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MICRO LEVEL FORECASTS FOR INDIAS EXPORT SECTOR
SPECIFIC COUNTRIES AND SPECFIC COMMODITIES
Analytics & Modelling Division
NATIONAL INFORMATICS CENTRE
Department of Information Technology
Ministry of Communication & Information Technology
New Delhi-110003
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Major input to Indias export model
for a financial year
Input to an econometric model to derive macro-level
forecasts for strategic planning for Indias export RIS
Study
NIC has developed micro-level forecasts for a financial
year for specific country and specific commodities (Totalvariables: 319)
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Monthly time series behavior is captured through Neural networkmethodology.
Final model selected has been simulated with-in and outside
sample and once stabilized with regard to error statistics forecasts
are generated .
4Thought/Freefore is the state-of-the-art software tool from
COGNOS which has been used to simulate and generate micro-
level forecast Indias export for a financial year.
The reliability of the forecasts and the degree of confidence are
part of the final model
Tools and technologies used :
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Table A: SUMMARY OF COUNTRY WISE DATA-SETS
(Time Series Forecasting Carried for the listed number of
data sets)
Country List Com-Codes
Var.
for
each
Code
Total
VblsExports Imports UVI ROW
Canada 13 4 52+2(rest)+1(all)
=55
Apr 1996to June
2003
Jan 1995to Nov
2003
Jan 1995to Nov
2003
Jan 95 toNov 2003
USA 17 4 68 Apr 1996to May
2003
Jan 1993
to Oct
2003
Jan 1993
to Oct
2003
Jan93 to
Oct 2003
China 10 4 40 Apr 1996to May
2003
Jan 1995
to Nov
2003
Jan 1995
to Nov
2003
Jan 1995
to Nov
2003
Japan 11 4 44 Apr 1996to June
2003
Jan 1994
to Nov.
2003
Jan 1994
to Nov.
2003
Jan 1994
to Nov
2003
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Table A: Contd.
Country List Com-Codes
Var.
for
each
Code
Total
VblsExports Imports UVI ROW
Malaysia * 1 1 1 Apr 1996 toAug 2002
NA NA NA
Singapore* 1 1 1 Apr 1996 to
Aug 2002
NA NA NA
Thailand* 1 1 1 Apr 1996 toAug 2002
NA NA NA
Hong Kong* 1 1 1 Apr 1996 toAug 2002
NA NA NA
Rest ofWorld*
1 1 1 Apr 1996 to
Aug 2002
NA NA NA
* Only single variable total export of All Commodities from India is
considered
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Country List Com-Codes
Var.
for
each
Code
Total
VblsExports Imports UVI ROW
European
Union
26 4 104
+2 (rest)
+1(all)
=107
Apr 1996
to June
2003
Jan 1996
to June
2003
Jan 1996
to June
2003
Jan 1996
to June
2003
TOTAL 319
No. of Obs
(Range)
77-92 90-130 90-130 90-130
PeriodRange
Apr 1996to June
2003
Jan 1993to Nov
2003
Jan 1993to Nov
2003
Jan 1993to Nov
2003
Table A: Contd.
Includes both the series- monthly as well as annual - with 26 items in each
series.
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Univariate ARIMA MODEL
1. In regression analysis, if the error terms are not independent i.e.
autocorrelated, the efficiency of the ordinary least-square (OLS) parameter
estimates gets adversely affected and the standard error estimates are
biased.
2. Auto Regressive Integrated Moving Average (ARIMA) model is fit for data
with autocorrelated errors. This happens frequently with time series data.3. The ARIMA procedure analyzes and forecasts equally spaced univariate
time series data, transfer function data, and intervention data using the
autoregressive moving-average or the more general autoregressive
integrated moving-average (ARIMA) model.
4. An ARIMA model predicts a value in a response time series as a linear
combination of its own past values, past errors, and current and past values
of other time series.
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An ARIMA model contains three different kinds of parameters:
the p AR-parameters;
the q MA-parameters;
and the variance of the error term.
This amount to a total of p + q + 1 parameters to be estimated.
These parameters are always estimated on using the stationary
time series (a time series which is stationary with respect to its
variance and mean).
Univariate ARIMA MODELContd.
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NEURAL NETWORK
Neural networks cannot do anything that cannot be done using traditional
computing techniques, BUT they can do some things which would
otherwise be very difficult (time consuming).
