ARIMA Intervention Model for Measuring the Impact of the Lobster Seeds Fishing and Export Ban Policy on the Indonesian Lobster Export

An intervention model is an analytical method for evaluating or measuring the impact of an external event called intervention, such as a natural disaster, holidays, sales promotions, and other policy changes. Two types of intervention variables will be used to represent the presence or absence of the event, i.e., a pulse or step. The pulse function is used to represent a temporary intervention, whereas the step function shows a long-term intervention. This study aims to develop a time series model with an intervention of step function for measuring the impact of two policies related to the prohibition of fishing and the export of lobster seeds on the export value of Indonesian lobster. These policies are the Ministerial Regulation No.1 of 2015 since January 2015 related banning of lobster seeds fishing (called first intervention) and the Ministerial Regulation No. 56 of 2016 since January 2017 related lobster seeds fishing and export ban policy (called second intervention). These regulations are designed to ensure lobster sustainability and add value to lobsters that are currently overfished. The results show that both policies significantly affect the export value of lobster in Indonesia, and the interventions have a permanent impact.


Introduction
Intervention analysis is a popular tool in economics. The main goal of this study is to determine the magnitude of the impact of an external event or intervention that can modify the pattern of time series data [1]. Two types of intervention variables that must be employed are the pulse and step function [2]. The pulse function represents temporary or transient interventions such as sales promotions, natural disasters, terrorist attacks, and etcetera. The impact of a pulse function intervention may be felt only at the time of intervention or may exist in the subsequent period. Meanwhile, the step function represents a long-term intervention, such as government or company policies. The impact of this type of intervention may remain constant over time, gradually decrease or increase, and decrease or increase linearly without bound.
Step function intervention analysis is commonly known to measure the impact of government policies on a country's import and export, such as the impact of anti-dumping regulations on US wooden bedroom furniture imports from China [3], policy impact air pollution prevention and control action, and zero percent import tariffs on coal exports of Indonesia to China [4], and the impact of anti-dumping policies on Indonesian iron imports [5]. This research focuses on the application of time series analysis, specifically ARIMA step function intervention, to account for the impact of the Ministerial Regulation No.1 of 2015 since January 2015 related banning of lobster seeds fishing (called first intervention) and the Ministerial Regulation No. 56 of 2016 since January 2017 related lobster seeds fishing and export ban policy (called second intervention). These policies are an attempt by the government to regulate overfished lobsters (Panulirus spp.) resources. These policies aim to preserve the stock and long-term viability of commodities that play a significant role in Indonesia's fishery export [6]. Furthermore, these regulations strive to improve the added value of lobster seeds, which are cheaper than lobster for consumption purposes [7]. The data for this study were collected monthly from January 2012 to April 2020 by the Central Bureau of Statistics (BPS). The period was chosen based on the increasing lobster seeds export [8] and the timeframe of these regulations' implementation.

Statistical model 2.1. ARIMA intervention model
An intervention is a disturbance in the data pattern caused by an external event that influences the time series data [1]. Intervention analysis can be used to examine disturbances in this data pattern. Intervention analysis is a time-series data analysis used to evaluate and measure the intervention's impact. The general model with multiple interventions is as written follows then, ( ) and ( ) are defined as There are two common types of intervention variables, i.e.,the pulse and step function [1]. The pulse function is an intervention taking place at only one period and does not continue. The pulse function may be written as in the following way While the step function is an intervention occurring at the time that remains in effect subsequently. Thus, the step function is denoted as where is the research time, and the intervention starts at .

The procedure of building the ARIMA intervention model
The procedure for developing an ARIMA intervention model is outlined below [9,10,11] :

Modeling the ARIMA pre-intervention.
Data before the intervention, January 2012 until December 2014, were modeled using the Box-Jenkins ARIMA method. Before modeling, the stationarity of the variance and mean should be checked. Box-Cox transformation method is used to test the stationarity of the variance, and the 3 stationarity of the mean should be checked using the ADF test. The model that has been created will be used to forecast the observed values throughout the next intervention period.

