Volume-3, Issue-6, November-2016 ISSN No:

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1 A STATISTICAL ANALYSIS OF STOCHASTIC DRIFT IN THE MARKET OF METALS PLATINUM AND IRIDIUM Arghajit Mitra Research Scholar, Christ University, Bengaluru, India Subhashis Biswas Research scholar, Christ University, Bengaluru, India Sandeep Kaur Research Scholar, Christ University, Bengaluru, India Abstract The six platinum-group metals are ruthenium, rhodium, palladium, osmium, iridium, and platinum. Their chemical and physical properties are almost similar, and have the tendency to occur together in the same mineral deposits. It is important as a metal because it is estimated that about 20% of products purchased either contain platinum or use it in production. This study concentrates on the stochastic drift between platinum and another metal iridium. The various sectors that can benefit from the study are- automotive, jewellery, chemical processing, electronics, petroleum refining and medical equipment. Predicting stock market behavior has been quite an extensive research domain for many years for now, and particularly when this kind of prediction is done on precious metals, it has got an extensive use. It makes the work easier and quite simple to derive the pattern out of a market movement if both of them are stochastically drifted in a similar direction. Keywords: Granger Causality, stochastic drift, cointegration JEL Classification: C5, C15 I. INTRODUCTION The term stochastic drift has extensively been used in financial glossary to mean the change in the average value of a random process. In other words, if there is a stochastic drift between two time series, they tend to move apart. Time series variables, for example, stock prices, gross domestic product (GDP) etc., generally evolve stochastically and often are non-stationary. This study tries to find a link between the patterns of the prices of two metals platinum and iridium. Wherever a high commonality in the markets of both these precious metals has been spotted, the movement pattern is bound to be similar too. As explained, Stochastic Drift refers to the change in the average value of any random process. As the movement of the prices of both the metals platinum and iridium is random in nature, so, it can be derived that both of them could be measured by Granger Causality, since both of them are falling into the same 37

2 basket of stochastic drift. Granger Causality could be the most apt test here to establish the linkage between their prices because here, one signal is determining the other. So, one signal that determines the other bears the clue for determining the second signal in its past behavioral pattern. Hence, a sound and plausible relationship could be established. II. LITERATURE REVIEW Many researchers in the past have done research based on stochastic drift. In 1998 Daniel, Kent, David Hirshleifer and Avanidhar Subramanyam proposed a theory of security market under and over reaction based on two well-known psychological biases.i.e. Investor confidence about precision of private information and biased self-attribution (which causes shifts in investor confidence as a function of their investment outcomes). In 2003, Chen AS, Leung MT and Daouk H used the probabilistic neural network (PNN) to forecast the direction of index return after it was trained by historical data. They also used generalized methods of moments (GMM) to measure and compare the statistical performance of PNN with Kalman filter. In 2005, one such research was done on liberalization and financial growth by Bekaert, Harvey & Lundblad. The research showed that the equity market liberalization on an average increased economic growth by 1%. A similar work on Brazilian stock market was done by E.L. de Faria, Marcelo P. Albuquerque, J.L. Gonzalez, J.T.P. Cavalcante and Marcio P. Albuquerque in The work is a predictive study of the Brazilian stock market through artificial neural network and adaptive exponential smoothing methods. The objective of the study is to compare the forecasting performances and accuracy of both methods to predict the sign of the market returns. The study shows that both methods produce similar results regarding the prediction of the index returns. On the contrary, the neural networks outperform the adaptive exponential smoothing method in forecasting and predicting the market movements, with relative hit rates similar to the ones found in other developed markets. Ghosh B & Srinivasan P in 2014 studied the impact of FII flows on the domestic stock market. The paper studies the changes in speculative activities and also the volatility that occurs due to such activities in the domestic stock market. The study concluded that though BSE 100 depends on FII & DIIs and their money inflow, but yet neither that impact is substantial nor there is any clear pattern to predict the future trend of BSE 100. III. RESEARCH METHODOLOGY This study tries to find a link between the patterns of the prices of two precious metals platinum and iridium in the New York market. Granger Causality test has been used to identify the link and establish a valid relationship between them. The study is conducted for a period of 24 years starting from 1 st July, 1992 to 4 th July, In this case, both type of Granger Causality tests have been performed which means platinum prices effecting iridium prices and iridium prices effecting platinum prices within the fixed time frame of 24 years. Moreover, Johansen Co-integration test has also been applied to understand the similarity of patterns in between the visual representation of the two waveforms of the prices of the two metals in consideration. Now, the research question lies in the fact that whether they follow the same 38