Neural networks form a model from training data (or possibly input data)
alone.
This is particularly useful when time series behavior is complex, and
forecasts for a period is input for the next period forecast.
In a time series, behavior is complex, follows an unknown pattern, has
large number of variables, Neural networks learns from the past behavior to
develop corresponding complex algorithm and then predicts. (ARIMA:Univariate, Multivariate)
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NEURAL NETWORK
-Neural networks are a form of multiprocessor computer system, with
simple processing elements
a high degree of interconnection
simple scalar messages
adaptive interaction between elements
A biological neuron may have as many as 10,000 different inputs, and may
send its output (the presence or absence of a short-duration spike) to many
other neurons.
Neurons are wired up in a 3-dimensional pattern.
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Example
A simple single unit adaptive network:
The network has 2 inputs I0 and I1, and one output. All are binary.
If W0 *I0 + W1 * I1 + Wb > 0, then Output is 1
If W0 *I0 + W1 * I1 + Wb
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Feed Forward Neural Network
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1. EU
Model Statistics
Model fit: 75.5004Test fit: 78.4198
Overall fit: 76.4137Adjusted fit: 65.3762Iterations: 69RMS error: 16.0265Standard deviation: 16.116395% confidence interval: 32.2326Mean absolute error: 12.5406Mean absolute error (%): 8.7764F-Statistic: 20.7884
Durbin-Watson Statistic: 1.0007
A. 30613 (Import of Shrimps and prawns frozen )
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STATISTICAL MEASURES
Model fit
A measure of how well the model fits to the original data used in modeling.100% represents a perfect fit. The model fit would approach 0% if you guessed
the average value for the target. If the value is negative, the fit is worse than if
you had guessed the average value for the target (that is, you had a naive
model). The model fit is based on an adaptation of the standard R^2 statistic
(that is, the proportion of the relationship explained between two variables).
Adjusted fit
The overall fit adjusted for the number of factors, and the number of rows of
data contained in the model. This assumes that a more complex model or lessdata will produce a less predictive model.
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Test fit
The percentage of variation in the test set explained by the model. Test fit (or
percent test fit) is a measure of how well the model predicts the test data,
and is the best measure of the genuine predictive performance of the model.
The test fit is an adaptation of the standard R^2 statistic. Unlike the model
fit, the test fit can be negative. This happens if the current model yields a
less accurate prediction of the test set than the naive model.
Overall fit
An indicator of the model quality, and is a combination of the model fit and
the test fit. The overall fit is the percentage of the variation explained in thedependent variable.
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B. 90111 (Export of Coffee neither roasted nor decaffeinated
Model Statistics
Model fit: 75.6046Test fit: 73.7038Overall fit: 75.2571
Adjusted fit: 64.0117Iterations: 54RMS error: 4.4336Standard deviation: 4.459395% confidence interval: 8.9186Mean absolute error: 3.1465Mean absolute error (%): 34.767F-Statistic: 18.7563
Durbin-Watson Statistic: 0.5446
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C. 251611 (Import of Granite,crude/rough )
Model Statistics
Model fit: 67.3539Test fit: 61.8533Overall fit: 66.0773
Adjusted fit: 56.5328Iterations: 66RMS error: 3.4094Standard deviation: 3.428595% confidence interval: 6.857Mean absolute error: 2.7858Mean absolute error (%): 6.6183F-Statistic: 12.4989
Durbin-Watson Statistic: 2.122
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2. CHINAA. 670300 (Import of Human Hair, dressed, thinned, bleached or otherwise worked; wool or other
animal hair or other textile materials, prepared for use in making wigs or the like )
Model StatisticsModel fit: 85.0775Test fit: 84.3229Overall fit: 84.9804
Adjusted fit: 74.6557Iterations: 30RMS error: 1.0522Standard deviation: 1.057195% confidence interval: 2.1143Mean absolute error: 0.7224Mean absolute error (%): 24.07F-Statistic: 44.3208
Durbin-Watson Statistic: 1.2491
