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Trends in marine fish production in Tamil Nadu using regression and autoregressive integrated moving average (ARIMA) model

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  • ICAR- National Institute of Agricultural Economics and Policy Research, New Delhi

Abstract and Figures

Tamil Nadu is situated in the south eastern coast of the Indian peninsula with a coastal line of 1076 km (13% of the country's coast line), 0.19 million sq.km of EEZ (9.4 % of total national EEZ) and a continental shelf of about 41,412 sq. km. This is one of the country's leading state in marine fish production and ranks third in marine fish production. In Tamil Nadu, Ramanathapuram district is a leading maritime district followed by Nagapattinam and Thoothukudi. The objective of this study was to investigate the trends in marine fish production in Tamil Nadu. Yearly fish production data for the period of 1988-1989 to 2012-2013 were analyzed using time-series method called Autoregressive Integrated Moving Average (ARIMA) model and Regression analysis (curve estimation). In our study, the developed best ARIMA model for Tamil Nadu marine fish production was found to be ARIMA (1, 1, 1) which have the minimum BIC (Bayesian Information Criterion). ARIMA model had got a slightly higher forecasting accuracy rate for forecasting marine fish production of Tamil Nadu than Regression trend analysis. The independent sample test showed there was no significant difference between the two models. The limitations of ARIMA model include its requirement of a long time series data for better forecast. It is basically linear model assuming that data are stationary and have a limited ability to capture non-stationarities and nonlinearities in series data. Both the models indicated that Tamil Nadu marine fish production has plateaued and fishermen should be encouraged to adopt sustainable fishing practices.
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Journal of Applied and Natural Science 9(2): 653 - 657 (2017)
Trends in marine fish production in Tamil Nadu using regression and
autoregressive integrated moving average (ARIMA) model
A. Anuja, V. K. Yadav*, V. S. Bharti and N. R. Kumar
ICAR, Central Institute of Fisheries Education, Mumbai-400061, INDIA
*Corresponding author. E-mail: vinodkumar@cife.edu.in
Received: May 9, 2016; Revised received: January 9, 2017; Accepted: April 2, 2017
Abstract: Tamil Nadu is situated in the south eastern coast of the Indian peninsula with a coastal line of 1076 km
(13% of the country’s coast line), 0.19 million sq.km of EEZ (9.4 % of total national EEZ) and a continental shelf of
about 41,412 sq. km. This is one of the country’s leading state in marine fish production and ranks third in marine
fish production. In Tamil Nadu, Ramanathapuram district is a leading maritime district followed by Nagapattinam and
Thoothukudi. The objective of this study was to investigate the trends in marine fish production in Tamil Nadu. Year-
ly fish production data for the period of 1988-1989 to 2012-2013 were analyzed using time-series method called
Autoregressive Integrated Moving Average (ARIMA) model and Regression analysis (curve estimation). In our
study, the developed best ARIMA model for Tamil Nadu marine fish production was found to be ARIMA (1, 1, 1)
which have the minimum BIC (Bayesian Information Criterion). ARIMA model had got a slightly higher forecasting
accuracy rate for forecasting marine fish production of Tamil Nadu than Regression trend analysis. The independent
sample test showed there was no significant difference between the two models. The limitations of ARIMA model
include its requirement of a long time series data for better forecast. It is basically linear model assuming that data
are stationary and have a limited ability to capture non-stationarities and nonlinearities in series data. Both the mod-
els indicated that Tamil Nadu marine fish production has plateaued and fishermen should be encouraged to adopt
sustainable fishing practices.
