In this research, we aim to predict the production of pulses in six countries (Afghanistan - Bangladesh - China - India - Nepal - Pakistan). In present studies these countries for selected for south Asian region on the basis of higher production. The study period extends (1961-2019 from
www.fao.org) an annual frequency. To forecast pulses production up to year 2027, we use three types of models Autoregressive Integrated Moving Average (ARIMA) - Nonlinear autoregressive neural network (NNAR) - Exponential Smoothing (ETS) first use the full forms followed by short forms) and compare their results. We will use data spanning from (1961-2015) for estimation and training by models and data from (2016 - 2019) to validate the models. Before that, our methodology goes through several stages:
DATA exploration
To visualize the data features (patterns, unusual observations, changes over time) we need to plot the data and then translate that through descriptive statistics and normal distribution of the data using the following statistic:
![](data:image/png;base64,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)
..........(1)
Where
n: Number of observations, S: Skewness, K: kurtosis.
DATA stationary
Time series that have a trend and volatility are not stationary, will affect the value of the time series at different time. Thus, the series cannot be predicted in the long run. One way to determine whether a time series is stationary or not is to use a unit root. The time series in Augmented Dickey-Fuller test is described by the equation (
Dickey and Fuller, 1981):
![](data:image/png;base64,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)
..........(2)
Where
c : constant, α: coefficient on a time trend, p: lag order of the autoregressive process. The ADF test is carried out under the null hypothesis δ = 0 (not stationary) against the alternative of d < 0 (stationary). If the null hypothesis is not rejected, we perform the first difference to make the series stationary:
![](data:image/png;base64,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)
..........(3)
Estimation of models
To forecast pulses production up to year 2027, following three types of models are used:
ARIMA model
ARIMA models are the most widely used statistical models for time series forecasting, this is done by describing the autocorrelation in the data
(Box et al., 2015). These models are divided into three parts, according to their nomenclature (Auto Regressive-Integrated-Moving Average) (p, d, q).
Autoregressive (p) refers to predicting a variable using a linear set of its preceding values, the model of order p can be written as:
