Nội dung

International Journal of Management (IJM) Volume 11, Issue 5, May 2020, pp. 476-485, Article ID: IJM_11_05_045 Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=11&IType=5 Journal Impact Factor (2020): 10.1471 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6502 and ISSN Online: 0976-6510 DOI: 10.34218/IJM.11.5.2020.045 © IAEME Publication Scopus Indexed COINTEGRATION ANALYSIS OF SELECTED CURRENCY PAIRS TRADED IN INDIAN FOREIGN EXCHANGE MARKET Rajesh Sadhwani Assistant Professor, Indukaka Ipcowala Institute of Management, CHARUSAT Off. Nadiad-Petlad Highway, Changa 388 421, Anand, Gujarat, India. ABSTRACT The main purpose of this research paper is to explore and understand the nature of association and the possible existence of a short run and long run relationship between US Dollar, EURO, British Pound and Japanese Yen. To find out the relationship among currencies USD/INR, EUR/INR, GBP/INR and JPY/INR pairs are considered. The main idea is to know how these selected indicators are related to each other. The daily basis 2781 observations for all four variables from year 2007 to 2018 are taken into consideration. Data are collected from website of Reserve Bank of India. The stationarity of time series is checked and differentiated as per requirement. Johansen cointegration test to know the long run relationship between variables is used. The result shows that there is no cointegration equation among the variables. The short run relationship is examined with help of Vector Autoregression (VAR) model and the short run relationship within different lags of variables has been identified. The correlation among variables has been examined with help of correlation matrix and Granger cause test is also used to understand the causal effect. Key words: Cointegration, Vector Autoregression, Correlation, Currencies Cite this Article: Rajesh Sadhwani, Cointegration Analysis of Selected Currency Pairs Traded in Indian Foreign Exchange Market. International Journal of Management, 11 (5), 2020, pp. 476-485. http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=11&IType=5 1. INTRODUCTION Considering the high volatility in currency markets it becomes very important to understand the relationship between the different currencies. All currencies offers different level of risk and return in certain market conditions, it performs differently from each other. This study proposes to explore the relationship between the currencies. The paper tries to understand the long run and short run relationship between the variables. Study considers the selected major currencies traded in Indian financial markets. We have considered the selected four currencies considering the ease of trading on exchanges, liquidity etc.. to all the type of hedgers, trader http://www.iaeme.com/IJM/index.asp 476 editor@iaeme.com Rajesh Sadhwani such as corporates, high net worth individuals, domestic and foreign institutional investors and all other market participants. The performance of the variables can be understood with the help of following graph. 110 100 90 80 70 60 50 40 30 07 08 09 10 EURO 11 12 GBP 13 14 USD 15 16 17 18 YEN Figure 1 Trend of EURO/INR, GBP/INR, USD/INR and JPY/INR pairs All the four currencies are in uptrend for the period of the study or in other words it shows the poor performance of Indian rupee. Indian rupee had persistently fallen against the major currencies in the world. Most of the currencies of developed economies have appreciated against Indian rupee while Indian rupee has failed to do so. US dollar has appreciated against all the major currencies in the world post 2007-08 financial crisis in US. US dollar index DXY is noted on all time high level nearly 100 against the basket of six major currencies including Canadian dollar (CAD), Swedish krona (SEK) and Swiss franc (CHF) in other three currencies. Hence understanding the relationship between major currencies against Indian rupee is very important. The outcome of the study will be especially helpful to pair traders, arbitragers and banks dealing in Indian foreign exchange markets. 