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ECONÓMICAS |
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Cancino, Cancino-Escalante and Cancino-Ricketts / Económicas CUC, vol. 44 no. 1, pp. 69–82, January – June, 2023 |
CUC |
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Modeling and forecasting blackberry production in Colombia using a Box Jenkins ARIMA approach Un modelo Box Jenkins ARIMA para modelar y pronosticar la producción de mora de castilla en Colombia |
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Blackberry production in Colombia contributes to the nation´s gross domestic profit, employment and farmers’ social well-being. It is considered of great economic importance as blackberry fruits are used as raw material for the agroindustry. In this manner, production instability affects farmers’ economic profitability; therefore, forecasting plays an important role in monitoring production as well as in farmers´ planting decision and resource allocation. Hence, the purpose of the study was to model and forecast blackberry production in Colombia using a Box-Jenkins ARIMA approach for the period 1992-2023. A quantitative, non-experimental, correlational and descriptive research design was selected. The appropriateness of the model and its predictive capacity was assessed by verifying the different goodness-of-fit criteria. Results showed that the ARIMA (1,1,0) was the most suitable model as it captured the behavior of the actual time series. Based on the forecasted values it is expected a 5.47% increase in blackberry production for the period 2021-2023 which will consequently improve farmers´ income and thus contribute to the reduction in poverty. Palabras clave: Predictive capacity; univariate analysis; data modeling; production Resumen La producción de mora de castilla en Colombia contribuye al producto interno bruto, al empleo y al bienestar social de los agricultores del país. Es considerado de gran importancia económica una vez que los frutos de la mora son utilizados como materia prima para la agroindustria. De esta manera, la inestabilidad de la producción afecta la rentabilidad económica de los agricultores; por lo tanto, el pronóstico de la producción de mora posee un importante papel en la asignación de recursos y la toma de decisiones de los agricultores. Por lo tanto, el propósito del estudio fue modelar y pronosticar la producción de mora en Colombia utilizando un enfoque ARIMA de Box-Jenkins para el período 1992-2023. Se seleccionó una investigación tipo cuantitativa, no experimental, correlacional y descriptiva. Se evaluó la adecuación del modelo y su capacidad predictiva mediante la verificación de los diferentes criterios de bondad de ajuste. Los resultados mostraron que ARIMA (1,1,0) fue el modelo más adecuado una vez que capturó el comportamiento de la serie temporal actual. Con base en los valores pronosticados se espera un aumento de 5,47% en la producción de mora para el período 2021-2023 lo que mejorará los ingresos de los agricultores y contribuirá, así a la reducción de la pobreza en el campo. Keywords: Capacidad predictiva; análisis univariado; modelado de datos; producción |
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Scientific and Technological Research Article. Date Received: 08/05/2022 Date of Return: 18/07/2022 Date of Acceptance: 10/08/2022 Date of Publication: 22/08/2022 |
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Universidad de Pamplona Pamplona, Norte de Santander (Colombia) susancancino@hotmail.com |
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Giovanni Orlando Cancino-Escalante Universidad de Pamplona Pamplona, Norte de Santander (Colombia) gcancino@unipamplona.edu.co |
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Daniel Francisco Cancino-Ricketts Pontifica Universidad Javeriana Bogotá, D. C. (Colombia) dfranciscocancino@javeriana.edu.co |
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. To cite this Article: Cancino, S. E., Cancino-Escalante, G. E. & Cancino-Ricketts, D. F. (2023). Modeling and forecasting blackberry production in Colombia using a Box Jenkins ARIMA approach. Económicas CUC, 44(1), 69–82. DOI: https://doi.org/10.17981/econcuc.44.1.2023.Econ.4 |
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JEL: C50, C51, C52, C53 |
Introduction
The Andean blackberry (Rubus glaucus) also known as “Mora de Castilla” is native to the tropical highlands of America, cultivated from the northern regions of the Andes to the southern highlands of Mexico (Franco & Giraldo, 1998). It is considered of great economic importance as blackberry fruits are used as raw material for processed products such as juices and jams and for consumption in the fresh state (Restrepo, Luna-Ramírez & Quintero-Castaño, 2019).