Keywords: ARIMA, BIC, Marine Production, Sustainable fishing, Trend line regression, Tamil Nadu
INTRODUCTION
Tamil Nadu is situated in the south eastern coast of the
Indian peninsula with a coastal line of 1076 km (13 %
of the country‟s coast line) (TNFD, 2016) and is com-
prising the Coramandel coast, Palk Bay, Gulf of man-
nar and West coast. The west coast offers excellent
scope for fishing throughout the year. The fishery
resources spread over the 0.19 million sq.km of EEZ
(9.4 % of total national EEZ) and a continental shelf of
about 41,412 sq. km (http://www.fisheries.tn.gov.in/
marine-main.html). The state ranks second in India‟s
marine fish production with a total catch landing of
6.88 lakh tonnes in 2013-14 (CMFRI, annual report-
2013-14). The state has huge fishery resources with
608 fishing villages and 13 coastal districts (Marine
Fisheries Census, 2010). The total marine fisher folk
population in the state was 7, 87,474 in 2010 (Tamil
Nadu marine fisher folk census 2010). Ramanathapu-
ram district was the leading maritime district in pro-
duction in the state followed by Nagapattinam and
Thoothukudi. The estimated marine fish production
was 432265.03 tonnes in 2013-14 and the most of the
fresh catch fish was consumed within the state itself.
The state‟s fishery resources were presently exploited
ISSN : 0974-9411 (Print), 2231-5209 (Online) All Rights Reserved © Applied and Natural Science Foundation www.jans.ansfoundation.org
jointly by traditional crafts and mechanized fishing
boats. The state had exported marine fish and fish
products to the level of 96429 tonnes, valued at
5316.29 crores in 2013-2014 (Tamil Nadu State
Fisheries Department (TNFD), 2014). The research
carried out in market had revealed the increasing de-
mands for marine products in foreign countries .The
forecasting of the marine production will be of im-
mense help to the Export Development Authority, as it
will facilitate better planning and export strategy
(Srinath and Data, 1985). An effort was made in this
paper to develop an Autoregressive Integrated Moving
Average (ARIMA) model and Regression analysis
(curve estimation) model for marine production data of
Tamil Nadu for the period of 1988-1989 to 2012-2013
and to apply the same in forecasting marine production
for the five leading years.
MATERIALS AND METHODS
Trend line curve estimation (Regression analysis):
When the data distribution is linear, the linear equa-
tion/models can be derived by using slope-intercept
formula but in the real world most data is not linear.
One of the methods to handle this type of data is trend
line. This is also known as a line of best fit and least
654
squares line. In statistics,, trend analysis often refers to
techniques for finding an underlying pattern of behav-
iour of observed data in a series. This pattern would be
hidden by noise (error) partly or nearly completely.
A simple description of these techniques is trend
estimation, which is basically a formal regression anal-
ysis(hps://en.wikipedia.org/wiki/Linear_trend_ es-
maon). This is the technique of estimating future
values of a time series data by extending the trend
line into future. Creating a trend line and calculating its
coefficients allows for the quantitative analysis of the
underlying data and the ability to both interpolate and
extrapolate the data for forecast purposes. The use of
this approach assumes that errors have zero mean and
constant variance. Unfortunately, this is not the case
most of the time.
Autoregressive integrated moving average
(ARIMA) model: ARIMA model has been popular
and widely chosen for modelling fisheries science‟s
time series data, since 1970 (Gutiérrez-Estrada et al,
2007, Stergiou et al, 1997, Bako et al, 2013). The
ARIMA model is a linear combination of time-lagged
variables and error terms. Autoregressive Integrated
Moving Average (ARIMA) model was introduced by
Box and Jenkins (1970) (hence also known as Box-
Jenkins model) in 1960s for forecasting a variable.
ARIMA method is an extrapolation method for fore-
casting and, like any other such method, it requires
only the historical time series data on the variable un-
der forecasting Box and Jenkins (1970). Among the
extrapolation methods, this is one of the most sophisti-
cated methods, for it incorporates the features of all
such methods, does not require the investigator to
choose the initial values of any variable and values of
various parameters a priori and it is robust to handle
any data pattern (Mandal, 2005).
Trend and prediction of time series can be computed
by using ARIMA model. ARIMA (p,d,q) model is a
complex linear model. p is order of process AR, q is
the order of process MA and d is the order of
A. Anuja et al. / J. Appl. & Nat. Sci. 9(2): 653 - 657 (2017)
Table 1. Total Fish Production (tonn) in Tamil Nadu (1998-
2013).