2. LITRATURE REVIEW To understand and examine the long run relationship between the variables cointegration test is been used by many central bankers and researchers. Jose A. Lopez (1999) examined the cointegration between the foreign exchange rates for different time period; he concluded the relationship between currencies changes over a period of time and relationship is also affected by central banks activities. Cointegration analyses of exchange rates in foreign exchange market were also checked by Chinese researcher between selected pair of currencies. He identified the long and short run relationship among them. Recursive cointegration analysis was used to examine the relation between foreign exchange markets by Mei-Se Chien and other two researchers. Gupta and Agarwal in 2011 examined the correlation between the Indian stock market and five other major Asian economies and found a weak correlation among the stock exchanges. This proved to have benefits of diversification to institutional and international investors. Similarly Sharma and Bodla in 2011 studied the linkages between Indian, Pakistan and Sri Lankan stock exchanges. The outcome suggested that Indian stock exchange Granger cause the Karachi Stock Exchange of Pakistan and the Colombo Stock Exchange of Sri Lanka. In similar fashion Ismail Aktar has done a study on Co-movement http://www.iaeme.com/IJM/index.asp 477 editor@iaeme.com Cointegration Analysis of Selected Currency Pairs Traded in Indian Foreign Exchange Market between Stock Markets of Turkey, Russia and Hungary. The study investigated the long run relationship and Granger Causality between Turkish, Russian and Hungarian stock indices for the period of January 5, 2000 to October 22, 2008. A study was done by Michalis Glezakos, Anna Merika & Haralambos Kaligosfiris on, “Interdependence of Major World Stock Exchanges: How is the Athens Stock Exchange Affected?” The paper investigates and examines the short and long-run relationships between major world financial markets with particular attention to the Greek stock exchange. Paper covered the data from 2000 to 2010 using monthly data. Murali Batareddy in 2012, Hoque in 2007 and Ibrahim 2005 found that the US market has an impact on the Asian markets. Sam Agyei Ampomah in 2011 examined the nature and extent of linkages among African stock markets and the relationships between the regional and global stock markets. Prof. Ritesh Patel paper published in 2012 examined the causal relationship among equity markets to better understand how shocks in one market are transmitted to other markets. He also examined the causal relationship, comovement and dependency among equity markets to understand shocks in one market are transmitted to other markets. More recently in 2015 Thangamuthu Mohanasundaram and Parthasarathy Karthikeyan examined thelong run and short run relationship between stock-market indices of South Africa, India and the USA. The paper applied the granger cause test. After testing the Granger cause relationship, the existence of a long run and short run relationship is tested. The long run relationships among the stock market indices were analysed, following the Johansen and Juselius multivariate cointegration test. The outcome suggested the absence of cointegrating equation among variables. The vector auto regression suggested the short run relationship among variables. 3. RESEARCH METHODOLOGY 3.1. Research Gap Most of the research is carried out to study the relationship between different assets classes and currencies of various developed countries etc... Hence we have examined the relationship between endogenous variables in Indian context. This will be helpful for all types of participants in Indian forex market. 3.2. Objectives The main objective of the research is to understand the long run and short run relationship between variables, also to check if any of it is useful to forecast other variables within the group. 