In Colombia, it is grown at altitudes between 1 800 and 2 300 meters above sea level, in eighteen departments of which Santander, Cundinamarca, Nariño and Huila are the most relevant producers with 60% of national production (Agronet, s.f.). Moreover, it is a vital source of income for small —and medium size farmers (Cárdenas et al., 2018; Cancino, Cancino-Escalante & Cancino-Ricketts, 2020) and has in the last decade created over 51 thousand jobs, of which 39 000 are employed directly and 12 000 indirectly (Ministerio de Agricultura & Desarrollo Rural-Minagricultura, 2021).
In view of the above, production instability affects farmers’ economic profitability therefore, it is essential to have thorough knowledge about the future development of blackberry production. In this manner, forecasting plays an important role not only in monitoring production but also in farmers´ planting decision and resource allocation (Khan et al., 2020). In fact, it can provide ground for policy makers to understand the early signs of short —and long-term changes and trend variations.
In this regard, there are a number of mathematical and statistical approaches available to help understand the dynamics of forecasting. These include the exponential smoothing approach; the single and simultaneous-equation regression methodologies; the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and the Vector Autoregression (VAR) models. Essentially, they are employed in different economic activities, including production, financial management, fiscal and monetary policies as well as in budgeting (Gujarati & Porter, 2010).
Despite their widespread application, each one has unique benefits and restrictions. When using data with cyclical or seasonal variations, for instance, the exponential smoothing strategy does not provide reliable forecasts, nonetheless it is very simple to use (Iqbal, 2020). The single and simultaneous-equation processes also have a number of restrictions, including the requirement to distinguish between the types of forecasting that can be produced (ex-ante and ex-post), and the fact that they can only be employed with at least two continuous variables (exogenous and endogenous) (Iqbal, 2020). Similar to this, the VAR technique also requires that data from many economic time series be incorporated into the forecasting procedure, and in some situations, this can lead to over-specified models (Brandt & Bessler, 1984); however, its advantage is that it can be estimated using ordinary least square, which is typically straightforward.
Therefore, due to the limitations of the previously mentioned methods the ARIMA approach is considered to be a viable alternative for modeling and forecasting as it is not only suitable for short-term time series, but it also increases the prediction accuracy whilst using a small number of parameters (Khan & Khan, 2020). In addition, when compared to other methodologies it is less sensitive to data fluctuations. However, one of its major disadvantages is that, unlike the exponential smoothing model, when new data becomes available the forecasting procedure has to be repeated, especially the diagnostic checking stage (Khan & Khan, 2020). Furthermore, there are a certain amount of subjective input at the different stages of the modeling process which makes it somewhat more than an art than a science (Sánchez-López, Barreras-Serrano, Pérez-Linares, Figueroa-Saavedra & Olivas-Valdez, 2013).
In essence it is a commonly used forecasting method and it assumes a linear dependence between the times series data (Sánchez-López et al., 2013), in which it is expressed in terms of its past values as well as the current and lagged values of a “white noise” error term (Meyler, Kenny & Quinn, 1998). It involves different steps of the modeling process: identification, parameter estimation, validation and forecasting; and the iteration of these stages is crucial in identifying the most adequate model (Chen, 2008). Although it is a theory free approach, it has proven to be more accurate for forecasting real world situation when compared to other regression and econometric methods (Afzal, Rehman & Butt, 2002). In this manner, the purpose of the current study is to model and forecast blackberry production in Colombia using a Box-Jenkins ARIMA (Integrated Moving Average Autoregressive Models) approach.
The present paper is structured as follows. After this introduction, the literature review is presented followed by the methodological approach, which includes model specification, data, variables and performed tests. The third section includes the empirical results whilst the last two sections discuss and summarizes the major findings.