![](data:image/png;base64,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)
..........(4)
Where
β
p: parameters of model, p: lag order of the autoregressive process, ε
t: error term. Integrated (d) refers to the degree of stationary of a variable that is determined using ADF test.
Moving average (q): uses past forecast errors in in regression. The equation will be in the form:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAWCAYAAACi7pBsAAARSElEQVRoBc2Ze5BdVZXGT9IJSQgBBQeTEVKIWCjogANMEtDA4JQDlSCBEBHBAhyxyhpmUB5OCaIwRLHk7QNEAoQAIiCiaFmAIek8ujtp8gAChLya7nTo7qRf93Xe5+zf1Lf27UBNjc5fTk1X3bq37z1n773W+ta3vrVOAHUcMXkBzkEBJEWOA/K8hBxwJdAgLysUlPaV3jNSoMSRk5KRk1CWoV2fJ/YTfqEYiiqUdUoH+kkvLV1q3xKKUpeWuLyBc5GtrNXRb7GuzCnIiMhtN8oGFBFaUGfWtVpTNugeiIARe3dk+sKfpYQyLyicPzcuhjKiQDaHkA1AWaUBVPH+0MqyUfY62ynHZXlzPefPDWSF/67M/X06lz+Mzl7aOWVrIKdH8agtUJYQFxCXuTnHHCa/xzJQDosYiSMzLk5lVEYU1+xAOnQ9GrXv5KDcQSbj5QSX4xqD4BIyB5GDtHQ485CdzJwVhnULrhwmB1ZSh2zLUx0/JysjYhJzPlkCcYjL5AhISgh1/tjv6fKarSWHR3ls12in+mjFoqwAx6lcm6BrXaGz1zn/rNOZND7g4iuuYnclJcodaZ7gnD+Drk/TqveXjJQtaWzQ0xVR7AFr7pb3DQHe4fpP1wQ+npnBrlHzaJHBtWpqV6Shd64clmeRsIDMocwgqbyLWXnTQZlGFC41nFVtU4hq/pBpViCfaPOoUgEhw4yPcIJ6mUI8QJmPMJymhjZDr3aJtWtEWlSJk7rijS3mEuKoSpT4dWVUkoXkRWS5OByFFsAoxwIoAOAyXJmSFzFJWodyBMLtfO/qy1n8n3dTjeCKf7uK79x6s9mhYJrvipKi0Q9FhTT1wS6ynLLIyMuCWtM+2YhSXT6ycHhny9qEkoCwF9K6IbMmP8oWpW0BYgqZUtjWGWkSkTpvHEVsyHV55DcQTaTeMEOpkU1OkY3YQkK1DLegiQvk5Di0LCrLnDRObD3cPpY+eDvzvnQpAzlUE0eS5pacQm3hqjinzGtGT+sLfTnUI4hFHWSWfXGeeXuA+5f+ks+fu9BAUR8ZaN4stCdQNCDu4ivz59K6epsFe3V7G5+adTz7ksRiW+jMSjuUET6jS91rQSyIm74TNEbTzAOo0O/GdXZcLaGcCMj28O2rruD+Z/7IOxYXIbzOd675Fk88/iu05Wg5Ykxq8EpHePml55gwLiAYHxAEARMnjOeAIKBl/GSWPPkiQ07OVQKLx3sg6+Fzp89iwoSDuO6me6kIdUVOmdTs0HZ4A0cV4l0sW3I7n130dfY10zGJPVrDAnInChplx5Z2zjrjJCZNCJjQEnDZ5dcYcAzpecNQnDrVAJ8Q9z74KOcsWOQhax4UxWF0Z6nX38WpR85g7fqd9EewbdtWzj77dN6pen4XhUVxlVR07Pay6/U2Fmj/IOCAieO47GtXW3B0OlUAg2+uLPI871HuQR1Q7WLjmhf4xq13MSxgq7BWejn2mOPZM1injtI8JtSSWQOyIbb86VkOaAkIWlo44MCptLRMZFwQMG7iZO5/8gWjHxmPE3/u4bqvn+eD1HIQwYFHsnLDLl9EnQqhR4u4mVw01MNzz/yCWfMvN6dXM18WQv1s52sQ1Xdz1IxDeOaXS41ynnn210ya+kE6Nu4gjDKyPCLLhLkE5UijcNz/0DIuuPASwtCSn1qcETuoitYFwcows2cczmuvdzNcwup17Xz3lhstM5W5mTKbBkPhbuJigL/78HSee+QXUNT4/e9/R9ByCCs63rQga7nRyqB3vPP2jTld74FQ3f3Wm5x25vn0DYkYBxnYuYlZZ36Bd1JtAw1FTIlaRlAfglAI9oWy0vBqxqeOpw9RUBmLazKo7eXjRxzOQ08+TX8G/7xoEdfd9B2qQm8pzSMsRiDUx3uhfJuHf7GYuedfjEhAQLAaojUb+m+U7p1b+MRHZzHQm9GIvM/qhc7p1Uup9HZ1yrgf52rkZcKyRx9n3vzz7EhJ0aS5pmIjyaF/G58+4hBWvtTKoR85jg/POoWtg3tRdgm4scSG0coAfd2v8ZEZxzA6kFlZ0iUKia6VyXHiC2dmGSX