Year Production (Tonn)
1998-1999 377483
1999-2000 373926
2000-2001 372402
2001-2002 373861
2002-2003 379214
2003-2004 381148
2004-2005 307693
2005-2006 389713.07
2006-2007 392191.32
2007-2008 393266.22
2008-2009 397117.22
2009-2010 401128
2010-2011 424823.85
2011-2012 426735.44
2012-2013 429641.24
Table 2. Constructed ARIMA model for marine fish
production in Tamil Nadu.
ARIMA (p, d, q) BIC
111 20.923
211 21.141
212 21.422
112 21.249
Fig. 1. District wise Tamil Nadu marine fish production
(source- Tamil Nadu State Fisheries Department (TNFD),
2014).
Fig. 2. Trends in Tamil Nadu marine fish production (in
tonn) (1998-2013).
Fig. 3. Forecasted marine fish production in Tamil Nadu.
655
difference. There are three parts (they do not have to
contain always all of these): AR (Autoregressive)
linear combination of the influence of previous values;
I Integrative) – random walk; MA (Moving average) –
linear combination of previous errors. These models
are very flexible, quite hard for computing and for the
understanding of the results.
They are basically linear models assuming that data are
stationary and have a limited ability to capture non-
stationarities and nonlinearities in series data ( Khashei
and Bijari, 2010 and 2011). If the data are highly non-
linear & have fuzziness, advance methods like artifi-
cial neural network (ANN), fuzzy inference system
etc. can be taken for better prediction of marine fish
production.
RESULTS AND DISCUSSION
Tamil Nadu marine fish production: The fish catch
records during the year 1998-2004 showed a slow
decline in growth irrespective of increased fishing
capacity during that period and the reason maybe
mainly due to the decline in oil sardine production.
Further, by the year 2004-2005, there was heavy
decline in marine fish production in the state due to the
occurrence of the natural catastrophe “Tsunami” in the
state by the end of the 2004 year. However, the year
2005-2010 showed an encouraging revival in fish
production with unexpected growth in oil sardine pro-
duction due to targeted fishing for the specific fish
species. Table 1 shows the total marine fish production
data in Tamil Nadu (1998-2013).
The district wise marine fish production during the
period 2000-2013 in the state had been led by Rama-
nathapuram district followed by Nagapattinam and
Thoothukudi as shown in Fig 1.
Trends in Tamil Nadu marine fish production:
Using the above Table 1 data, a trend line and forecast
of marine fish production was constructed as shown in
Fig 2 using regression analysis (curve estimation). The
figure showed the trends in fish production in Tamil
Nadu for the indicated respective periods of time. The
severities in fluctuations in production were
pronounced and were underscored by the best fit given
by the polynomial of degree 6. The sudden drop in
production during 2004-05 was due to tsunami while
2010-2013 production trends shows a plateau indicat-
ing the stagnant production during that particular
period of time.
The forecasted marine fish production for the period
2013-2018 was shown in figure 3 using regression
analysis (curve estimation) and the graph indicates the
marginal increasing trend in production.
Tamil Nadu marine fish production by ARIMA
model: As ARIMA model requires a large data set, the
data for Tamil Nadu marine fish production during
1998-2013 was used from Table 1 so as to fit the mod-
el. ARIMA model for any variable involves three steps
such as identification, estimation and verification.
ARIMA model was estimated only after transforming
A. Anuja et al. / J. Appl. & Nat. Sci. 9(2): 653 - 657 (2017)
Table 3. ARIMA Model Parameter Estimation.
ARIMA Model Parameters
Estimate SE t Sig.