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B. CHINA (Import of rest of the codes)
Model StatisticsModel fit: 87.8544Test fit: 82.4129Overall fit: 87.1099Adjusted fit: 76.5264
Iterations: 126RMS error: 2828.6593Standard deviation: 2841.970795% confidence interval: 5683.9414Mean absolute error: 2114.0386Mean absolute error (%): 12.5192F-Statistic: 52.9366
Durbin-Watson Statistic: 0.8763
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C. CHINA (Unit value index for rest of the codes)
Model StatisticsModel fit: 61.607Test fit: 76.4597Overall fit: 66.02Adjusted fit: 57.6874
Iterations: 46RMS error: 6.1855Standard deviation: 6.215795% confidence interval: 12.4314Mean absolute error: 4.2899Mean absolute error (%): 4.5121F-Statistic: 14.5718
Durbin-Watson Statistic: 0.9655
3 USA
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3. USA
MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA
Number of Residuals (R) =n 70
Number of Degrees of Freedom =n-m 62
Residual Mean =Sum R / n .683103E-02
Sum of Squares =Sum R**2 121.321
Variance var=SOS/(n) 1.73316
Adjusted Variance =SOS/(n-m) 1.95679
Standard Deviation =SQRT(Adj Var) 1.39885
Standard Error of the Mean =Standard Dev/ .177655
Mean / its Standard Error =Mean/SEM .384512E-01
Mean Absolute Deviation =Sum(ABS(R))/n .992518
AIC Value ( Uses var ) =nln +2m 54.4962
SBC Value ( Uses var ) =nln +m*lnn 72.4841
BIC Value ( Uses var ) =see Wei p153 -95.0882
R Square = .887551
Durbin-Watson Statistic =[A-A(T-1)]**2/A**2 1.95492
D-W STATISTIC SUGGESTS NO SIGNIFICANT AUTOCORRELATION for lag1
A. 420310 (Import of Articles of apparel )
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MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA
Number of Residuals (R) =n 103
Number of Degrees of Freedom =n-m 97
Residual Mean =Sum R / n -.783408E-14
Sum of Squares =Sum R**2 1578.37
Variance var=SOS/(n) 15.3239
Adjusted Variance =SOS/(n-m) 16.2718
Standard Deviation =SQRT(Adj Var) 4.03383
Standard Error of the Mean =Standard Dev/ .409574
Mean / its Standard Error =Mean/SEM -.191274E-13
Mean Absolute Deviation =Sum(ABS(R))/n 3.10562
AIC Value ( Uses var ) =nln +2m 293.130
SBC Value ( Uses var ) =nln +m*lnn 308.938
BIC Value ( Uses var ) =see Wei p153 -26.2750
R Square = .858561
Durbin-Watson Statistic =[A-A(T-1)]**2/A**2 1.88808
D-W STATISTIC SUGGESTS NO SIGNIFICANT AUTOCORRELATION for lag1.
B. 570110 ( Import of Carpets and other textile coverings of wool or fine animal hair
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MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA
Number of Residuals (R) =n 105
Number of Degrees of Freedom =n-m 99
Residual Mean =Sum R / n -.708456E-01
Sum of Squares =Sum R**2 10575.5
Variance var=SOS/(n) 100.719
Adjusted Variance =SOS/(n-m) 106.824
Standard Deviation =SQRT(Adj Var) 10.3355
Standard Error of the Mean =Standard Dev/ 1.03876
Mean / its Standard Error =Mean/SEM -.682020E-01
Mean Absolute Deviation =Sum(ABS(R))/n 7.73821
AIC Value ( Uses var ) =nln +2m 496.295
SBC Value ( Uses var ) =nln +m*lnn 512.219
BIC Value ( Uses var ) =see Wei p153 165.540
R Square = .848765
Durbin-Watson Statistic =[A-A(T-1)]**2/A**2 2.04567
D-W STATISTIC SUGGESTS NO SIGNIFICANT AUTOCORRELATION for lag1.
C. 610510 (Import of Men's or boys' shirts of cotton, knitted or crocheted )
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Conclusion :
Time Constraint :
No. of independent variable for which forecast are to be generated isapproximately 319.
As the time series data keep coming over time and forecasts are to be
generated based on the latest monthly time series data within a period of
approximately 2 weeks forecasts are to be generated for 319 independentvariables.
Each variable forecast is an independent exercise.
Existing software tools arte not fully automated and the subject and toolspecialist intervention is a must.
Traditional Statistical/Econometric model techniques/software tools are
major constraint in terms of automation.
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What is Required :
NIC can develop fully automated forecasting system by
developing algorithms and testing with state-of-the-art tools
available with limited interface.
The state of the art software tool and techniques will require
funding. Manpower and resource mobilization to the tune of
Rs. 10 lakhs and for a period of 8 months.
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