Prediction of Fruit Production in India: An Econometric Approach

Trend	Additive Error Models	Trend	Multiplicative Error Models
N	y_t = l_t₋₁ + ɛ_t l_t = l_t₋₁ + αɛ_t	N	y_t = l_t₋₁ (1 + ɛ_t) l_t = l_t₋₁ (1 + αɛ_t)
A	y_t = l_t₋₁ + b_t₋₁ + ɛ_t l_t = l_t₋₁ + b_t₋₁ + αɛ_t b_t = b_t₋₁ + βɛ_t	M	y_t = (l_t₋₁ + b_t₋₁) (1 + ɛ_t) l_t = (l_t₋₁ + b_t₋₁) (1 + αɛ_t) b_t = b_t₋₁ + β(l_t₋₁ + b_t₋₁)ɛ_t
AD	y_t = l_t₋₁ + ϕb_t_−q + βɛ_t l_t = l_t₋₁ + ϕb_t₋₁ + αɛ_t b_t = ϕb_t₋₁ + βɛ_t	MD	y_t = (l_t₋₁ + ϕb_t₋₁) (1 + ɛ_t) l_t = (l_t₋₁ + ϕb_t₋₁) (1 + αɛ_t) b_t = ϕb_t₋₁ + β(l_t₋₁ + ϕb_t₋₁)ɛ_t

[i] α – smoothing factor for the level, β – smoothing factor for the trend, ϕ – damping coefficient; l – initial level components, b – initial growth components, estimated as part of the optimization problem

Table 1.

Descriptive statistics of the empirical data set

Statistic	APPLE	BANANA	GRAPE	MANGO	PINEAPPLE
Mean	1153.465	12282.65	889.9539	11091.62	904.2272
Median	1120.822	7503.050	414.3915	9559.610	837.1935
Maximum	2891.000	31504.00	3125.000	25631.00	1984.000
Minimum	90.00000	2257.000	70.00000	6988.000	76.00000
Std. Dev.	751.9735	10155.63	928.9188	4863.780	515.1081
CV (%)	65.1925	82.6827	104.3783	43.8509	56.9666
Skewness	0.428803	0.763810	1.081578	1.592267	0.344042
Kurtosis	2.330973	2.019532	2.922950	4.824546	2.073819
Jarque–Bera (Statistic)	2.957718	8.237345	11.71295	33.67557	3.328177
Probability (Jarque–Bera test)	0.227898	0.016266	0.002861	0.000000	0.189363

Forecast and actual values of the five fruits using ARIMA forecasting

Forecast and actual values of the five fruits using ETS forecasting

Table 2.

Unit root test results

Fruit	Ng–Perron test				Park test
Fruit	MZa	MZt	MSB	MPT	Statistic	Critical % value
APPLE	−4.655	−1.399	0.287	18.353	0.473	−2.250
D (APPLE)^*	−44.491	−4.683	0.105	2.220	−10.140	−3.058
BANANA	−1.800	−0.841	0.467	42.823	0.751	−2.302
D (BANANA)^*	−28.083	−3.747	0.133	3.246	−5.941	−3.103
GRAPE	−4.829	−1.323	0.274	17.601	2.367	−2.166
D (GRAPE)^*	−66.590	−5.769	0.086	1.370	−7.225	−3.032
PINEAPPLE	−16.870	−2.898	0.171	5.438	0.063	−2.072
D (PINEAPPLE)^*	−28.758	−3.783	0.131	3.215	−6.279	−2.992
MANGO	−1.232	−0.429	0.348	32.137	3.472	−2.342
D (MANGO)^*	−28.891	−3.730	0.129	3.559	−7.334	−3.170
Critical 5% value	−17.3	−2.91	0.168	5.48

* first order of difference

Table 3.

Model selection: ARIMA and Holt's nonlinear ETS model and fit criteria

Fruit	MODEL	AIC	RMSE	MAE	MAPE	Theil	BP	VP	CVP
ARIMA
APPLE	(2. 1. 0)	13.43	258.97	215.547	35.440	0.088	0.387	0.052	0.560
BANANA	(0. 1. 1)	16.90	6026.99	4972.23	80.192	0.171	0.616	0.070	0.313
GRAPE	(0. 1. 2)	13.46	813.57	710.26	219.61	0.260	0.760	0.003	0.236
PINEAPPLE	(0. 1. 3)	11.83	113.25	87.964	11.792	0.053	0.075	0.004	0.919
MANGO	(2. 2. 4)	16.59	7706.93	6078.89	47.890	0.240	0.622	0.283	0.093
Holt's nonlinear ETS
APPLE	M M A	842.86	240.93	147.58	12.97	0.086	0.014	0.026	0.95
BANANA	M M A	1032.30	1085.85	696.71	5.732	0.033	0.005	0.659	19.53
GRAPE	M M A	774.118	202.411	93.524	12.162	0.078	0.006	0.011	0.69
PINEAPPLE	M A N	763.445	89.846	60.584	7.219	0.043	0.005	0.000	0.138
MANGO	M M N	1038.17	918.334	520.421	4.014	0.038	0.022	0.353	13.84

Table 4.

Parameters of ETS models

Fruit	Parameters			Initial states
Fruit	α	β	ϕ	level	trend
APPLE	0.000	0.000	0.965	172.295	1.055
BANANA	0.165	0.000	1.000	2133.632	1.049
GRAPE	0.000	0.000	0.430	62.190	1.070
PINEAPPLE	0.944	0.000	-	39.588	33.480
MANGO	0.728	0.055	-	6907.784	0.055

Table 5.

Results of statistical tests to compare actual and forecast results between ARIMA and ETS models

Fruit	Diebold–Mariano test		Giacomini–White test		Clark–West test
Fruit	statistic	p	statistic	p	statistic	p
APPLE	0.235	0.814	0.116	0.733	3.734	<0.000
BANANA	4.746	0.000	9.879	0.001	8.209	<0.000
GRAPE	6.017	<0.000	16.849	<0.000	10.337	<0.000
PINEAPPLE	2.052	0.046	3.182	0.074	4.163	<0.000
MANGO	4.142	<0.000	6.835	0.008	6.953	<0.000

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/johr-2023-0005 | Journal eISSN: 2353-3978 (formerly 2300-5009) | Journal ISSN: 2300-5009

Journal RSS Feed

Language: English

Page range: 25 - 34

Submitted on: Apr 1, 2023

Accepted on: Jun 1, 2023

Published on: Jul 16, 2023

Published by: National Institute of Horticultural Research

In partnership with: Paradigm Publishing Services

Keywords:

ARIMA,

ETS,

Related subjects:

Ecology,

© 2023 Soumik Ray, Pradeep Mishra, Hicham Ayad, Prity Kumari, Rajnee Sharma, Binita Kumari, Abdullah Mohammad Ghazi Al Khatib, Anant Tamang, Tufleuddin Biswas, published by National Institute of Horticultural Research
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 31 (2023): Issue 1 (June 2023)

Prediction of Fruit Production in India: An Econometric Approach

Figures & Tables

Table A.

Table 1.

Figure 1.

Figure 2.

Table 2.

Table 3.

Table 4.

Table 5.

Paradigm

My account