org/10.1257/002205103322436197
West, K. 1996. Asymptotic inference about predictive ability,
Econometrica 64(5): 1067-1084. http://dx.doi.org/10.2307/2171956
Rangan GUPTA, Yuxiang YE, Christopher M. SAKO
Department of Economics, University of Pretoria, 0002 Pretoria,
South Africa
Received 14 April 2012; accepted 04 August 2012
Corresponding author Rangan Gupta
E-mail: Rangan.Gupta@up.oc.za
Rangan GUPTA. Doctor, Professor at the Department of Economics,
University of Pretoria. First degree in Economics, Calcutta University
(1997); Master of Science (1999); Doctor (2005). Author of about 130
scientific articles. Research interests include macroeconomics and time
series econometrics.
Yuxiang YE. She is a PhD candidate in Economics at the Department
of Economics, University of Pretoria.
Christopher SAKO. He is a PhD candidate in Economics at the
Department of Economics, University of Pretoria.
(1) Refer to Stock and Watson (2003) and, more recently, Rossi and
Sekhposyan (2010) and Espinoza et al. (2012), for a detailed literature
review in this regard.
(2) The study found that barring the gold price inflation and the
exchange rate, the three other financial variables Granger-caused
commodity price inflation.
(3) A bridge equation is generally designed to "bridge"
early releases of monthly indicators with quarterly GDP.
(4) See Bruno and Lupi (2004) for further details regarding the
importance of forecasting industrial production.
(5) For further details, refer to Rapach and Weber (2004).
(6) For further details regarding the intuition of these rankings
and the potential gains associated with the ENC-type statistics over the
MSE-types, refer to Rapach and Weber (2004).
(7) Note that our data sources provide a series for the real
effective exchange rate on its own, hence, it was not necessary for us
to convert the nominal effective exchange rate to its real counterpart.
(8) The stationarity of the variables were tests using standard
unit root tests. These results are available upon request from the
authors.
Table 1. Forecasting test results for the out-of-sample period
Horizon(h) 1 month 3 months 6 months
M0 growth
[q.sub.1] 11 9 6
[q.sub.2] 11 11 11
Wald 105.02(0.00)# 70.57(0.00)# 26.86(0.00)#
U 0.89 0.90 0.99
MSE-T 1.97(0.01)# 0.93(0.06)# 0.12(0.22)
MSE-F 18.40(0.00)# 16.81(0.00)# 1.71(0.01)#
ENC-T 3.24(0.00)# 1.76 (0.05)# 0.89(0.13)
ENC-NEW 16.25(0.00)# 16.61(0.00)# 5.70(0.00)#
M1 growth
[q.sub.1] 12 12 6
[q.sub.2] 1 1 10
Wald 0.43(0.56) 0.38(0.54) 18.64(0.01)#
U 1.01 1.01 1.05
MSE-T -0.44(0.39) -0.52(0.39) -0.56(0.48)
MSE-F -0.94(0.68) -0.88(0.75) -5.85(0.97)
ENC-T 0.72(0.16) 0.75(0.15) 1.28(0.09)#
ENC-NEW 0.71(0.11) 0.65(0.07)# 6.13(0.00)#
M2 growth
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 8.62(0.02)# 5.44(0.03)# 1.65(0.26)
U 0.98 0.99 1.01
MSE-T 1.76(0.00)# 1.97(0.00)# -0.82(0.58)
MSE-F 2.51(0.01)# 1.92(0.01)# -1.18(0.82)
ENC-T 2.77(0.00)# 2.27(0.01)# -0.30(0.52)
ENC-NEW 2.41(0.01)# 1.13(0.04)# -0.21(0.71)
M3 growth
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 5.49(0.06)# 3.90(0.09)# 0.01(0.94)
U 0.99 0.98 1.01