7VPyboHFyelbFJQmLLvwqnetfhXwfTz5wJ1fe/FP2aCFDlzRQKKuh0QfxsOd81b6mzGyUBQqNrg9VVLVLvcGWla0cNuVA3h5qoLLbMOEl4SfuleyUMmjw2qoXOCwImBYETJgQEEw9jGDSEQSHHMnyja9jFGQycZAirXDR+V9hQ0eXr0UqD7a3I9UH0Wg6yKb231mGtWi9ICAYdwDjJx7MpIOn89yajQaoWApERbrez6nTD2bd+o0mFdd3beO0eWcx3HCEAqvlWRXyPgj7uXTRZaxb+4Y52RTOmJSW2iveLTleusrxPmMVwMDQ5ep88/pvs+ShB6C2m9tu+HfueepZ+poRVLVXepWpnL2LraufoEVGBBOMy6dOCDDDWqbw89+sMeda/cgyOpa/yNzZsxmueRkYOmWGnB2RSKpJsbiMzatfZGoQcNDE5lqTZxC0zCQ46Eheevl1q1cUhdfS1BnY/SafnTuboOVAjv7kSQwlCfWyoPCCAZJ9rGt92pw+viWgpaXFnB4EU5h40OE8v36LZVAsZyqTB/s5ffqHWPNKt9FaEo7w5QvOYc2GHQxJjhpSS1NWuGF6t67n7DPm0DJ+Eh87/kTqScOUfKzslYxsBl+WOrGESWeBNCWgHAZXY9WaFSy84Fzj1Y8fNYM39o0iVlLbYBJLoRLS8i42rXiMCUHApImTOXTKeCariKqgTPsb7n78RfY2gS5V1LHiBT4962QqjRhRwGiqRkpnaGo+ySrp+FD8r36hl0cevpvPzL/U9he/ilMLoScrKVydaq2bLyw4k189cr/ZUknUlnmaidQEmIF1cFI2auoSHln2GOcuWGT9gJwiJw6mauhySCvQv5vTps/kd2u2Gq1RDnHDv17MVd+704KwN/Y6jmwY0r18eeHZPL50iSFYSZ1mzvqblJwwV8MlitVRcuJMZ/Hnj/KQAKE3r1FUKlyy8AJ+89tn+OQpsxlV7yE2sqYgszKvzrCQRDR+921XvSoF4nOnUU+N18wBKiBEbF71Bw6eEDBQqVsGiJ9rzhFHDS+rpI+sOdN6dWi8zqMPLGbuon+xTFNXGGWpsVVizcww/T1bWDjvi4z0xyZjrdGR75opnGYhRSEFIzIrrJD+5OdLOPf8C4lVa9RtRn5N09PhMOzbwT8edwwvbeoy5sbt4obrFnLl93/EXm8xomLiHoa3buCMuQsZrHpnh2GI+jf5q1Ik1p0bG1lx036ZFXgVUf1nHamKDnGVC+fN46KvXcm1P/ixaV75u/edbl59bYNpcOl9uXIkblCqewwj4y/R4ljbL//7UUFKIVRUd3L8zGksXfawoeumHy/hrC9canEyhNtRM2vN89qgFdJfP3YHJ8//IrubxsZxSJh67U2xl/bWP3DwAYdRG8oQDfT39fD+Q4+hbd0Otu3qYuv2LUYGOkc1L+zMSx59cr9kdFlMURQkidJe3DECI9s5YcZU1mzeYcMDGODaqy/ivqefo6+EeiylVYWsj80r/sjkKTPZM6D+LmV3zy6mH3kiKzt38kZPD69sfQXkvESNw4ipPjm8kmDnCbJ8EJf2QdTLUw/+lGDSB/jZr1cYsiTnNqxvpXXln/arld7GkLXi6lBVunNRophHTUmWmxCIUs0jRB+q+LtYfN0FHGg1YDxBy5F84+YHTLNIvXjDRR9K0gzSPh564HY+f8kVxrlaO4q88lXxzQkZqfRy/NEf4qml99kejzx0H+NaDmXD5t2s6VhHa9sKqxqZKy3Qyk3p9PnnnGfNURbqXLnNX3RKs6WynTM/cggXX/ZVeuqwq3svMz54NG/3afSgP0nRYVISRtMKRx1xGE88/FNEz48//iDBuINZtaGL1o5X6dz0qslW035uGBePGsLrDmqFI3BWw4esQO7Z2s7UmSewqU9O07nqzD/7DE6dM4vBvQ0ktSQh6zQo0hpFo0a9kZiC0GxC7bDus+ptJFyFcCdkb7PgjBOtDlz8testFEP7dbcaU+WP7pN5dcqyTi336SoJVuaOslRJymk4VZkGu7dvZP4Zf2+FfMrkFpY99luGKgULLriQWXNOJowqxuVKZyO63Cstq8jiXHXMha8FhWZLo7uYM30Sv3zqaabM+BjHfuJ0Nm3osU5XcHjzrZd5//TJzDjuGG699y7e3rme+f/0SWuOtP/SJ55FHf3n5p3HybPnMDQybIO7d7o3ctTMQznmuFO55baHLICBUjAJ+6B8i87lyzh2zjn0KJMEgTSlrW0NG199DRUobT4cK9a+QBgyDdG5dZiFSQfdmFnBkpz0UZAHJRj99FAmhyqKzZ/lcJOeRUZU699/nRxvwfcIoBYOmUJQFlnhLTKKxA+zxvhy+fK1bHj5FfJEaG5QklKNNJTzf0nDT0GtDpRWRjVOhUo/p82czsq1nT7DpEAS34PUi5Trb/4mnZtW0t6xmhtvvAGHZjsqx5llq4CmM6xet4JV7a1etpZw3X9cyer252lrf5mbbrmduCwJNJ8w/GY7+e7Vl3DNTXczqLvlkShjXed6XmxttUPr4KoNmugpWEUZWzRVXDUolSGllIBLrJprCRtP2LSxJIpGyF3YHKOqidAsRXfi5ysac1pIVYzkLl+odEHWnAhqLmRNhzIpLYw6NW+ppyb+6OjYTEdbp42IpcqKUgOJ3DLFppV2Fj+G8CaWuCSDsMGJH/pb2ja8Zv1Gog65OfxQa3Pv/XcSx4Ps2Po6d9z+I5O9Nu9snt8PwDJWr1vO6rYVLJj/JU464TP8+L57iIoaXV1dLF78A3NroEi9vfMNpr9vIh+YNokVqzq9sYJzCa2rV9H+ckezkcn3Kwk5SpO1/SFtIsnHW5Z5lOoS+VJTRA229Cqcd4IoQ4Ow977kRaMqhVDqz166Zux7vas9bb6ED1eiOYuGqmvWttPZ2WkO01nG7tM9tl/x7p6+jkg0RRDGfOqjx7Krv8+aozHbNOaWlTd86xo2d3awdn0b1954vX0Xxg2zRfYIcALDylXL2bRpgzfewbXXXs2mVzby/IsvcMv3F5sfg7A2yOBALx887FC+9MWL7WJJP3NqAava1jJn7mwGhvtJnVK5pNaoms15oav+8t97HfrX+KxZd16qlvhzta9rY9acf6C3t9cOZgFqHnEsyGMnHgsCecmeN7Zz9Iwj6BkaMNKw7EsSk8xSLsO7+zh82vs4+viP8YOf3W31QIDze+fo+UI9rLFx40ZOOeUU9vYPmC+7u7uZNm0aJ51yMj+8/TajusDSuYip10QLXkFJRWnTMNLAyBFmDZIybo5MRQeeEv53l4+Z99d711ne6/gki/cHwc8+/vzecroMzTUEq0uNQd1l5vRQErGZL0K6q8dImr3V08Utd91mWa4apv31MGQs8FmWkatGKBHzwrIriiLe2r6NH915h0e6zVRcak2G6CSJC0Tzcqhe4nwlrom1rGGbyLCoWcD+vEn/N7/IaKV3I6rbzF2fdT696/WX/uR0OckM1Zy3VKn35VGUZVreFRi/W+8WsbV7F7f+5C67RTeIvjQi0V4KsiSw1s1tpv7u07Gt297ijnvutiFfIC2ux3GuOfcd83acaM7hedujKfISTI+u/h8hPUr85N6fyae7HGCP2Mwp/3M+inbkVDlIiESz4xJGs4i65bcPl6FclavmH+zoIYSkgLpQ1R81birU2tPO0Kwd5rzSWVC1T5pnzXpYEhRSBS4nzxKSKCaO8v0PiseURbVesWbDD298wVCh8cXmL2Hpr//bmLPFp+9FuL6XKH0vp//3z6IBhcScLiRHemRTmpbW93JsmPrGzJ54iAmEfLHA/ifg2idjpDLsVZVEZJY1Hz86TzVijNSPd8Ms4r8Aoyv1pqPJgr4AAAAASUVORK5CYII=)
..........(5)
Where
β
q: Parameters of model, q: Lag order of the moving average, ε
t: Error term.
Whereas (d) is determined by ADF test, (p) and (q) are determined by the autocorrelation r(p) function and the partial autocorrelation function R(p), which are given according to the following:
![](data:image/png;base64,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)
..........(6)
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)
..........(7)
NNAR model
Neural network autoregressive models are statistical models that allow complex nonlinear relationships to predict a variable using its lagged values. Where lagged values of the time series can be used as inputs to a neural network.
(Hyndman et al., 2012) previously suggested this method. These models are distinguished from ARIMA models by the presence of a hidden layer, in which the linear weighted input is modified by a nonlinear function before it is output:
![](data:image/png;base64,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)
..........(8)
