International Journal of Mathematics and Mathematical Sciences

Volume 2016, Article ID 6382926, 6 pages

http://dx.doi.org/10.1155/2016/6382926

## Modelling the Impact of Government Policies on Import on Domestic Price of Indian Gold Using ARIMA Intervention Method

^{1}Research and Development Centre, Bharathiar University, Coimbatore 641046, India^{2}Department of Statistics, Kristu Jayanti College, Bangalore, Karnataka 560077, India^{3}Department of Statistics, Bharathiar University, Coimbatore 641046, India

Received 29 May 2016; Revised 10 August 2016; Accepted 11 August 2016

Academic Editor: Shey-Huei Sheu

Copyright © 2016 Jyothi Unnikrishnan and Kodakanallur Krishnaswamy Suresh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The study attempts to determine the impact of government policies of import of gold in India on the domestic price of gold during 2013 using Autoregressive Integrated Moving Average (ARIMA) intervention model. 2013 was an amazing year for Indian gold market where the price had reached its zenith. In April 2013, to curb a record trade deficit, India imposed an import duty of 10 percent on gold and tied imports for domestic consumption to exports, creating scarce supply of the yellow metal and boosting premiums to curtail the Current Account Deficit (CAD). The objective of the paper is to model the impact of this intervention by the government on the domestic price of Indian gold. Suitable ARIMA model is fit on the preintervention period and thereafter the effects of the interventions are analysed. The results indicate that ARIMA is the most suitable model during preintervention period. Intervention analysis reveals that there is significant decrease in domestic price of gold by 56% from 2013. The model may be used by policymakers to analyse the future of gold before framing regulations and policies.

#### 1. Introduction

Gold has always been an integral part of the socioeconomic ethos of Indian household. Demand for gold is either as bullion for investment or jewellery for gift. India is the second largest importer of gold after China. This is mainly because India limits the use of recycled gold. Import of gold has added to the burden of Indian economy. Import of gold leads to Current Account Deficit as majority of the gold imported is not being monetised. In 2014, Indian household has held more than 22000 tonnes of gold and the gold imported was worth $34 billion. If the import of gold has been lower than $34 billion, the trade deficit would have been narrower than $138 billion [1]. India has formulated various policies since 1947 with different perspectives. 2013 was an important year in the Indian gold market as we witnessed extreme variations in the price of gold. This can be attributed to the changes of import duties which were increased from 2 to 10 percent to impose restrictions in the gold market [2]. The objective of the paper is to model the impact of a government policy introduced in 2013 [3] to reduce its import on the domestic price of gold. ARIMA intervention method is compared with Holt linear trends methods.

#### 2. Review of Literature

The concept of intervention analysis was introduced by Box and Tiao [4]. In their article, the model is developed which can find the impact of an intervention and noise on a response variable using difference equation model. The article also discusses the properties of maximum likelihood estimator of parameters and two applications of the model. Chung et al. [5] in their study have modelled the financial crisis in China’s manufacturing industry that occurred in 2008. They modelled the impact of the recession that had influenced the entire world abruptly. They claim the model to be more precise at explaining and analysing. Ray et al. [6] investigated the effect of introduction of Bt Cotton variety in the year 2002 on the yield of cotton for Gujarat and Maharashtra. This study also concludes that intervention ARIMA model is superior to conventional ARIMA models. Acquah et al. [7] applied intervention ARIMA model to analyse the impact of two different interventions of which one is a step function and the other a pulse function. The objective of the study is to quantify the effects of the review of the timber export levy downwards and the regulation of trade of a wood on the trade policies of wood products in Ghana. Bianchi et al. [8] in their research to find an improved forecasting model for telemarketing centers found that ARIMA intervention model performs better than the simple models such as additive and multiplicative versions of Holt-Winters exponentially weighted moving average models.

#### 3. Materials and Methods

##### 3.1. Materials

The daily traded value of gold in Multicommodity Exchange of India (MCX) Limited from March 2011 to March 2016, consisting of 1409 observations obtained from the official website of MCX [9], is used for analysis in the study. The whole set of data is divided into two pre- and postintervention periods. This division is based on Zivot-Andrews Unit Root test. 692 observations till 29th June 2013 are considered preintervention period and the remaining 717 observations as postintervention observations.

##### 3.2. Methodology

###### 3.2.1. ARIMA Model

The ARIMA model (8) of a time series refers to the model which is stationary at level with autoregressive terms and moving average terms. It may be denoted by where – is the noise term and is the backshift operator.

ARIMA model is developed in three steps: model identification, parameter estimation, and diagnostic checking. The correlogram of a stationary series will give us a rough picture of the lags of the model. Parameters are tentatively selected at the identification stage and are estimated by method of iterative least squares. The best model among a few selected tentative models is decided on the basis of the least values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). AIC and BIC values are computed as follows:where and are the parameters of ARIMA model, is the standard deviation of the model, and is the number of observations used in estimating the model.

Diagnostic checking does the tests of adequacy of the selected model. This is done by checking if the error terms of the selected model are white noise using Ljung-Box test which has null hypothesis that the noise terms are random and the test statistic where is the number of observations used in estimating the model and is the maximum number of lags.

###### 3.2.2. ARIMA Model with Intervention

The ARIMA model with intervention suggested by Box and Tiao [4] is widely used to analyse the impact of external events on time dependent variables. The methodology of intervention analysis is as follows:(i)Develop a model for the time series before intervention.(ii)Add one or more dummy variables that represent the timing of the intervention.(iii)Reestimate the model, including the new dummy variables for the entire series.(iv)Interpret the coefficients of the dummy variables as measures of the effect of the intervention.The intervention model has two components: the noise component which represents the preintervention period and the intervention component that incorporates the effect of the intervention in the model. It may be represented as where is the response series, is the indicator variable coded as a binomial variable with values 0 and 1 to identify the intervention period, is the slope parameter, is the impact parameter, is the autoregressive parameter, is the moving average parameter, and is the backshift operator.

###### 3.2.3. Holt’s Linear Trend Method

This method [10] is adopted to check if a better model can be developed by forecasting with trend. The forecast equation and the two smoothing equations developed are as follows:where denotes an estimate of the level of the series at time , denotes an estimate of the trend (slope) of the series at time , is the smoothing parameter for the level, , and is the smoothing parameter for the trend,

###### 3.2.4. Comparing the Model Performance

The forecasting performance of this model can be assessed by the Mean Absolute Percent Error (MAPE) value which is supposed to be minimum. MAPE is defined as where is the actual value and is the forecast value.

#### 4. Result and Discussion

The data used for the study has 1409 observations; the descriptive statistics of the data are depicted in Figure 1.