MSE-T 0.96(0.04)# 2.11(0.00)# -1.22(0.75)
MSE-F 1.63(0.05)# 2.55(0.02)# -0.88(0.75)
ENC-T 1.46(0.05)# 2.20(0.01)# -1.14(0.81)
ENC-NEW 1.24(0.08)# 1.40(0.05)# -0.40(0.86)
Lending rate, first difference
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 4.06(0.10)# 2.92(0.18) 2.37(0.27)
U 1.04 1.00 1.00
MSE-T -1.21(0.73) -0.33(0.35) 0.53(0.20)
MSE-F -5.46(0.97) -0.49(0.54) 0.37(0.18)
ENC-T 0.88(0.15) 0.52(0.24) 0.81(0.24)
ENC-NEW 1.19(0.08)# 0.60(0.13) 0.30(0.24)
3-month Treasury bill rate, first difference
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 1.83(0.20) 2.17(0.20) 1.12(0.36)
U 1.01 1.00 1.00
MSE-T -0.56(0.43) 0.10(0.25) -0.13(0.33)
MSE-F -1.56(0.84) 0.20(0.20) -0.05(0.31)
ENC-T -0.02(0.36) 0.71(0.20) 0.31(0.31)
ENC-NEW -0.03(0.38) 0.70(0.12) 0.06(0.34)
Term spread
[q.sub.1] 12 12 6
[q.sub.2] 3 1 1
Wald 1.67(0.23) 0.27(0.65) 3.09(0.19)
U 1.06 1.06 0.98
MSE-T -2.38(0.99) -1.73(0.84) 1.14(0.07)#
MSE-F -8.09(0.99) -7.66(0.97) 2.56(0.08)#
ENC-T -1.24(0.83) -1.34(0.79) 1.24(0.13)
ENC-NEW -1.92(0.98) -2.70(0.97) 1.54(0.14)
Dividend yield, first difference
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 1.83(0.25) 1.19(0.36) 0.00(0.95)
U 1.00 1.00 1.01
MSE-T 0.76(0.09)# 0.15(0.22) -1.94(0.95)
MSE-F 0.52(0.14) 0.15(0.22) -0.88(0.70)
ENC-T 0.90(0.14) 0.27(0.31) -1.80(0.95)
ENC-NEW 0.31(0.24) 0.13(0.31) -0.40(0.81)
Real effective exchange rate, first difference
[q.sub.1] 12 12 6
[q.sub.2] 3 1 1
Wald 2.49(0.18) 2.86(0.16) 0.14(0.74)
U 1.03 1.02 1.01
MSE-T -1.99(0.92) -1.47(0.80) -2.01(0.95)
MSE-F -4.60(0.97) -2.74(0.92) -0.86(0.69)
ENC-T -1.02(0.73) -0.54(0.57) -1.69(0.93)
ENC-NEW -1.13(0.94) -0.48(0.82) -0.35(0.76)
Real share price growth
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 4.91(0.08)# 8.41(0.01)# 1.72(0.26)
U 0.99 0.98 1.00
MSE-T 1.08(0.04)# 0.75(0.09)# 0.61(0.14)
MSE-F 1.90(0.04)# 2.33(0.03)# 0.54(0.17)
ENC-T 1.55(0.05)# 1.33(0.07)# 0.71(0.22)
ENC-NEW 1.40(0.08)# 2.33(0.03)# 0.33(0.25)
Real non-food credit growth
[q.sub.1] 12 12 6
[q.sub.2] 1 1 1
Wald 0.11(0.79) 0.42(0.64) 0.11(0.81)
U 1.01 1.02 1.02
MSE-T -1.09(0.69) -1.87(0.91) -1.16(0.68)
MSE-F -0.88(0.62) -2.27(0.84) -2.28(0.86)
ENC-T -0.63(0.63) -1.44(0.90) -1.00(0.73)
ENC-NEW -0.25(0.63) -0.87(0.91) -0.99(0.92)
Horizon(h) 9 months 12 months
M0 growth
[q.sub.1] 3 0
[q.sub.2] 8 1
Wald 35.25(0.00)# 0.53(0.65)#
U 0.99 1.00
MSE-T 0.15(0.24) -0.19(0.46)
MSE-F 1.35(0.03)# -0.08(0.44)
ENC-T 0.91(0.15) -0.03(0.58)
ENC-NEW 3.84(0.00)# -0.01(0.57)
M1 growth
[q.sub.1] 3 1
[q.sub.2] 7 5
Wald 9.22(0.02)# 7.10(0.04)
U 1.09 1.14
MSE-T -0.89(0.58) -1.36(0.78)
MSE-F -10.00(0.99) -14.35(0.99)
ENC-T 0.17(0.36) -0.26(0.48)
ENC-NEW 0.93(0.04)# -1.29(0.98)
M2 growth
[q.sub.1] 3 1
[q.sub.2] 1 1
Wald 0.34(0.64) 1.58(0.25)
U 1.01 1.01
MSE-T -1.79(0.90) -0.96(0.61)
MSE-F -0.86(0.76) -1.05(0.81)
ENC-T -1.24(0.82) -0.29(0.51)
ENC-NEW -0.26(0.78) -0.17(0.67)
M3 growth
[q.sub.1] 3 0
[q.sub.2] 1 1
Wald 0.07(0.78) 0.01(0.94)
U 1.00 1.00
MSE-T -1.38(0.79) -1.81(0.89)
MSE-F -0.29(0.46) -0.58(0.72)
ENC-T -1.22(0.82) -1.75(0.91)
ENC-NEW -0.12(0.59) -0.28(0.82)
Lending rate, first difference
[q.sub.1] 3 0