Literature Review
Even though there are many studies on the biological and agricultural aspects of blackberry production, forecast analysis has received very little attention in the literature, most probably because in many countries the data on the quantity of production is inaccurate or lacking (Cancino, Cancino & Cancino, 2021). Nonetheless, this methodology has been widely employed in other fruit crops to forecast production, consumption, imports and exports.
The most similar works to blackberry production forecast are those of Khan et al. (2020) whom using time series data over the period 1997-2015 employed a Box-Jenkins approach to predict guava area and production in Pakistan. The study found that the projected area was static and that production showed an upward trend with an average 2.12% increase for the period 2015-2030. Moreover, Ullah, Khan and Zheng (2018) forecasted peach area and production in Pakistan for the period 1997-98 to 2014-15 by also applying the Box-Jenkins ARIMA methodology. The best model’s predictability power, performance and quality were, according to the authors, measured based on error value of the root, mean square error, mean absolute error and mean absolute prediction error. The findings of their study determined that the ARIMA model is an efficient tool and that in the short run both peach area and production showed a declining trend, due probably to high input costs, lack of cold storages and government attention to the crop.
In this same context, Hamjah (2014) forecasted the production of major fruit crops in Bangladesh using ARIMA model. Furthermore, Akın et al. (2021) employed the same method to forecast the growth trends of cherry production in Turkey, whilst Mehmood and Ahmad (2013) and Burhan and Khalid (2006) predicted mango and kinnow production in Pakistan, using the same approach.
Methodology
A quantitative, non-experimental, correlational and descriptive research design was selected in order to address the purpose of the study. Respective time series Data on Annual Production (PROD) in tons for the 1999-2020 period was obtained from Colombia´s Ministry of Agricultural and Rural Development and the Food and Agriculture Organization of the United Nations (FAO, s.f.) database. In addition, a Box-Jenkins methodology using an Autoregressive Integrated Moving Average (ARIMA) model was applied to describe and forecast the yearly behavior of the proposed time series. The estimation and analysis were performed employing the E-views® software (v. 9).
ARIMA model identification and estimation
In order to identify the correct ARIMA model the unit root test, Autocorrelation (ACF) and Partial Autocorrelation Functions (PACF), as well as the selection criteria, are the primarily tools. In this manner, the general ARIMA (p, d, q), where the p and q parameters denote the Autoregressive (AR) and Moving Average (MA) order and d the degree of differencing, can be written as (1) (Judge, Hill, Griffiths, Lutkepohl & Lee, 1988):
Where:
φ(B) = Represents the autoregressive term of order ´p´ and is the back-shift operator B = BmXt = Xt – M (m = 0, 1, 2 …p).
∇ d Xt = Is the back-shift difference operator defined as ∇ = ∇ Xt = (Xt – X t—1 ) = (1 – B)Xt.
θ(B) = Refers to the moving average term of order ´q defined as θ(B) = 1 – θ1 B1 – θ2 B2 – … θqBq.
Ut = Is a white noise process.
With the aim to determine whether differencing (d) is required, namely if the time series statistical properties (mean, variance, and covariance) do not change with time the Augmented Dickey-Fuller (1979) (ADF) and the Phillips-Perron (1988) (PP) stationary tests were employed. Thus, both method tests the null hypothesis that a time series is integrated of order one I (1), specifically, if it presents a unit root (non-stationary) against the alternative that it is stationary. The ACF and PACF functions were also employed to help determine the order of the AR and/or MA terms; whereas the Akaike Information Criterion (AIC) was used to choose which model was the best fit for the time series data. Finally, after the p, d and q values were determined the coefficients were estimated.
Model validation and forecast error evaluation
Diagnostic checking is a key aspect for verifying the model´s goodness of fit and its forecasting ability. Therefore, the residuals were tested for white noise (normal error, independent, zero mean and constant variance) by employing the Ljung-Box Q statistics tests. The stationarity condition of the ARIMA model was also analyzed using the inverse roots of characteristic AR polynomial.