Tamil Nadu-Model_1 Tamil Nadu Natural Log
Constant -0.014 0.019 -0.770 0.459
AR Lag 1 -0.140 0.380 -0.368 0.721
Difference 1.00
MA Lag 1 0.983 5.819 0.169 0.869
Year No Transformation Numerator Lag 0 0.003 0.002 1.410 0.189
Table 4. Forecasted Tamil Nadu marine fish production (in
tonn) by using regression analysis and ARIMA model.
Year Forecasted by
regression Forecasted by
ARIMA
1998-1999 378526.4
1999-2000 373913.6 376090.3
2000-2001 370678.3 373332.3
2001-2002 368820.6 372323.2
2002-2003 368340.4 372854.5
2003-2004 369237.9 375014.7
2004-2005 371512.9 378663.8
2005-2006 375165.5 382488.7
2006-2007 380195.6 376321.9
2007-2008 386603.4 384551.6
2008-2009 394388.7 393546.5
2009-2010 403551.6 403144.3
2010-2011 414092.1 413845.2
2011-2012 426010.1 424542.3
2012-2013 439305.7 439507.9
2013-2014 453979 455528.8
2014-2015 470029.8 471164
2015-2016 487458.1 490564.1
2016-2017 506264.1 512047.2
2017-2018 526447.6 536124.6
Fig. 4. Tamil Nadu marine fish production (in tonn) by
ARIMA model.
656
the variable under forecasting into a stationary series.
The stationary series is the one whose values vary over
time only around a constant mean and constant
variance. If the given data is non-stationary in mean, it
is corrected through appropriate differencing of the
data; the next step is to identify the values of p and q.
The ACF and PACF of the order of p and q can at
most be 1. We constructed four tentative ARIMA
models (Table 2) and chose that model which has min-
imum BIC (Bayesian Information Criterion). The
models and corresponding BIC values was listed in
Table 2.
Model parameters were estimated (Table 3) using
SPSS package, and with low BIC values, the most
suitable model was ARIMA (1, 1, 1).
Where,
C = Constant term;
ɸj = jth auto regression parameter;
Θ1 = Moving average parameter
et = error term at time t
So the fitted ARIMA model for fish production is
The forecasted marine fish production in the state as
shown in figure 4 using ARIMA model indicates the
increasing trend in production during the selected peri-
od of time.
Forecasted marine fish production values of Tamil
Nadu using regression analysis (curve estimation) and
ARIMA model are shown in Table 4.
112111 ttttt eeyyCy
1211 983.0140.014.ttttt eeyyy
In time series forecasting, the forecasting accuracy of a
model is commonly measured in terms of Mean Square
Error (MSE) or in terms of Average Error. Lower the
MSE or average error, better the forecasting method.
MSE is defined as
Mean Square Error =
and forecasting error as
Forecasting error (in percent) =
Average forecasting error (in percent) =
With the above comparison of actual production of
marine fish production of Tamil Nadu with the fore-
casted production by regression analysis and ARIMA
model, average forecasting error (%) are 3.09 and
3.03, respectively. Hence, the ARIMA model can get a
slightly higher forecasting accuracy rate for forecasting
marine fish production of Tamil Nadu than Regression
trend analysis.
The comparative forecasted value analysed with
regression analysis and ARIMA model for the year
2013-2018 are being displayed below in figure 5.
Independent samples test of forecasted value by
Regression and ARIMA: The independent samples
test (Table 5.) showed that there was no significant
difference between the two models; regression and
ARIMA models.
Conclusion
ARIMA model offers a better technique for predicting
the magnitude of any variable than the regression anal-
ysis. Its limitations include its requirement of a long
time series data for better forecast. They are basically
linear models assuming that data are stationary and
have a limited ability to capture non-stationarities and
nonlinearities in series data. In our study, the devel-
oped model for Tamil Nadu marine fish production
was found to be ARIMA (1, 1, 1). ARIMA model had
got slightly higher forecasting accuracy rate for fore-
casting marine fish production of Tamil Nadu than
n
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n
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2
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valueactual
valueactaulforecasted
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A. Anuja et al. / J. Appl. & Nat. Sci. 9(2): 653 - 657 (2017)
Table 5. Independent sample test of forecasted value with regression analysis and ARIMA model.