In the hidden layer, this is modified using a nonlinear function:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF4AAAApCAYAAAC89Z4XAAAS+klEQVRoBe1bC7BV1XneF7iIHWK1NQ9xaqczMSakGB95jFZtG0Fe6uVpfQ1tlUzUCREEohBUIDKtiXW0JkYT5P2QVzEkBkVtZqS2TQWtikHoBeQhj/s695x99mutvffX+f5/r3OOxjwQMt427Jl99z57r732Wt///9//WPt6+D3d8jwHd5ulyGAA+IiSDqRpDuRAEucFMhmATK7xen0rrtcvHNWZd1St/x81bgQ+h0VsOpDmZZlhUE2RpW6yJ4B3SByXowOencVJFTkqCKI2zJgxAytXrBUNN4bonwD+uADuOnHAx3EMwCJDGaPGDEFTUxMWL1ohwMcxKegE8A6z43J0wLOzICxjytSvYOurL2L06NECfE68ZTsBvEPiuBwd8FlGYK0418R2CfDLlq6CNYC1BegnnOtxwVw6ccAzUvErXbBpF4Aqhg4ditWr1ksAwyAmR1bsGtjUR+CEUr9yNGe/91FNZlMg13DS9w9h/PjxWLJ4pQBvrAOdx+MMfJqmoLlZa2VvlBq1ghvvcYuiSI7uGf7gOdu5NrwWhqG0c8/Ljx72x2k8gc8N51WBMV0YNmxYDXibMs43SHOLNAMyhviyE5dj1PhGcHjuhOCO6vXr4CsnKooEm8C7zYHPNo3X3f2edJR5C5LEUDU+jjswduxYrFu7AcYCiUkF9AypgN4IfJ67UPODzUqohuASKALHATmwXZfGGNF2B6Y7uvvOEvg82/5f2BzwNoqBNEFmuxCGbRg5ciSWL1uNKFZ6sUgJe41qnMYfM/AcgNPU9wKWJElNGLxHwAks21OrSSk85y4TKTpovP7ePnvKbwe8ImqRmk5xriOGDceihcvlMumFwHN3HH/cgCcQBJiAOk12FsB7DlC2+XUb7zdaSiMl/brnPqx7NeCzHFkcSDhZKu3HuDFjRePpc+lck9zAwErAaXPledX/Y+T4RkB/FTdXq1XBxzlNPhMEHCxEYK4PCs73/RqWTpC1Cz3oxAGfxgmQW/zw8Qdw5pl/iF5eEzyvGX8+6AKUuisCvICfAyaDOlnR/2ME3tEMNZ7AOw13YDvwqM2Oyx3gPDrNdoLgNfeMu9eD8K4NxQGfsyxgWTbwwXDScUoYkdsh2v470fg8s7BRFbA+clvFtLtnwevdjAu/eCn8SoQ8zfD2nl0YNWoMtr25HUEUwqQaXrKESu6j0Gbc9Q0sWbxQBh4n1AZu7qjz4UQcVxYNPvjBdcTju/rlOzk+EkKDU3RvKp6TSJlN5beFjUsMhDW4iJTTtZd3czwjG/Z6zM4V5LfUB8Ld2PJv63Dx+FHYA+CK0TejysuVMq4eMRTb32pFlAJ+GiHOjZgcw3sOTuZuqrh7+lTMnv0ADOvZCe9YULAcaoIM1KvQ5vBDq88QDJmJ1sANzZ795XnNamg9Yjl8SRH+2SStv5gekO+jr5KH+b4QOWJhZgrb7TJO6ccB7gbvhMVn65u0d03ql4/6jOOv+z++K4PHrC1p3w2YnZj5tdH47oYN2Aegk/PJgTn3zMPSxctQrYZFRcMKgBLG5lAwGcvnoZjs+HE3YdfbZQHWWkLB5CyBnwUIxHALQXFChQlo9gjIsbAggt9IVXGo1pfFKbtUNFm2TUgVKeiFxBPZCLBl2NxHjBg0PsopLhY9wGcYn1NpUtKiCpkC/iC7RjkusVKl4djd7miX0iIzcPBxHMJLbAgkHYBpxdyvX4OHl67DEVbsEKNUOYJzzr4YpQ5m1RFMVkWHzSH5axoC1S747jcsTFDB/MeX4NvffhTVKFdNswnSLEYCiyBPkLLslwORXwF4nuUyIB2UDrxSqajgitUI54dE1ejkYivgZ1Gi3q5QAFoUWbmu8Ux9VEbUZZ6DRTHuamTyxO/yj9N0d1StyeAZMdAy1j48DWf08eCddDq8fh9FZ2k7XtmyEcNH34JQuNBgzNWXw+t3GoaNuQEo78e1Q7+EppP74+uz5glQnNA7rXvx5UsHo6PbwjcKJIFnQEYNzHKNIoTiChrixF3E5DSFZl73JaqNEjEVVJFGVk2H1paRWNT6IP1HspzH+JvsRNApDiESZqmZEWvm73pcXtfS2hgaNPdXXftthObmxra+X0aWWXisRcB0AXYP7rj5avxw3UbQzcDswX23X4/J9z+BPRx1HODgjtfQf8A52H24DNiDqLS+hIsuH4LDtHhqVJwg7WrH5wd+Bh1VNX3h+zSQ7I9AEII06ARoMSZAlsQ6eYIfJWB9hGAV1C0CdVzLYWUSTBfEy9ptTvgyAVWALWDmM40774nGsyAmRbHi92+D3DG0cT6KtKnU6TiehJmVgWAH/umer+KhJ9eiwhdVWzFxyPl4cNUm7OfUEoPcL+PPPncJXnrlTSDcg9eeW4bps+/DYWfqlSqQdOJvRw3Hps2vo7vQshwGlTBAlMRAFiLpPoSzP3EqTuvbC81NHvr27QevqTf+6I8/iua+/XDu585Hd9mXBIbgRTFDXZ29ONYCUXXcCjwvCbANIijMUKKbGvDU/VxJSdsfA6o1i3GWoxbeaB2NNEm6YTRkTAyP4SJMNxDtEOf6yJp1CnznTkwafhG+v/oZvF1MKjcWN0+ZiWmz7gXsYax57B+w+ZVtYCU75MyJTncrJlx5GeYv/6kAX0oM4iwSONiE/IvcB5JuIKmKh40Trf751VDASzL1D7QW7mInNlNLSFN4nieJTpPnwWsqdq8XPO78zeteM5pkd/eb5VpvzwN3fa6PPiPt3XNHd2xq6o13702yfMglRO4cS58+fI9X03ihGk3HfCD6BWbfMR7fW/8UWLWAvxdf+avz8IO1m3AAQHugMfvPXvwPqeAhOIJ77pyEtghCTVVRKQP4/4Prh3weK3+8GQcMxBEzEo6Z9VGACZ1qVTSfiQsFL9qq/g5xqrQRGiUm/uZzwtX1pX/lEYmoGZry5bq52L1eteU9U6MdZfvG3+7JD3b8TVGN03gX3VDjuXsSayUlIPlvzPrGODyw8inIRw4VAn8uHl//AloZXhaceWDbNgwcMAA/37oFY266SayjVICKqAxUd2LC0C9g6doX0FE4vHJYUeYVurAodx3CJ//0TPTxPDQ3N4v2NfXuheaT+sJr6oVzL7gQ3VX6hbrG8/sXCohm7CIDm0awdNyZZt2ELrFG/ASBJ/2bhKWNeh0qSqrieFnyZU8KjPIu+3WJEY9pSiecIoqC2nVeY7sw1DIKlwcdDcrQan1q+EjAOWYHfJIwJmQczywoagPsL/DNyePw0OqNQh3o3Ilbh30B31vzDPYCQhsy4SP7MLFlBK69dTIe+dHzaGOMzKkxPq60AcleTGy5DM+++Jr0w2mzrMrkS/YkRJZGMKEvNMM6j0KZSxRDsCthJKAHiZFjZFVDuSAhk44qiEJ6ItX2OEsQMbQsNsbmCRlNDMEiikryI2VoW/gdOvL6psATZAe8zBUEVd/JXIQ7gSdH8z6PEplyAhKZqe9wtStVEi2hkN+dcxWqSUwFyErAkVcxccRfYOq8x5Vq0gOYM2kcJt37HXGu7DKvVIC4DXOn3QrvD87AyyWgq+DgoJuRig90bMfFA/8E+zpCAZ7PxYZRvIZzJBYmENxc7M5JML6ntvI+tZt87wQiR1kl04Qsz3hk9kwBZUgKazBJjsAPNTFj4kR+46cbpiz0lhmfHkboj77DaSjf/17AHfAOZILFc9eOc1iyZJEGBoV/ue66G2pzamtrkzm6PxQCrYvCowV5VoZSxoaHZ+MTdDJ9B2DTlp2APYDX/3M9Wm6cKNQTsOjIZZngILZufhaX3TBJM1wiKsjEQNSFrt2v4opLv4jOEPKc8HOWCaP5cVoLE1nzIcCcIM2PEQ+7oQBqtFJ0XWayJaRtkaUxUhsiy5RCojSWGJ3ZaRBqYsWXxDwn9Ri2qwKGaaEv1Egq5Zvlhe8DOsGlZjttd/TSKAwCyHFTePLZn7N69l2syjnNp4I5rudz7MdL4COzJcD4QKUChsmqjyUk0T4MPHcQdrS+oyPlmmvchZee34iH1m7C7kJ70jBEWjki0dHyBY9h7ty5qGbaTxjGMkFGLk5GHJgC7UzZIgj8woR1bZdCoAW4SRAMSb4E5hjUXlLWlOnTsOpffoSAUSLBJKKkPdZvhKIy5CmjtrcBc1jKCu3MnEm1fOB96IXvcprtFENphbRFQSo1qUBEvkK1jutJKdRwpRb1Iw54CpPge0YZGqa7SwbNhysRvyWkO+3G9Mm34ek1q4Coim9Nm4KkvQ033jgBO0oGB1IWvTgOqzST+hh/zbXYe7hbzLnKD0ClsEU+5KKxOiLVBGp2LOUER0LqeHSgCppqDyfI7FeikzxEGHYIfVx15VCc/JH+ePCR70sCFzBNYEbLSCmztVq6aHyyC/ffcwseW/0TkASoqVISroU/SjeNgBNgpUWtN/E3x0Lg2I7n+pkfx6xzc6A7oJ3i8LqW2rUPL2YHHIixYAGKOKqRGmRhB2xpP64dfBH2/ftz+PuWkfjm3Adw5YTbxCrYLuXqADnblDFr+iTMmvcg2hPlUalBEntRL61UsgLJEJIRiQvt4kgdZWppuko/orxSuNIogqOyJpDSNX3J7Lun4eWXN2Pc+L/BslXrVH2oiPTgsriRgOUQ9pZE7UDWiru+NgaPrn5aalFSr6J5NwDvqIXXOA5aoQOZAqC2O+Cd5pNmqKysxqqjLb5CthblchlnnXUW7rzzTrS0tGDOnDmoVpU2vYhOq9AASo1xs+wEkxle6qN9x1bcNPQSXHHRhTjnwr9Ea6lI0aWOr2n7rKm34cnli4RiGGhRPxPG6fQLTJeTEAKsK+NKWKWcTVDVYSr1UPOdxqgAtNKSi9aTugKYWIPVocNGYNHSJ1VhnMxMrEKCQcTSRN4NpG/h3tvHS5RGtmeRk1RDShDGoQgkgiEaBnnoo+PQAfz1kMHwenmYM/c+5RQ+WwQHHCPB5s5N+d7UQk32vWDBAmzbtg3z5y9AqUTvkqlzdS91vb77dxEMs7bB+JXflxBQHbNqCx+g1hShHu+LIH+pQ+VFd1mPRdbkXip96R3HkbzEYhk1jaWHLOdiBauXLDb5GD58ONaueUotT2iNg3MfKUVImSXnHYD/Bv7xjhvwz6s2SpRGpk5MXsuMI8v4iNweAlwU8Uu4bsRQPLFqJQ5Zg7PO/ixe3vJaLWx19aTafGpj5+y5qyD27NmFZcuW4In5i6UYy+tR7OPD/5KMA6ZMeKwNXjVR+NLdynMYGyKVaIafVZcRRZ1oaRmNJYuWq+z5mUqeiaDEgvJIyxPpESB+C/Nuvx4/eOpfsauo3dOOuDBDdpIyRW6RMJlMfVTeeAWfOf007Opsk/B66qxvYebMuUIpHCaFRiX75Y29clfgWY2cOHEintn4AsJAv8igEvUM4B3o7wO8c146wYIG8ipSRioIheMXLliqwuNnJrzKckOewMZlfHLAaTiznyeh8kcYLjefDq//p+D1PgXnXXyJAM9FknLAvIEaEMB0H0Trz57F4PMH4VDoi0+4ZcpdmDPnfhkGQ2Eub4pl02hr4+bzqvH0ES6qmT17LtqOdMmHsOyADrdnAa/oyl9HNe4SIyFqvGpTIJ/bGevjy5cPweo16xV490mGkEYGwyJc2A2EB4G0Fffd9XdYtE5LGWTbIM8QWAvn56IkhGHBMPPx+k834BQK6qQ+8E49FV6vkzFy5FgBmRFaTVdqwDdSKQt6ugAURymWLlkpfoDP6ZIoegDwDtnakblrJhksaaNWChCt4uToawKJzZOkjKtarsSKlWv4MZh8LCCZLGIYXnBcn3UCXf+FudOuxyNLf4x20WsgyjTqobaTNphhS1iQ+Xhj09MYfMF56EwiycBZBKRmOwvU724a6bEOPJWGWbVNQ3x24HnyLaYLoTnNoJr0POC1ulgHngNltMUwVGotLHIx2Ut9pGkVLaOvxJKlK0Xj+a1swnVWhLq4zKgls0gDJoCMaq7Bd5f9RIDvSqQ4IavAAnqqJQsBPunGO1t/jk+f8THs7+xAewZExeIMx9Poe+p+iRRD8Av/lMcCPO+LPIViirg/7wEaXzNZ50RF1+vA899hRMsKjWdxjZ+hkN+DSjuuahmBhUtXIKhq0lq1viwyisASrUBmph0I3sTdk67BwvXP453iqwQmZRR0nFows+Yrqn4XchbVTBVjhw3G5JkzJNvdsPE5ETC1mUt5YaTt68DXNV7AB4t/Rnmdy49FnYb3SD8fOsf/JuA5UG5MuvilgayX2hCL5z+KAR8/Fc0n9UHzyf0xaNCXsGffEflvJiZOShukDyZqlMo+zLp9Ah5fsV5qSCQVLvTzKzFCyHEQfNaCJH8Jy9i/YztO+fjH4PVpxoSbv6pt5H+mNABjiuKAp0CcxuuxbgFuGYFtaL3ceizwSjkyRv1Tk1CRM8jyXVEuLpqxCadLUBUTtqVPoFPmSnJVrjO5433uGr2TdhyGJHMmjqw/UChuMcfdLzTbPcBjbeM913Ptop649sXl/wU2ySsdtLmJ0wAAAABJRU5ErkJggg==)
..........(9)
Where
b
i and ω
i parameter of model are learned from the data. This model can be written as
NNR(
p, k) where
p lagged input and
k nodes in the hidden layer. Model is neural network with observations (y
t-p) used as inputs for forecasting the output y
t and with
k neurons in the hidden layer, with neglecting the effect of seasonality because the data is annual. The optimal number of lag
p as (
p, q) in ARIMA model is chosen using akaike information criterion (AIC), which is given as follow:
![](data:image/png;base64,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)
..........(10)
Where
maximum value of the likelihood function. We remind that this model does not assume restriction about the stationary and therefore the random part is included in the predictions,
Lama et al., (2021).
ETS Model
Whereas ARIMA model describe autocorrelation in the data, exponential smoothing model (ETS) are based on describing the trend in the data, which was suggested by (
Holt, 1957),
Mishra et al., (2021), Devi et al., (2021) and
(Winters, 1960).
ETS models are a systematic development in which exponential smoothing models (ETS) are combined into a nonlinear dynamic model. Analysis of these models using state-space based likelihood calculations, with support for model selection and calculation of forecast standard errors
Hyndman et al., (2002).