In addition, the ARIMA forecast predictive capacity, that is, the degree to which the predicted result matches with the actual result was also evaluated. Thus, different accuracy metrics to evaluate forecast errors as proposed by Brooks (2008), particularly Theil’s inequality coefficient, the mean absolute percentage error and the bias proportion, were employed. Generally, the smaller the criteria, the smaller the error size.
Results
The first step was to examine the time plot of the blackberry production data and to identify whether or not it could be the outcome of a stationary process. From a visual inspection of the graph of the given observations (Figure 1), it can be noted that the time series showed an upward trend, with a slight decrease during the period 2010-2011 due probably to the impact of weather changes associated with La Niña that caused a reduction in blackberry production. Notwithstanding, the presence of an upward trend suggests that the times series are non-stationary in level.
Figure 1. Blackberry production (ton) 1999-2020.
Source: Own elaboration.
In this manner, the non-stationarity of the times series was also confirmed with the ADF and PP tests (Table 1) that showed that for both constant and constant and trend the t-statistic values were greater than the critical value of the significance level of 0.05. However, at first difference the null hypothesis of the unit root was rejected which can be concluded the data is stationary of order one I (I).
Unit root test results (ADF and PP).
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Test |
Variable |
Level |
First difference |
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t-statistics |
Critical values |
t-statistics |
Critical values |
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1% |
5% |
10% |
1% |
5% |
10% |
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ADF |
PROD |
Constant |
–0.06 |
–3.80 |
–3.02 |
–2.65 |
Constant |
–6.82 |
–3.80 |
–3.02 |
–2.65 |
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Constant & trend |
–2.53 |
–4.49 |
–3.64 |
–3.26 |
Constant & trend |
–6.66 |
–4.49 |
–3.65 |
–3.26 |
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PP |
PROD |
t-statistics |
Critical values |
t-statistics |
Critical values |
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1% |
5% |
10% |
1% |
5% |
10% |
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Constant |
0.02 |
–3.78 |
–3.01 |
–2.64 |
Constant |
–6.92 |
–3.80 |
–3.02 |
–2.65 |
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Constant & trend |
–2.44 |
–4.46 |
–3.64 |
–3.26 |
Constant & trend |
–6.89 |
–4.49 |
–3.65 |
–3.26 |
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Source: Own elaboration using E-views® (v. 9).
Model identification and estimation
Having determined the degree of differencing the AR and MA orders were selected by examining the ACF and PACF samples. As shown in Figure 2 the first order differenced time series of blackberry production exceeds the significance limit at lag 1 for both ACF and PACF, followed by a significant fall, hence p = 1 and q = 1 were tentatively considered.
Figure 2. Autocorrelation and partial autocorrelation function of the PROD series.
Source: Own elaboration using E-views® (v. 9).
However, due to the subjective nature of the ARIMA methodology in order to identify the best model that fits the data a larger range of p and q values was also examined as shown in Table 2, Table 3 and Table 4. Thus, after analyzing the AIC values in conjunction with the coefficients and statistics the ARIMA (1, 1, 0) model was chosen as it provided a more adequate representation of the available data.
ARIMA (1, 1, 0) model.
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Dependent Variable: PROD |
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Convergence achieved after 21 iterations |
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Coefficient covariance computed using outer product of gradients |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
3984.707 |
1353.509 |
2.943982 |
0.0087 |
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AR (1) |
–0.430253 |
0.184401 |
–2.333248 |
0.0314 |
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SIGMASQ |
47311951 |
15921530 |
2.971571 |
0.0082 |
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R-squared |
0.198720 |
Mean dependent var |
4017.476 |
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Adjusted R-squared |
0.109689 |
S.D. dependent var |
7873.865 |
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S.E. of regression |
7429.487 |
Akaike info criterion |
20.80561 |
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|
Sum squared resid |
9.94E+08 |
Schwarz criterion |
20.95483 |
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Log likelihood |
–215.4589 |
Hannan-Quinn criter. |
20.83800 |
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F-statistic |
3.882032 |
Durbin-Watson stat |
2.016132 |
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Prob(F-statistic) |
0.056163 |
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Source: Own elaboration using E-views® (v. 9).