[q.sub.2] 1 1
Wald 4.87(0.10)# 0.00(0.98)
U 0.99 1.01
MSE-T 0.75(0.15) -0.91(0.57)
MSE-F 0.95(0.07)# -1.00(0.76)
ENC-T 0.78(0.26) -0.80(0.67)
ENC-NEW 0.52(0.15) -0.43(0.84)
3-month Treasury bill rate, first difference
[q.sub.1] 3 1
[q.sub.2] 1 1
Wald 0.43(0.59) 0.34(0.61)
U 1.00 1.02
MSE-T 0.37(0.22) -1.18(0.70)
MSE-F 0.07(0.28) -2.31(0.92)
ENC-T 0.42(0.32) -0.96(0.70)
ENC-NEW 0.04(0.40) -0.82(0.93)
Term spread
[q.sub.1] 3 1
[q.sub.2] 2 1
Wald 4.74(0.12) 0.46(0.61)
U 0.99 1.00
MSE-T 0.71(0.14) -0.50(0.46)
MSE-F 1.39(0.13) -0.53(0.44)
ENC-T 0.96(0.20) -0.18(0.48)
ENC-NEW 1.00(0.20) -0.09(0.48)
Dividend yield, first difference
[q.sub.1] 3 0
[q.sub.2] 1 1
Wald 2.94(0.17) 1.85(0.26)
U 0.99 1.00
MSE-T 0.84(0.13) 1.07(0.11)
MSE-F 0.95(0.09)# 0.37(0.17)
ENC-T 0.91(0.21) 1.11(0.19)
ENC-NEW 0.52(0.15) 0.20(0.26)
Real effective exchange rate, first difference
[q.sub.1] 3 0
[q.sub.2] 1 1
Wald 0.45(0.60) 2.05(0.26)
U 1.01 1.00
MSE-T -1.37(0.77) -0.33(0.44)
MSE-F -0.88(0.72) -0.33(0.55)
ENC-T -1.06(0.75) 0.26(0.38)
ENC-NEW -0.32(0.75) 0.12(0.34)
Real share price growth
[q.sub.1] 3 1
[q.sub.2] 1 1
Wald 4.19(0.10)# 3.45(0.15)
U 0.99 0.99
MSE-T 1.01(0.09)# 0.64(0.18)
MSE-F 1.86(0.04)# 0.82(0.16)
ENC-T 1.25(0.13) 1.21(0.18)
ENC-NEW 0.23(0.08)# 0.73(0.19)
Real non-food credit growth
[q.sub.1] 3 1
[q.sub.2] 1 1
Wald 1.94(0.26) 0.09(0.78)
U 1.00 1.01
MSE-T 0.43(0.17) -0.85(0.59)
MSE-F 0.29(0.20) -1.11(0.75)
ENC-T 0.46(0.30) -0.64(0.62)
ENC-NEW 0.15(0.32) -0.42(0.80)
Notes: The out-of-sample period is 2005:4-2011:4. q and q are the
lags of the ARDL equation. Wald is computed using data over 1994:1-
2011:4 period. Boot strapped p-values are given in parentheses. 0.00
signifies < 0.005. # = Bold numbers indicate significance at the 10%
level according to the bootstrapped p-values.
Table 2. Least squares estimations of 1
Horizon(h) 1 month 3 months 6 months 9 months 12 months
M0growth
[lambda] 0.9056 0.9124 0.2350 0.2124
U 0.8891 0.8958 0.9507 0.9508
M1 growth
[lambda] 0.2614 0.1048 0.1044
U 0.9898 0.9542 0.9506
M2growth
[lambda] 0.9631 0.9688
U 0.9645 0.9588
M3growth
[lambda] 0.9047 0.9450
U 0.9691 0.9278
Lending rate, first difference
[lambda] 0.1745
U 0.9849
Real share price growth
[lambda] 0.9493 0.9515 0.9218
U 0.9740 0.9763 0.9458
Notes: l is the estimated weight attached to the unrestricted model
out-of-sample forecast in an optimal composite out-of-sample
forecast; the weight is estimated using a regression model with an
intercept term.
Table 3. Data-mining-robust boot strap critical values for the
maximal out-of-sample statistic
Horizon (h) 1 month 3 months
Sig. Level 10% 5% 1% 10% 5% 1%
MSE-T 1.64 1.88 2.28 1.85 2.21 2.76
MSE-F 3.42 4.45 6.48 3.68 4.64 7.26
ENC-T 2.22 2.44 2.77 2.40 2.67 3.74
ENC-NEW 3.44 4.55 6.60 3.56 4.96 7.33
Horizon (h) 6 months 9 months
Sig. Level 10% 5% 1% 10% 5% 1%
MSE-T 2.29 2.56 3.11 2.49 2.72 3.39
MSE-F 4.14 5.62 11.13 5.46 8.12 12.42
ENC-T 2.83 3.10 3.78 3.11 3.46 4.92
ENC-NEW 4.26 6.14 10.86 5.60 9.06 16.79
Horizon (h) 12 months
Sig. Level 10% 5% 1%
MSE-T 2.85 3.28 4.04
MSE-F 5.41 6.90 12.20
ENC-T 3.60 4.18 5.54
ENC-NEW 4.70 7.00 11.68