3.3 Sample and Data Collection The research is carried out through secondary data sources. The data for USD/INR, EUR/INR, GBP/INR and JPY/INR are collected Reserve bank of India and Indian government websites and some and some other authenticated sources are used for data collection. The 2781 observations based on closing price from January 2007 to January 2018 were taken into consideration. 3.4. Research Tools & Techniques 3.4.1. Unit Root Test The unit root test is used to examine the stationarity and non-stationarity of time series. The presence of the unit root test in all four variables is checked with the help of Augmented Dickey Fuller (ADF) test. http://www.iaeme.com/IJM/index.asp 478 editor@iaeme.com Rajesh Sadhwani 3.4.2. Linear Correlation The linear correlation shows the association between two variables. Correlation analysis is used to understand how two variables move in relation to each other. 3.4.3. Granger Causality Test Granger cause test is used to examine the causality between two variables in time series. The test check the particular variable come before another, Hence this help in determining whether a time series X is helpful in forecasting another Y. 3.4.4. Cointegration Test If time series variables are integrated of order d, and linear combination of those variables is integrated of order less than d, then the collection is said to be cointegrated. It means if two or more series are individually integrated but the linear combination of them has a lower order of integration then series are said to be cointegrated. 3.4.5. Vector Autoregression Model Vector autoregressin explores interrelationship between the endogenous variables. The relationship between the variables depend on previous change in one variables on current change. Model includes lagged values of the existing variables as repressor. This allows for estimating not only the instantaneous effects but also dynamic effects in the relationships up to n lags. 4. RESULTS AND DISCUSSION During the period of January 2007 to January 2018 there were no outliers identified, in Table 1 summary statistics results for Mean, Median, Standard deviation, minimum and maximum are computed for closing prices. Table 1 Summary Statistics, using the observations 2007 to 2018 Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Sum Count EURO/INR GBP/INR USD/INR JPY/INR 69.5446 85.1660 54.6242 54.6219 69.7000 83.9990 54.3885 55.7600 7.8119 9.7946 9.4299 9.1135 2.3362 2.0652 1.5005 3.1100 0.0755 0.2176 -0.0509 -0.7608 54.32 65.64 39.27 32.69 91.46 106.02 69.05 72.12 193403.5 236846.7 151910.0 151903.6 2781 2781 2781 2781 4.1. Stationarity Check of Data Time series diagram is firstly used for all four currency pairs data based on closing price for January 2007 to January 2018. The clear non stationary trend can be identified from figure 2 (a) the fluctuation trend breaks the hypothesis of weaker stationary. In Box-Jenkins method, a first order defferencing is computed for the time series data. The time plot of the same differencing data is shown in figure 2(b) The differencing data shows the stationarity of the data and hence the value of d(I) is 1. http://www.iaeme.com/IJM/index.asp 479 editor@iaeme.com Cointegration Analysis of Selected Currency Pairs Traded in Indian Foreign Exchange Market EURO GBP 100 110 90 100 80 90 70 80 60 70 50 60 07 08 09 10 11 12 13 14 15 16 17 18 07 08 09 10 11 USD 12 13 14 15 16 17 18 13 14 15 16 17 18 YEN 70 80 65 70 60 55 60 50 50 45 40 40 35 30 07 08 09 10 11 12 13 14 15 16 17 18 07 08 09 10 11 12 Figure 2 (a) Time plot of EURO/INR, GBP/INR, USD/INR and JPY/INR pairs at level DEURO DGBP 4 4 3 2 2 0 1 -2 0 -4 -1 -6 -2 -3 -8 07 08 09 10 11 12 13 14 15 16 17 18 07 08 09 10 11 DUSD 12 13 14 15 16 17 18 14 15 16 17 18 DYEN 3 4 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 07 08 09 10 11 12 13 14 15 16 17 18 07 08 09 10 11 12 13 Figure 2 (b) Time plot of first order differencing on EURO/INR, GBP/INR, USD/INR and JPY/INR pairs Further