Independent Samples Test
Levene's Test for
Equality of Variances t-test for Equality of Means
F Sig. t df Sig.
(2-tailed) Mean
Difference Std. Error
Difference
95% Confidence Inter-
val of the Difference
Lower Upper
Forecast Equal variances
assumed 0.001 0.970 -0.143 36 0.887 -2403.17904 16788.2038 -36451.234 31644.876
Equal variances
not assumed -0.143 35.989 0.887 -2403.17904 16788.2038 -36451.582 31645.224
Fig. 5. Comparative forecasted value (in tonn) with regres-
sion analysis and ARIMA model.
657
Regression trend analysis. The independent samples
test showed that there was no significant difference
between the two models; regression and ARIMA mod-
els. From the forecast available by using the developed
ARIMA model and regression analysis, indicated that
Tamil Nadu marine fish production has plateaued.
From this we can suggest that Fishermen should be
encouraged to adopt sustainable fishing practices. It is
necessary to increase awareness on sustainable fisher-
ies. The focus of the Government should be towards
promotion of sustainable fisheries rather than on wel-
fare aspects. If the relationships between different vari-
ables in fisheries are highly non-linear and also data
have fuzziness, advance methods like artificial neural
network (ANN), fuzzy inference system etc. can be
taken for better prediction of marine fish production.
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A. Anuja et al. / J. Appl. & Nat. Sci. 9(2): 653 - 657 (2017)
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Artificial neural networks (ANNs) are flexible computing frameworks and universal approximators that can be applied to a wide range of time series forecasting problems with a high degree of accuracy. However, despite all advantages cited for artificial neural networks, their performance for some real time series is not satisfactory. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In this paper, a novel hybrid model of artificial neural networks is proposed using auto-regressive integrated moving average (ARIMA) models in order to yield a more accurate forecasting model than artificial neural networks. The empirical results with three well-known real data sets indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by artificial neural networks. Therefore, it can be used as an appropriate alternative model for forecasting task, especially when higher forecasting accuracy is needed.
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Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the hybridization are quite different. In the literature, several hybrid techniques have been proposed by combining linear and nonlinear models, in order to overcome the deficiencies of single models and yield results that are more accurate. However, recent research activities in hybrid linear and nonlinear models indicate that these models have two basic limitations that have decreased their popularity for time series forecasting. These two basic limitations are: a the hybrid linear and nonlinear models have some assumptions that will degenerate their performance if the opposite situations occur, and b the hybrid linear and nonlinear models require a large amount of historical data in order to produce accurate results. In this paper, a novel hybrid model is proposed for time series forecasting by combining linear autoregressive integrated moving average ARIMA, nonlinear artificial neural networks ANNs, and fuzzy models. In the proposed model, no prior assumption of traditional hybrid linear and nonlinear models is considered for the relationship between the linear and nonlinear components. In the proposed model the data limitation of traditional hybrid linear and nonlinear models is also lifted through investing on the advantages of the fuzzy models. Empirical results of financial markets, especially exchange rate market, forecasting indicate that proposed model performs significantly better than its components used separately, traditional hybrid linear and nonlinear, and other fuzzy and nonfuzzy models in incomplete data situations.
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A new hybrid methodology for nonlinear time series forecasting. Modelling and Simulation in Engineering Forecasting sugarcane production in India with ARIMA model from https
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  • M Bijari
Khashei, M. and Bijari, M. (2011). A new hybrid methodology for nonlinear time series forecasting. Modelling and Simulation in Engineering, 2011, Article ID 379121, 5 pages Mandal, B. N. (2005). Forecasting sugarcane production in India with ARIMA model, Pp.1-13. Retrieved January 9, 2017 from https://www.researchgate.net/ publication/256079794
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Srinath, M. and Datta, K. K. (1985). Forecasting marine product exports time-Series analysis. Indian Journal of Fisheries, 32(2): 264-267