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Cointegration analysis of selected currency pairs traded in Indian foreign exchange market
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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.

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  1. 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

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  2. 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 11 12 13 14 15 16 17 18

    EURO GBP USD 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

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  3. 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.

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  4. 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
    EURO/INR GBP/INR USD/INR JPY/INR
    Mean 69.5446 85.1660 54.6242 54.6219
    Median 69.7000 83.9990 54.3885 55.7600
    Standard Deviation 7.8119 9.7946 9.4299 9.1135
    Kurtosis 2.3362 2.0652 1.5005 3.1100
    Skewness 0.0755 0.2176 -0.0509 -0.7608
    Minimum 54.32 65.64 39.27 32.69
    Maximum 91.46 106.02 69.05 72.12
    Sum 193403.5 236846.7 151910.0 151903.6
    Count 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.

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  5. 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 12 13 14 15 16 17 18

    USD 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 13 14 15 16 17 18

    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

    -2 -6

    -3 -8
    07 08 09 10 11 12 13 14 15 16 17 18 07 08 09 10 11 12 13 14 15 16 17 18

    DUSD 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 14 15 16 17 18

    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,

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  6. Rajesh Sadhwani

    Table 2 Result of Augmented Dickey Fuller Unit Root Test
    At Level At First Difference
    Variable 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
    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 LogL LR FPE AIC SC HQ
    0 -36031.44 – 2277781 25.99022 25.99877 25.99331
    1 -4558.96 62831.46 0.000319 3.302535 3.345288* 3.317975*
    2 -4541.46 34.8860 0.000319* 3.301453* 3.378408 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

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  7. 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 Observations F-Statistics P-value Decision on H0
    GBP does not Granger cause EURO 0.2524 0.7770 Not Rejected
    2779
    EURO does not Granger cause GBP 0.8826 0.4138 Not Rejected
    USD does not Granger cause EURO 1.2721 0.2804 Not Rejected
    2779
    EURO does not Granger cause USD 3.6093 0.0272 Rejected
    YEN does not Granger cause EURO 0.8088 0.4455 Not Rejected
    2779
    EURO does not Granger cause YEN 2.7117 0.0666 Not Rejected
    USD does not Granger cause GBP 1.2965 0.2736 Not Rejected
    2779
    GBP does not Granger cause USD 4.1128 0.0165 Rejected
    YEN does not Granger cause GBP 3.3842 0.0340 Rejected
    2779
    GBP does not Granger cause YEN 0.9474 0.3879 Not Rejected
    YEN does not Granger cause USD 1.1613 0.3132 Not Rejected
    2779
    USD does not Granger cause YEN 0.9260 0.3962 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)
    Hypothesized No. 0.05 critical
    Eigenvalue Trace Statistics Prob.**
    of CE(s) value
    None 0.0039 21.1410 47.8561 0.9834
    At most 1 0.0021 10.2146 29.7970 0.9770
    At most 2 0.0014 4.1778 15.4947 0.8887
    At most 3 6.1000 0.1694 3.8414 0.6806
    Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
    Hypothesized No. 0.05 critical
    Eigenvalue Trace Statistics Prob.**
    of CE(s) value
    None 0.0039 10.9263 27.5843 0.9673
    At most 1 0.0021 6.0368 21.1316 0.9822
    At most 2 0.0014 4.0083 14.2646 0.8584
    At most 3 6.1000 0.1694 3.8414 0.6806
    **MacKinnon, Hug and Michelis (1999) p-value
    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

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  8. 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.

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  9. 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.

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