ARIMA (0, 1, 1) model.
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Dependent Variable: PROD |
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Convergence achieved after 9 iterations |
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Coefficient covariance computed using outer product of gradients |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
C |
3899.240 |
1180.419 |
3.303267 |
0.0040 |
|
MA (1) |
–0.423645 |
0.327676 |
–1.292877 |
0.2124 |
|
SIGMASQ |
47510440 |
16876760 |
2.815140 |
0.0115 |
|
R-squared |
0.195359 |
Mean dependent var |
4017.476 |
|
|
Adjusted R-squared |
0.105954 |
S.D. dependent var |
7873.865 |
|
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S.E. of regression |
7445.055 |
Akaike info criterion |
20.81947 |
|
|
Sum squared resid |
9.98E+08 |
Schwarz criterion |
20.96869 |
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Log likelihood |
–215.4994 |
Hannan-Quinn criter. |
20.84185 |
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F-statistic |
2.185107 |
Durbin-Watson stat |
2.123406 |
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Prob(F-statistic) |
0.141391 |
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Source: Own elaboration using E-views® (v. 9).
ARIMA (1, 1, 1) model.
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Dependent Variable: PROD |
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Convergence achieved after 26 iterations |
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Coefficient covariance computed using outer product of gradients |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
C |
3955.169 |
1285.786 |
3.076072 |
0.0068 |
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AR (1) |
–0.266144 |
0.877048 |
–0.303454 |
0.7652 |
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MA (1) |
–0.215644 |
1.069727 |
–0.201588 |
0.8426 |
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SIGMASQ |
46539825 |
15808277 |
2.944016 |
0.0091 |
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R-squared |
0.211797 |
Mean dependent var |
4017.476 |
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Adjusted R-squared |
0.072702 |
S.D. dependent var |
7873.865 |
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S.E. of regression |
7582.241 |
Akaike info criterion |
20.88573 |
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Sum squared resid |
9.77E+08 |
Schwarz criterion |
21.08469 |
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Log likelihood |
–215.3002 |
Hannan-Quinn criter. |
20.92891 |
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F-statistic |
1.522683 |
Durbin-Watson stat |
2.086495 |
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Prob(F-statistic) |
0.244717 |
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Source: Own elaboration using E-views® (v. 9).
Model validation and forecast error evaluation
The appropriateness of the model was also assessed by verifying the different goodness-of-fit criteria. As can be seen in Figure 3, the proposed ARIMA model (1, 1, 0) confirms the non-existence of autocorrelation of the residuals, given that all the lags’ coefficients are within the significance bands. Moreover, the Q-statistics and the p-values results presented in the last two columns corroborate that the residuals are white noise, that is, the time series is independent with zero mean and constant variance.
Figure 3. ACF and PACF Residual.
Source: Own elaboration using E-views® (v. 9).
In addition, the estimated ARIMA structure was examined in order to confirm its stability. As outlined in Figure 4 the inverse AR root lies inside the unit circle, which therefore can be concluded that the model is dynamically stable, thus the results suggest that the ARIMA model (1,1,0) is efficient to accurately forecast blackberry production.
Figure 4. Inverse roots of the AR polynomial.
Source: Own elaboration using E-views® (v. 9).
As a result, the model´s accuracy was confirmed when analyzing the predicted (forecast) blackberry production values against the actual trend as shown in Figure 5. The forecast curve, in general terms, captures the behavior of the actual time series, except for the period 2010-2011 when, as previously mentioned, production suffered a significant decrease due to climate changes. It also shows a better fit when compared to the other proposed models as the mean absolute percentage error (7.7%) presented a small variation between the actual and predicted series, as the error was less than 10 per cent. Moreover, Theil´s inequality coefficient (0.04) was close to zero, which indicates that the estimated results are better than the observed values. As for the bias proportion (0.05), which measures the systematic error of the forecast, that is the difference between the actual and forecasted series, was very negligible.