Interested in the model in three main component of time series: trend (T), seasonal (S), error (E). Reflects the trend term of the long-term movement of time series and the error term is the unpredictable component of the time series. In our case, do not care about the seasonal term because the data annual. The components we need are combined in our model, in various additive and multiplicative combinations to produce y
t. We have additive model y
t = T+E or multiplicative model like y
t = T. E. where the individual components of the model are given as follows:
E [A, M]
T [N, A, M, AD, MD]
S [N, A, M]
Where
N = None, A = Additive, M = Multiplicative, AD = Additive dampened and MD = Multiplicative dampened (damping uses an additional parameter to reduce the impacts of the trend over time). The models that we are interested in estimating can be written (after selecting S [N]) in the following Table A:
Performance indicators
To compare the prediction performance of the three models used, we first test the validity of the model by calculating mean absolute percentages error (MAPE) between the estimated data and the actual data during the period (2015-2019):
![](data:image/png;base64,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)
..........(11)
Then we evaluate the performance of the model by calculating root mean square error (RMSE) and (MAPE) between the estimated data and actual data during the period (1961-2015):
![](data:image/png;base64,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)
..........(12)
Where
t : the forecast value, y
t: the actual value, n: number of fitted observed. The last stage is to predict the pulses production for the countries of the study sample until 2027, the model that hasthe least values of (RMSE-MAPE) is the best and the uncertainty is included in the expectations 95% prediction interval is given by (Mishra
et al.,2021):
![](data:image/png;base64,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)
..........(13)
Where
T + h observation that will be predicted, Zα/2=1.96, sh: forecast variance.
Empiricial study
To know the development and trends in pulses production for (Afghanistan-Bangladesh-China-India-Nepal-Pakistan) we present the following Fig 1.
Fig 1 shows that both China and Nepal achieved significant growth in the pulses production until the year 2019 almost exponentially. Afghanistan has achieved this development to 2015 and then production decreased after this year. Bangladesh and Pakistan have a similar situation they achieved a development in production until 1995 and then production decreased after this period similar to a second-order polynomial. As for India, it notices the high volatility in pulses production during the studied period and as it was shown to us that production is down trend. Descriptive statistics show the most important values of changes in data through Table 1.
Table 1 shows us that the data for (Afghanistan- China -Nepal-Pakistan) are not distributed normally, as the probability (Jarque-Bera) is less than the level of significance 5%. Thus the estimator here (Mean and standard deviation) are useless because they are breakdown points. These countries experienced significant changes in pulses production during the studied period, as shown by the maximum-minimum values and skewnes and kurtosis coefficient that Pakistan has the greatest development, where production reached 414.4 thousand tons in 1989 before it decreased to 80.7 in 2014. We also note from the Table 1 that the data from India and Bangladeshshare distributed normally, the production of pulses in India and the largest producer among the six countries, changed from 1506 thousand tons in 1991 to 535.2 in 1992. In order to find out the effect of these volatility and trends on the stationary of the variables, we use ADF test and we get the results from Table 2.
Table 2 shows that (Afghanistan-India) is stationary in level with linear trend for Afghanistan and around constant for India as shown in Fig 1. For the rest of the countries, the high volatility during the studied period made it a stationary series at the first difference. With the aim of forecasting the pulses production for six countries up to 2027, we use (ARIMA-NNAR-ETS) models; we use the data during the period (1961-2015) to estimate using models (training) and (2016-2019) to verify the validity of the model (testing). The following table shows the results of estimating the ARIMA model for the six countries:
Table 3 shows that all selected b models have better out-of-sample prediction results, as the value of (MAPE-Testing) is less then (MAPE-Training) for all models except Afghanistan, where the model failed to predict lower values after 2015. The best model is ARIMA (1,1,0) for Nepal, which achieved the lowest values of (AIC, RMSE, MAPE) among the selected models. We note from table that there is no autocorrelation problem for the residual values in all models. We estimate NNAR model for all countries and get the following results:
Table 4 shows the prediction using NNAR models is better than the prediction using ARIMA inside the sample (Training), but the good performance decreases outside the sample. The best model among selected models is for India NNAR (1,1), Which is better than the corresponding ARIMA model
(Mishra et al., 2020). We estimate ETS model for all countries and get the following results:
Table 5 shows that the best ETS model among the estimated models is for Nepal (M,N,N), which has the lowest values of (RMSE-MAPE in-out of the sample), similar to the results of the ARIMA model. Among all selected models, we choose the best model for forecasting pulses production to 2027 for each country:
According to these models (Table 6), a forecast of pulses production for 2027 is obtained with the inclusion of uncertainty in the forecast, as shown in the following Fig 2.
Fig 2 shows that (Afghanistan, China, India) are expected to increase the quantities of pulses production until 2027, with relative stability in the volume of production for the rest of the countries. The following table shows the expected production quantities for the six countries until 2027 with prediction interval 95% (Table 7).
Table 7 shows that India is the largest producer of pulses among all six countries, where production is expected to reach 1088.778 thousand tons in 2027, with a growth rate 15.73% during the period 2020-2027. In addition, Afghanistan and China have an extreme growth rate of 25.19%, 11.95% respectively.