on, unit root also has been tested using Augmented Dickey Fuller test ADF test. The output of the same has been shown below, http://www.iaeme.com/IJM/index.asp 480 editor@iaeme.com Rajesh Sadhwani Table 2 Result of Augmented Dickey Fuller Unit Root Test At Level At First Difference Result T Value Probability T Value Probability EURO -1.5448 0.5108 -51.4368 0.0001* I(1) GBP -1.5308 0.5179 -51.4995 0.0001* I(1) USD -0.3969 0.9074 -39.3598 0.0000* I(1) YEN -1.9298 0.3187 -53.4397 0.0001* I(1) *Rejection of null hypothesis at 5 per cent and therefore data series is stationary Variable The unit root is present at the level of existing series and series is non-stationary in nature, but the series is found to be stationary at first level of difference as suggested in above table. The p value of both constant and constant & trend is below 0.05 at first level of difference. Hence first order of differencing is considered to make the series stationary. Table 3 Correlation Matrix EURO GBP USD YEN EURO 1.0000 GBP 0.7520 1.0000 USD 0.8199 0.7058 1.0000 YEN 0.6512 0.2747 0.6431 1.0000 Most of the currencies have positive correlation with each other GBP and EUR have a positive association 0.7520, USD and GBP has also also strong positive correlation 0.7058 between them indicates both variables are following almost same trend over applicable period of time. Also there is positive correlation between USD and EUR 0.6431. Overall there is positive association among these variables. Here it can be observed that all the variables are in positive correlation and following almost same trend over a given period of time. However the value of all foreign currencies are against Indian rupee, hence possible effect of weakening Indian rupee against all the major currencies can not be rejected. The positive correlation among the variables leads to the further examination of variables, to know if one variable is useful to predict the present or future value of the other variable. This is evaluated with the help of the Granger causality test. The Granger causality test is highly sensitive to the order of the lags selection. The optimal levels of lags are selected through VAR lag order selection criteria. Table 4 VAR Lag order selection Lag 0 1 2 LogL -36031.44 -4558.96 -4541.46 LR 62831.46 34.8860 FPE 2277781 0.000319 0.000319* AIC 25.99022 3.302535 3.301453* SC 25.99877 3.345288* 3.378408 HQ 25.99331 3.317975* 3.329245 *Indicates the lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Optimal Lag selection based on AIC = 2 http://www.iaeme.com/IJM/index.asp 481 editor@iaeme.com Cointegration Analysis of Selected Currency Pairs Traded in Indian Foreign Exchange Market The optimal level of lag length is 2 and it is based on the lowest value of Akaike informationi criterion (AIC) which is 3.3014 in our case. It is also supported by FPE values, which are lowest at lag 2, suggest the same level of lags. Table 5 VAR Granger Causality / Block xxogeneity Wald test Null Hypothesis GBP does not Granger cause EURO EURO does not Granger cause GBP USD does not Granger cause EURO EURO does not Granger cause USD YEN does not Granger cause EURO EURO does not Granger cause YEN USD does not Granger cause GBP GBP does not Granger cause USD YEN does not Granger cause GBP GBP does not Granger cause YEN YEN does not Granger cause USD USD does not Granger cause YEN Observations 2779 2779 2779 2779 2779 2779 F-Statistics 0.2524 0.8826 1.2721 3.6093 0.8088 2.7117 1.2965 4.1128 3.3842 0.9474 1.1613 0.9260 P-value 0.7770 0.4138 0.2804 0.0272 0.4455 0.0666 0.2736 0.0165 0.0340 0.3879 0.3132 0.3962 Decision on H0 Not Rejected Not Rejected Not Rejected Rejected Not Rejected Not Rejected Not Rejected Rejected Rejected Not Rejected Not Rejected Not Rejected Granger causality test results shows that null hypothesis EURO does not Granger cause USD, GBP does not granger cause USD and YEN does not granger cause GBP are rejected, whereas all other hypothesis are not. This indicates that EURO can be used to forecast USD, GBP