Figure 5. Actual and forecast of blackberry production (1999-2020).
Source: Own elaboration.
Data forecasting
Having satisfied the model´s performance the next step was to forecast blackberry production values for the following 3 years (2021-2023). As can be seen in Table 5 it is estimated that production should increase from 145 535 tons to 153 504 tons, that is, a 5.47% growth. It is however important to emphasize that blackberry production for the year 2021 has not yet been officially announced when writing this article that is why it was included in the forecast.
Forecasting blackberry production for the 2021-2023 period.
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Year |
2021 |
2022 |
2023 |
|
Forecast (ton) |
145.535 |
149.519 |
153.504 |
Source: Own elaboration using E-views® (v. 9).
Therefore, the results obtained in the present study are similar to those of Khan et al. (2020) in guava; Hamjah (2014) in major future crops; Mehmood and Ahmad (2013) and Burhan & Khalid (2006) in mango; Ullah et al. (2018) in peach. In the sense that the use of ARIMA models are a viable alternative and an efficient tool for predicting the magnitude of any variable
Discussion
Agriculture plays a vital role in Colombia´s economy as it contributes to the nation´s gross domestic profit, employment and farmers’ social well-being (Cárdenas et al., 2018; Arguello & Valderrama-González, 2015; Henley, 2012). However, the uncertainty of agricultural production makes investment and planting decisions difficult therefore, forecasting production provides farmers with information that will allow them to become more efficient and allocate resources optimally. Thus, the Box-Jenkins ARIMA methodology is an important tool in forecasting blackberry production in Colombia.
Likewise, in addition to contributing to the knowledge of blackberry production in Colombia, the ARIMA model has many other strengths. First, it is appropriate for any time series data, and second, there is no need for the forecaster to choose a prior value of any parameter (Gajbihe, Wankhade & Mahalle, 2010). Moreover, the structural approach of the ARIMA technique is to build candidate models, remove incorrect ones, and thus use the most suitable model. This methodology prevents the choice of a particular model that may not be the most appropriate one (Majid & Mir, 2018).
Furthermore, it can be argued that within the structure of univariate time series-modeling studies, the ARIMA approach is also a significant tool for formulating agricultural policies (Khan et al., 2020). Therefore, it is quite essential to have a clear understanding of the present as well as forecasting the future when aiming to ensure farmers´ income and improve crop production productivity.
Conclusions
In this manner, the present study used historical yearly blackberry production (1999-2020) to forecast future production (2021-2023) by employing a Box-Jenkins ARIMA approach. The predictability power of the developed model was assessed by comparing the actual and the simulated values and the results revealed that the selected model (1, 1, 0) showed a high accuracy and ability to simulate the dynamic behavior of blackberry production in Colombia. As such, the projected blackberry production in Colombia is quite favorable as it is expected a 5.47% growth for the following three years. This will improve farmers´ income and thus contribute to the reduction in poverty.
There is no doubt that the research findings are important as it is not only a useful tool to forecast blackberry production, but it also provides policy makers and farmers to valuable information on planning and planting decisions as well as resource allocation. Nonetheless, it is recommended that for future studies a larger data set should be included in order to provide higher accuracy level.
Declaration of Authorship
Cancino: Formal analysis, Research, conceptualization, methodology, Writing - Preparation of original draft.
Cancino-Escalante: Acquisition of funds, Research, Writing-Preparation of original draft, Writing-Revision and editing.
Cancino-Ricketts: Research, Data curation, Writing-Preparation of original draft, Writing-Revising and editing.
Acknowledgments and Thanks
This article is a product derived from the research project entitled “Molecular characterization of cultivated Rubus sp species and clonal multiplication of promising accessions with characteristics of high productivity and disease tolerance”.