Modeling the ARIMA first intervention.
a. Making residual plot.
The residuals from the forecasting results are plotted to determine the b, s, and r order with a confidence interval of width ±2 times the RMSE of the previous model. Order b is the delay time or the first time the intervention has an effect, and although indicated by the residual, that was the first to pass the confidence interval. Meanwhile, s order gives information about the major residual fluctuation or the time required for the intervention's impact on being stable, and r is the pattern of the impacts of an intervention or lags after a period (b + s) where the residuals form a pattern. To determine the best b, s, and r order involve trial and error of the many alternatives identified by the residual plot. b. Parameter estimation of ARIMA intervention.
Estimate and check the significance of the b, s, and r parameters for the first intervention ARIMA model. Calculations can use the conditional least square method by minimizing the conditional sum of squares errors. c. Diagnostic checking model.
The diagnostic test of the model is based on the examine assumption, i.e., normality distribution and white noise of errors. Shapiro-Wilk is used for error normality testing, and Ljung-Box is used for white noise error testing. d. Selection of the best models.
Several possible models are usually formed during the identification of the intervention order.
After confirming that all possible models satisfy the assumptions of white noise and normality of error, the best model can be chosen based on the smallest AIC, SBC, and RMSE values.
In the modeling of the 2nd intervention ARIMA model and so on, the steps taken are the same as the first intervention ARIMA modeling stage.

Measuring the impact of interventions.
Based on [9], the ARIMA intervention model equation can be written as where the actual data is denoted as , is ARIMA pre-intervention model for error, and * is the intervention's impact. So that, the estimated impact of the intervention can be determined using the equation below. * =̂−̂ (7) where * is the intervention's impact, ̂ is the forecasting value according to ARIMA preintervention model and ̂ shows the forecasting value according to ARIMA intervention model. This calculation can be done with the original data, but it must be returned to its original form before the calculation can be done with the transformed data.

ARIMA pre-intervention
Before the pre-intervention ARIMA model can be developed, the data must satisfy the assumptions of stationarity in terms of mean and variance. Based on the results of the Box-Cox plot and the unit root ADF-test, the data was found to be stationary both in variance and mean. As a result, model identification can carry out using the original data's ACF and PACF correlograms.

ARIMA first intervention model
After obtaining the ARIMA pre-intervention model, forecasting for the data in the first intervention period, January 2015 to December 2016, was performed, and the residual value was obtained to determine the first intervention model. The first intervention in this analysis is implementing Ministerial Regulation No. 1 of 2015 related to the fishing lobster seeds ban policy since January 2015, which follows the step function. The resulting residual plot is shown in Figure 3. It is known that at the time 1 and 1 + 9 the residual reaches the confidence interval of RMSE. Hence the order of b = 0 or b = 9 is suspected. Furthermore, the residual at 1 + 12 and 1 + 23 approaches and exceeds the confidence interval of RMSE. A trial and error procedure is used to find the best combination based on these times. Following the estimation procedure and diagnostics checking models, the optimal orders were b = 9, s = (3,14), and r = 0. The estimation and diagnostic checking model of the first intervention model are presented below.  T  T+1 T+2 T+3  T+4 T+5 T+6 T+7 T+8 T+9 T+10 T+11 T+12 T+13  T+14 T+15 T+16 T+17 T+18 T+19 T+20 T+21 T+22 T+23 ICSMTR According to table 2, all intervention parameters are significant at a significance level of 5%. Model diagnostics checking shows that the normally distributed and white noise errors assumptions were met by the first step function intervention of the ARIMA model. Therefore, the ARIMA first intervention model of the lobster (Panulirus spp.) export value in Indonesia can be written as

ARIMA second intervention model
After getting the first intervention model, data forecasting was carried out in the second intervention period, January 2017 to April 2020, applying the first intervention model. The second intervention in this analysis is the implementation of Ministerial Regulation No. 56 of 2016, which follows the step function, and is related to the fishing and export lobster seeds ban policy since January 2017. The residual value is then calculated to determine the second intervention model. Based on the residual value plot in Figure 4, it is known that the residuals cross the confidence interval at time T, T+1, T+3 to T+8, T+10, T+11, T+13, thus the value of order b is presumed to be one of them from that period. However, the value of order r = 0 since the residuals are random or have no pattern. After a lot of trial and error, it was discovered that the order b = 11, s = (10, 22, 23, 25, 26), r = 0 is the optimum one for achieving parameter, white noise, and error normality significance. The following table summarizes the outcomes of parameter estimates and diagnostics checking models.  T  T+2  T+4  T+6  T+8  T+10  T+12  T+14  T+16  T+18  T+20  T+22  T+24  T+26  T+28  T+30  T+32  T+34  T+36  T+38 ICSMTR

The impact of the first intervention
According to model (9), the impact of the Ministerial Regulation No.1 of 2015 or the first intervention has been delayed for nine months because it only began in October 2015, caused at the time the policy is strictly enforced [12]. The difference between the estimated value of the first intervention in equation (9) and the estimated value of pre-intervention ARIMA in equation (8) is used to calculate the magnitude of the first intervention's impact. Table 4 presents the magnitude impacts of Ministerial Regulation No.1 of 2015 or the first intervention.