3 stochastic drift or not, and if so, whether they are co-integrated or not. In case, they are found to be co-integrated, then the arbitrage opportunities within will automatically tend to come down. Obviously, this will make the markets increasingly efficient. But, in case, they are not found to be co-integrated, then the significant arbitrage opportunity within will tend to make both of them a weak form of efficiency. IV. STUDY OUTPUT Table I: NORMALITY TEST (JARQUE-BERA TEST) Platinum Date: 31/07/2016 Time : 07:28 Sample: 01/07/1992 to 04/07/2016 PRICEL Mean Median Maximum Minimum Standard deviation Skewness Kurtosis Jarque-Bera Probability Sum Sum squared deviation Observations 6065 Iridium Date : 31/07/2016 Time : 07:35 Sample : 01/07/1992 to 05/07/2016 PRICEL Mean Median Maximum Minimum Standard deviation Skewness Kurtosis Jarque-Bera

4 Probability Sum Sum squared deviation Observations 6064 Table II: REGRESSION TEST Platinum Dependent variable: PRICEL Method: Least Squares Date: 07/07/2016 Time : 23:23 Sample (adjusted) : 02/07/1992 to 04/07/2016 Included observations: 6064 after adjustments Variable Coefficient Std. Error t-statistic Probability C PRICEL(-1) R-Squared Mean dependent var Adjusted R-Squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criterion F-Statistic Durbin-Watson stat Prob (F-Statistic) Iridium Dependent variable: PRICEL Method: Least Squares Date: 07/07/2016 Time : 21:45 Sample (adjusted) : 02/07/1992 to 05/07/2016 Included observations: 6063 after adjustments Variable Coefficient Std. Error t-statistic Probability C PRICEL(-1)

5 R-Squared Mean dependent var Adjusted R-Squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criterion F-Statistic Durbin-Watson stat Prob (F-Statistic) Table III: AUGMENTED DICKEY-FULLER UNIT ROOT TEST Platinum Null hypothesis: D (PRICEL) has a unit root Exogenous: Constant, Linear Trend Lag length: 0 (Automatic - based on SIC, maxlog = 33) t-statistic probability Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller test equation Dependent Variable: D(Pricel,2) Method: Least Squares Date: 07/07/16 Time: 23:25 Sample: 03/07/1992 to 04/07/2016 Included Observations: 6063 after Adjustments Variable Coefficient Std. Error t-statistic Prob D(PRICEL(-1)) C ( 7/01/1992 ) -5.58E E

6 R-squared Mean Dependent Var 1.07E-06 Adjusted R-squared S.D Dependent var S.E of regression Akaike info criterion Sum Squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob (F-statistic) 0 Iridium Null hypothesis: D (PRICEL) has a unit root Exogenous: Constant, Linear Trend Lag length: 14 (Automatic, Based on SIC, maxlag = 33) t-statistic probability Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller test-equation Dependent Variable: D (Pricel,2) Method: Least Squares Date: 08/01/16 Time: 17:53 Sample (adjusted): 23/07/1992 to 05/07/2016 Included Observations: 6048 after adjustments Variable Coefficient Std.Error t-statistic Prob D(PRICEL(-1)) D(PRICEL(-1),2) D(PRICEL(-2),2) D(PRICEL(-3),2) D(PRICEL(-4),2) D(PRICEL(-5),2) D(PRICEL(-6),2) D(PRICEL(-7),2) D(PRICEL(-8),2) D(PRICEL(-9),2) D(PRICEL(-10),2)

7 D(PRICEL(-11),2) D(PRICEL(-12),2) D(PRICEL(-13),2) D(PRICEL(-14),2) C 1.91E /01/1992 ) 1.37E E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Table IV: JOHANSEN TEST Date: 09/07/16 Time: 18:26 Sample (adjusted): 6064 Included observations: 6059 after adjustments Trend assumption: Quadratic deterministic trend Series: IRL PTL Lags interval (in first differences): 1 to 4 Unrestricted Co-integration Rank Test (Trace) Hypothesized no. of CE(s) Eigenvalue Trace statistic 0.05 critical value Prob.** None At most Trace test indicates no cointegration at the 0.05 level *denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values 43