References
Afzal, M., Rehman, H. U. & Butt, A. R. (2002). Forecasting: a dilemma of modules (A Comparison of Theory Based and Theory Free Approaches). Pakistan Economic and Social Review, 40(1), 1–18. Available: https://www.jstor.org/stable/25825233
Agronet. (s.f.). Blackberry statistical data [Database]. Available: http://www.agronet.gov.co/estadistica/Paginas/home.aspx
Akın, M., Eyduran, S., Çelik, Ş., Aliyev, P., Ayko, S. & Eyduran, E. (2021). Modeling and forecasting cherry production in Turkey. The Journal of Animal and Plant Science, 31(3), 773–781. https://doi.org/10.36899/JAPS.2021.3.0267
Arguello, R. & Valderrama-González, D. (2015). Sectoral and poverty impacts of agricultural policy adjustments in Colombia. Agricultural Economics, 46(2), 259–280. https://doi.org/10.1111/agec.12155
Burhan, A. & Khalid, M. (2006). Forecasting Kinnow production in Pakistan: An econometric analysis. International Journal of Agriculture & Biology, 8(4), 455–458. Available from https://www.fspublishers.org/published_papers/6916_..pdf
Brandt, J. & Bessler, D. (1984). Forecasting with Vector Autoregressions versus a Univariate ARIMA Process: An empirical example with U.S. Hog Prices. North Central Journal of Agricultural Economics, 6(2), 29–36. https://doi.org/10.2307/1349248
Brooks, C. (2019). Introductory econometrics for finance. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781108524872
Cancino, S., Cancino-Escalante, G. y Cancino-Ricketts, D. (2020). Modelo econométrico para el cultivo de mora de castilla (Rubus glaucus) en los municipios de Pamplona y Chitagá, Norte de Santander, Colombia. Aibi Revista de Investigación, Administración e Ingeniería, 8(1), 37–43. https://doi.org/10.15649/2346030X.752
Cancino, S., Cancino, G. y Cancino, D. (2021). Análisis de regresión de los factores que afectan la rentabilidad económica de la producción de curuba. Dictamen Libre, (29), 1–13. https://doi.org/10.18041/2619-4244/dl.29.7861
Cárdenas M, Echavarría J, Hernández G, Maiguashca A, Meisel A, Ocampo, J. y Zárate, J. (2018). Coyuntura del sector agropecuario colombiano. [Informe de la Junta Directiva al Congreso de la República]. Bogotá, D.C.: Banco de la República. Disponible en https://www.banrep.gov.co/es/recuadro-2-coyuntura-del-sector-agropecuario-colombiano
Chen, C.-K. (2008). An integrated enrollment forecast model. AIR IR Applications, 15, 1–18. Available: https://eric.ed.gov/?id=ED504328
Dickey, D. & Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431. https://doi.org/10.2307/2286348
E-views (version 9.0). Econometric Views. [Software]. London: IHS. Available: www.eviews.com
Franco G. y Giraldo, M. (1998). El cultivo de la mora. Mosquera: Corporación Colombiana de Investigación Agropecuaria-CORPOICA. Disponible en http://bibliotecadigital.agronet.gov.co/handle/11348/4039
FAO. (s.f.). FAOSTAT. Crops and livestock products. [Database]. Available: https://www.fao.org/faostat/en/#data/QCL
Gajbihe, S., Wankhade, R. & Mahalle, S. (2010). Forecasting chickpea production in India using ARIMA model. International Journal of Commerce and Business Management, 3(2), 212–215. Available from http://researchjournal.co.in/upload/assignments/3_212-215.pdf
Gujarati, D. y Porter, D. (2010). Econometría. México D.F.: McGraw Hill.
Hamjah, M. A. (2014). Forecasting Major Fruit Crops Productions in Bangladesh using Box-Jenkins ARIMA Model. Journal of Economics and Sustainable Development, 5(7), 96–107. Available from https://core.ac.uk/download/pdf/234646336.pdf
Henley D. (2012). The agrarian roots of industrial growth: rural development in South-East Asia and sub-Saharan Africa. Development Policy Review, 30(51), 25–47. https://doi.org/10.1111/j.1467-7679.2012.00564.x
Iqbal, M. A. (2020). Application of regression techniques with their advantages and disadvantages. Elektor Magazine, 4(1), 11–17. Available: https://www.elektormagazine.com/magazine-archive/2020
Judge, G., Hill, R., Griffiths W., Lutkepohl, H. & Lee, T. (1991). An introduction to the theory and practice of econometrics. [2 ed.]. New York: Wiley.
