find the best model. On the other hand, machine learning methods are concerned with finding it based on the

highest performance in the testing data. This research proposes a mixture approach in the development of the

ARDL (Autoregressive Distributed Lags) model to predict the Cayenne peppers price. Multiple time series data

are formed into a matrix of input-output pairs with various lag numbers of 3, 5, and 7. The dataset is normalized

with the Min-max and Z score transformations. The ARDL predictor variables of each lag number and dataset

combinations are selected using the forward selection method with a majority vote of four criteria namely the

lag 3 with the original dataset outperforms in the RMSE and MAE metrics while the ARDL lag 3 with the Z

be maintained by the government because they have

an important impact on various sectors including the

economic, social, and political aspects of a nation,

[1]. However, the Indonesian government still does

not have a consistent list of staple food commodities

until now. The commodity of chilies is not part of

staple food commodities, but it is highly sought after

by customers. In particular, Javanese people don't

even care about the very expensive price, [2].

Meanwhile, there are various types of chilies

cayenne pepper accurately can be a tool for the

government to control the price.

of proving the hypothesis through experiment

designing, data collecting, and data analyses, [6]. A

regression model captures the relationship between

independent and dependent variables and can draw

causal inferences from the data, with attention to

causal confounding, [7]. From an engineering field's

does not require the dimension of the response

variables to be the same as predictor variables, [19].

The forward variable selection is carried out to

obtain the predictor variables with significant

contributions to the response variable, [20].

either the conventional statistic or machine learning

approaches, are rarely acquired in literature. In

particular, the developed predictive models employ

multiple time series data where the data are

available in almost every sector of life. The time

multiple regression models with forward selection

can be found in many literatures. However, the

ARDL modeling with the forward selection

employed in the multiple time series forecasting

faces a sophisticated identification of the optimal

subset predictor variables. Rarely works published

in the domain. Hence, the development of predictive

models that are easy to interpret and powerful in

performance is still an open problem.

respectively the minimum of X, maximum of X,

mean of X, and standard deviation of X. The

transformation outputs yielded by the min-max

method seem more natural because they are all

positive values, but the Z score method yields the

transformation output which can be used to

investigate the outlier data.

a significant contribution to predicting the response

variable value, [23]. Some time series data are

related to each other so time series modeling by

considering some related ones to develop a

predictive multivariate time series model is

supposed to be a comprehensive approach. An

ARDL model is one type of econometrics model

referring to a model involving some lags coming

from both the dependent and independent variables,

variable having the highest contribution to the

explaining response variable, [30]. The forward

selection method worked firstly by searching a

predictor variable having the minimum value of

residual sum square (RSS), and then calculating the

model goodness of fit criteria such as the Cp statistic,

Akaike’s Information Criterion (AIC), Bayesian’s

associated to the minimum RSS value. All of the

above criteria are calculated involving the RSS

value or its derivation where their formulas are

predictor variables.

The forward selection algorithm, in summary, is

given in the following stages, [32]:

measures how coincidence between the prediction

value generated by the model and the associated

can predict the actual value perfectly with 100%

accuracy, [34]. When it is presented in a scatter plot

of the actual versus prediction values, both values

coincide and overlap perfectly with each to other.

Here are the formulas to calculate the MAE, RMSE,

corresponding actual value.

Fig. 2: The research schema on developing ARDL models using a machine-learning approach

To make simpler in naming the predictor variables

used in the study, some terms are used namely the

‘L-1’, ‘L-2’, ‘L-3’, ‘L-4’, ‘L-5’, ‘L-6’, and ‘L-7’ of

the predictor variable names for the large chilies on

the lag of p = 1, 2, 3, 4, 5, 6, and 7 respectively. It is

also used for naming the datasets of Curly chilies

(C), and Cayenne peppers(P) by replacing the ‘L’ to

be the ‘C’ or ‘P’ respectively. The model that be will

and ‘C-1’ to ‘C-5’. A similar condition is run for k =

3 and k = 5 where the response variable Pt has to be

influenced respectively by 9 and 21 predictor

selected in each input-output pairs matrix of the

training data on the original dataset and both

normalized datasets with the min-max and Z score

transformation.

the goodness of fit criteria curve. As an example,

Table 1 shows a matrix describing the variable

selection process in the Z score dataset on the input

lag 5, while, Figure 3 presents a plot of 4 criteria

values in Table 1. The plot will help to find the

optimal criteria value of Cp, BIC, and AIC, and

determined using the goodness of fit criterion with

the majority vote.

calculation of each residual sum square (RSS) and

finding the minimum one to select the predictor

variable that enters the linear model. The best RSS

is used to calculate the associated criteria of the Cp,

goodness of fit criteria for selecting the best

predictor variables of the ARDL model.

implies that the ‘P-1’ variable has the minimum RSS

value and it is picked up as the first predictor

variable of the linear model. The succeeding

The linear model with 2 predictor variables of [‘P-1’,

‘P-4’] has the minimum RSS value which means the

‘P-4’ variable entered into the linear model with 2

predictor variables then 4 associated goodness of fit

criteria are calculated. The sequence processes of

the fitting linear model with adding one variable of

remaining variables, calculating their RSS, picking

up the variable with the minimum RSS, and

calculating the associated goodness of fit criteria are

carried out until the remaining variable is empty.

models for 3 input lags and 3 datasets