can be used to forecast USD and YEN causes GBP. The correlation and Granger causality can be further verified for long run movement among the variables by cointegration test. Time series data for the all variables are non-stationary at the level but stationary at first order difference. Johansen cointegration test is applied to know the long run relationship between the variables. Table 6 Johansen Cointegration Test Unrestricted Cointegration Rank Test (Trace) 0.05 critical Eigenvalue Trace Statistics value 0.0039 21.1410 47.8561 0.0021 10.2146 29.7970 0.0014 4.1778 15.4947 6.1000 0.1694 3.8414 Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. 0.05 critical Eigenvalue Trace Statistics of CE(s) value None 0.0039 10.9263 27.5843 At most 1 0.0021 6.0368 21.1316 At most 2 0.0014 4.0083 14.2646 At most 3 6.1000 0.1694 3.8414 **MacKinnon, Hug and Michelis (1999) p-value Hypothesized No. of CE(s) None At most 1 At most 2 At most 3 Prob.** 0.9834 0.9770 0.8887 0.6806 Prob.** 0.9673 0.9822 0.8584 0.6806 Cointgration Rank Test at 0.05 Trace No cointegration equation Maximum Eigen Value No cointegration equation Johansen cointegration test indicates there is no cointegration equation between the variable. The same is supported by trace statistics and Maximum Eigenvalue of rank test as shown in above table. Hence there is no long run relationship between the variables. As there http://www.iaeme.com/IJM/index.asp 482 editor@iaeme.com Rajesh Sadhwani is no cointegration between the variables, to understand the short run relationship vector autoregressin (VAR) can be used. Table 7 Vector Autoregression Estimates Variable / Lag Parameter EURO GBP USD YEN Coefficient 1.0040 0.0285 0.0257 0.0496 Standard error (0.0256) (0.0327) (0.0153) (0.0270) EURO(-1) t-statistics [39.1038] [0.8719] [1.6834] [1.8337] p-value 0.0000* 0.3833 0.0923 0.0667 Coefficient -0.0074 -0.0254 -0.0228 -0.0499 Standard error (0.0256) (0.0327) (0.0153) (0.0270) EURO(-2) t-statistics [-0.2884] [-0.7781] [-1.6222] [-1.8487] p-value 0.7730 0.4365 0.1048 0.0645 Coefficient 0.0090 1.0224 0.0181 -0.0050 Standard error (0.0198) (0.0252) (0.0118) (0.0208) GBP (-1) t-statistics [0.4561] [40.5472] [1.5381] [-0.2414] p-value 0.6483 0.0000* 0.1240 0.8092 Coefficient -0.0097 -0.0265 -0.0181 0.0042 Standard error (0.0197) (0.0252) (0.0118) (0.0208) GBP (-2) t-statistics [-0.4921] [-1.0537] [-1.5371] [0.2047] p-value 0.6227 0.2920 0.1243 0.8378 Coefficient 0.0195 0.0149 1.0041 0.0423 Standard error (0.0442) (0.0563) (0.0264) (0.0466) USD(-1) t-statistics [0.4426] [0.2654] [38.0268] [0.9090] p-value 0.6581 0.7907 0.0000* 0.3634 Coefficient -0.0175 -0.0139 -0.0049 -0.0413 Standard error (0.0442) (0.0563) (0.0263) (0.0466) USD(-2) t-statistics [-0.3955] [-0.2476] [-0.1870] [-0.8877] p-value 0.6924 0.8044 0.8516 0.3747 Coefficient 0.0140 -0.0719 -0.0283 0.9506 Standard error (0.0242) (0.0390) (0.0144) (0.0255) YEN(-1) t-statistics [0.5773] [-2.3270] [-1.9597] [37.1858] p-value 0.5637 0.0200* 0.0501* 0.0000* Coefficient -0.0137 0.0709 0.0282 0.0471 Standard error (0.0242) (0.0309) (0.0144) (0.0255) YEN(-2) t-statistics [-0.5669] [2.2968] [1.9508] [1.8460] p-value 0.5708 0.0216* 0.0511* 0.0649 Coefficient 0.1719 0.1323 -0.0072 0.1654 Standard error (0.0923) (0.1176) (0.0550) (0.0972) C t-statistics [1.8622] [1.1254] [-0.1317] [1.7010] p-value 0.0626 0.2604 0.8952 0.0890 *Significant at 5 per cent level The vector auto regression estimates shows that all four variables EURO, GBP, USD and YEN are function of their own lags EURO(-1), GBP(-1), USD(-1) and YEN(-1). Apart from it GBP EURO can be defined with 1st and 2ns lag lags of YEN, While USD can be defined with 1st and 2nd lag of YEN along with its own lag. While the YEN cannot be influenced with any of the variables, it is the function of its own lag YEN(-1) only. EURO cannot be defined by any of these variables in short run, even though it is highly correlated with USD. http://www.iaeme.com/IJM/index.asp 483 editor@iaeme.com Cointegration Analysis of Selected