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Prediction of Fruit Production in India: An Econometric Approach

Soumik Ray
Soumik Ray
, 
Pradeep Mishra
Pradeep Mishra
, 
Hicham Ayad
Hicham Ayad
, 
Prity Kumari
Prity Kumari
, 
Rajnee Sharma
Rajnee Sharma
, 
Binita Kumari
Binita Kumari
, 
Abdullah Mohammad Ghazi Al Khatib
Abdullah Mohammad Ghazi Al Khatib
, 
Anant Tamang
Anant Tamang
 e 
Tufleuddin Biswas
Tufleuddin Biswas
   | 16 lug 2023
Journal of Horticultural Research's Cover Image
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Pubblicato online: 16 lug 2023
Pagine: 25 - 34
Ricevuto: 01 apr 2023
Accettato: 01 giu 2023
DOI: https://doi.org/10.2478/johr-2023-0005
Parole chiave
© 2023 Soumik Ray et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Forecast and actual values of the five fruits using ARIMA forecasting
Forecast and actual values of the five fruits using ARIMA forecasting

Figure 2.

Forecast and actual values of the five fruits using ETS forecasting
Forecast and actual values of the five fruits using ETS forecasting

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

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
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

Parameters of ETS models

Fruit Parameters Initial states
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

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

State space equations for each of the models in the Holt's nonlinear

Trend Additive Error Models Trend Multiplicative Error Models
N yt = lt−1 + ɛtlt = lt−1 + αɛt N yt = lt−1 (1 + ɛt)lt = lt−1 (1 + αɛt)
A yt = lt−1 + bt−1 + ɛtlt = lt−1 + bt−1 + αɛtbt = bt−1 + βɛt M yt = (lt−1 + bt−1) (1 + ɛt)lt = (lt−1 + bt−1) (1 + αɛt)bt = bt−1 + β(lt−1 + bt−1)ɛt
AD yt = lt−1 + ϕbt−q + βɛtlt = lt−1 + ϕbt−1 + αɛtbt = ϕbt−1 + βɛt MD yt = (lt−1 + ϕbt−1) (1 + ɛt)lt = (lt−1 + ϕbt−1) (1 + αɛt)bt = ϕbt−1 + β(lt−1 + ϕbt−1)ɛt

Unit root test results

Fruit Ng–Perron test Park test
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
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