Khan, S. & Khan, U. (2020). Comparison of Forecasting Performance with VAR vs. ARIMA Models Using Economic Variables of Bangladesh. Asian Journal of Probability and Statistics, 10(2), 33–47. https://doi.org/10.9734/ajpas/2020/v10i230243
Khan, D., Ullah, A., Bibi, Z., Ullah, I., Zulfiqar, M. & Khan, Z. (2020). Forecasting area and production of guava in Pakistan: An econometric analysis. Sarhad Journal of Agriculture, 36(1), 272–281. http://dx.doi.org/10.17582/journal.sja/2020/36.1.272.281
Majid, R. & Mir, S. (2018). Advances in Statistical Forecasting Methods: An Overview. Economic Affairs, 63(4), 815–831. https://doi.org/10.30954/0424-2513.4.2018.5
Mehmood, S. & Ahmad, Z. (2013). Time series model to forecast area of mangoes from Pakistan: An application of univariate ARIMA model. Academy of Contemporary Research, 2(1), 10–15.
Meyler, A., Kenny, G. & Quinn, T. (1998). Forecasting Irish inflation using ARIMA models [Technical Paper 3/RT/98]. Dublín: Central Bank of Ireland. Available: https://www.centralbank.ie/docs/default-source/publications/research-technical-papers/3rt98---forecasting-irish-inflation-using-arima-models-(kenny-meyler-and-quinn).pdf
Phillips, P. & Perron, P. (1988). Testing for a unit root in time series regression. Biometricka, 75(2), 335–346. https://doi.org/10.2307/2336182
República de Colombia. MinAgricultura. (2021). Cadena productiva de la mora Dirección de Cadenas Agrícolas y Forestales. Marzo de 2021. Bogotá, D.C.: Minagricultura. Recuperado de https://sioc.minagricultura.gov.co/Mora/Documentos/2021-03-31%20Cifras%20Sectoriales.pdf
Restrepo, M., Luna-Ramirez, J. & Castaño-Quintero, V. (2019). Evaluation of the shelf-life of blackberry pulp fortified with physiologically active compounds. Respuestas, 24(2), 16–26. Available: https://revistas.ufps.edu.co/index.php/respuestas/article/download/1827/2203?inline=1
Sánchez-López, E., Barreras-Serrano, A., Pérez-Linares, C., Figueroa-Saavedra, F. & Olivas-Valdez, J. (2013). Using an ARIMA model to forecast bovine milk production in Baja California, México. Tropical and Subtropical Agroecosystems, 16(3), 315–324. Available: https://www.revista.ccba.uady.mx/ojs/index.php/TSA/article/view/1290
Ullah, A., Khan, D. & Zheng, S. (2018). Forecasting of peach area and production wise econometric analysis. The Journal of Animal & Plant Sciences, 28(4), 1121–1127. Available: http://www.thejaps.org.pk/docs/v-28-04/23.pdf
Biodata
Susan Cancino is an economist from the Universidade Federal de Pernambuco (Brazil). MBA from the University of Nottingham (United Kingdom). Independent Researcher, member of the Plant Biotechnology Group, University of Pamplona (Colombia). ORCID: https://orcid.org/0000-0001-7827-8502
Giovanni Orlando Cancino-Escalante is a biologist from the Pontificia Universidad Javeriana (Colombia). PhD from the University of Nottingham (United Kingdom). Full Time Professor, University of Pamplona (Colombia). ORCID: https://orcid.org/0000-0002-3812-1129
Daniel Francisco Cancino-Ricketts is a final-year biology student from the Pontificia Universidad Javeriana (Colombia). ORCID: https://orcid.org/0000-0003-4605-6360