Currency Pairs Traded in Indian Foreign Exchange Market 5. CONCLUSION OF THE STUDY All the variables found to be non-stationary in nature. Hence we have made time series stationary, using first order difference. There is a strong positive correlation among the variables. There is strong positive correlation between USD/INR and EURO/INR and GBP/INR and comparatively weaker positive correlation with YEN/INR. The correlation direction is further verified using Granger Causality test; this shows that EURO granger cause on USD, GBP can be used to forecast USD and YEN granger cause causes GBP at 5 per cent level. Johansen cointegration test shows that there is no cointegration equation between the variables hence there is no long run relationship between variables. We have also examined the short run relationship between the variables using vector auto-regression test, this indicates there is short run relationship between the variables with different legs of variables. Hence we conclude that regardless of strong correlation between variables USD, EURO and YEN there is no long run relationship between all four variables. All the four variables are independent in the long run. REFERENCES [1] Dickey, D.A. & Fuller W.A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427-431. [2] Johansen, S. (1988). Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control, Vol. 12 pp. 213-254. [3] Gonzallo, J. & Granger, C.W.J. (1995). Estimation of common long-memory components in cointegrated systems. Journal of Business and Economic Statistics, 13(1), pp. 27-35. [4] Joze A. Lopez (2005). Exchange Rate Cointegration Across Central Bank Regime Shifts. Research in Finance, Vol. 22, pp. 327-356. [5] Mei-Se Chien, Te-Chung Hu and Meng-Huei, Su (2014). Recursive cointegration analysis of foreign exchange market stability: An application for ASEAN countries. International Journal of Science Commerce and Humanities, Vol-2, Iss 2, pp 39-54 [6] Rajesh Sadhwani and Tanvi Pathak (2019). A study and forecast of MCX comdex commodity index using arima model. International Journal of Research in Engineering and Management, Vol-05, Iss 5, pp. 211-216 [7] Hoque, Hafiz Al Asad Bin (2007). Co-movement of Bangladesh stock markets: Cointegration and error correction approach. Managerial Finance, 33(10), pp. 810-820. [8] Rajiv Meno, N. Subha, M.V. & Sagaran S. (2009). Cointegration of Indian stock markets with other leading stock markets. Studies in Economics and Finance, 26(2), pp. 87-94. [9] Raja Sethu Durai, & Bhadurai. (2011). Correlation dynamics in equity marketsevidencefrom India. Research in International Business and Finance, Elsevier, 25(1), pp. 64-74. Available at: http://ideas.repec.org/a/eee/riibaf/v25y2011i1p64-74.html [accessed 2020-03-17]. [10] Sowmya Dhanaraj. Goplaswamy, A.K. & Suresh Babu M. (2013). Dynamics interdependence between US and Asian markets: An empirical study. Journal of Financial Economic policy, 5(2), pp. 220-237. [11] Valadkhani, A. & Chancharat, S. (2008), Dynamic linkages between Thai and international stock markets. Journal of Economic Studies, 35(5), pp. 425-441. [12] Chakrabarty, A., & Ghosh, B.K. (2011). Long run financial market cointegration and its effect on international portfolio diversification. Indian Journal of Finance, 5(4), pp. 27-37 http://www.iaeme.com/IJM/index.asp 484 editor@iaeme.com Rajesh Sadhwani [13] Qadan, M., & Yagl, J. (2015). Are international economic and financial co-movement characterized by asymmetric co-integration?” Review of Accounting and Finance 14(4), 398-412. DOI: http://doi.org/10.1108/RAF-02-2015-0026 [14] Vohra, P.S. (2016). A study of co-movement among indices of Bombay stock exchange. Indian Journal of Finance, 10(9), 11-29. DOI:10.17010/ijf/2016/v10i9/101476 [15] Patel, R. J. (2017). Co-movement and integration among stock markets: A study of 14 countries. Indian Journal of finance, 11(9), 53-66. DOI:10.17010/ijf/2017/v11ip/118089 [16] Data source www.rbi.org.in, http://www.iaeme.com/IJM/index.asp 485 editor@iaeme.com