8 Unrestricted Cointegration Rank Test Hypothesized no. of CE(s) Eigenvalue Max-Eigen Statistic 0.05 critical value Prob.** None At most Max-eigenvalue test indicates no cointegration at 0.05 level *denotes rejection of the hypothesis at 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted cointegrating coefficients (normalized by b *S11*b=1) IRL PTL Unrestricted Adjustments coefficients (alpha) D (IRL) D (PTL) Cointegrating equation(s): Log likelihood Normalized cointegrating coefficients (standard error in parentheses) IRL PTL ( ) Adjustment coefficients (standard error in parentheses) D (IRL) ( ) D (PTL) ( ) 44

9 Table V: SINGLE EQUATION TEST Engle-Granger Cointegration Test Series: IRL PTL Sample: Included observations: 6064 Null hypothesis: Series are not cointegrated Co integrating equation deterministic: C Automatic lags specification based on Schwarz criterion (maxlag=33) Dependent tau-statistic Prob.* z-statistic Prob.* IRL PTL MacKinnon (1996) p-values. Intermediate Results: IRL PTL Rho Rho S.E Residual variance Long-run residual variance Number of lags 0 6 Number of observations Number of stochastic trends" 2 2 **Number of stochastic trends in asymptotic distribution Table VI: GRANGER CAUSALITY TEST Pairwise Granger Causality Tests Date: 07/31/16 Time: 22:15 Sample: Lags: 1 Null Hypothesis: Obs F-Statistic Prob. PT_LOG does not Granger Cause IR_LOG IR_LOG does not Granger Cause PT_LOG

10 V. CONCLUSION Jarque-Bera Test: Since, probability in both the cases is , the given datasets are normal and hence time series in both the cases can be predicted. The dataset of Platinum passes the normality test with value Ideally, values greater than 1000 are considered normal and even. In this case, though the value is less than 1000, still it is considered to be normal, but not even, rather odd. Similarly, the dataset of Iridium too passes the normality test at , though fails to qualify to be called an even dataset. Regression Test: In this method, lag 1 is used to predict the original time series. The probabilities of both the time series of the prices of Platinum and Iridium are which means that their level of occurrence are 100% in both the cases. The values for the three information criterions Akaike, Schwarz and Hannan-Quinn show that there is volatility present in the prices of platinum and iridium in the New York market. The value of DW stat for platinum is , which is almost equal to 2. The value of λ 1 from the equation DW = 2(1-λ 1 ) which comes out to be , which is neither close to positive autocorrelation nor negative auto-correlation. Similarly, from the DW stat , λ 1 for iridium can be calculated which comes out to be , thus drawing the same conclusion as of platinum. In both the cases the DW stat values are greater than the values of the respective R squared, which indicates that the datasets are good and there are no trace of spuriousness in them. ADF Test: Probability for Platinum is and for Iridium is Both these values are very low and almost close to zero. Since probability is low, so the datasets are stationary. The log-likelihood value for Platinum is 17,347 and for Iridium is 18,605. Generally the critical value for log likelihood is Since, the values are much more than 2000, it indicates that the datasets are extremely volatile and indeed their respective markets. Johansen Co-integration Test: Trace test indicates that there is no indication of co-integration between Platinum and Iridium market prices at 0.05 level. Thus there arises no question of the impact of co-integration. It is hence revealed in the maximum Eigen-value test which also says that there is no co-integration at 0.05 level. Granger Causality Test: It is seen that p value of the second one is lower. In that instance, for the null hypothesis that Iridium does not cause Platinum, the probability is also high at 6.38%. Thus, null hypothesis is accepted. Hence, prices of iridium have no effect on the prices of platinum. For the other instance, that platinum does not cause iridium, the probability is high at 12.96%. So, null hypothesis is accepted. Hence platinum prices have no effect on the prices of Iridium. 46

11 VI. LIMITATIONS OF THE STUDY AND SCOPE OF FUTURE WORK Artificial Neural Network & Fuzzy Neural Network are better tools for these kind of research works. Henceforth, they could be used in the same study too, and that too from a different perspective. However, the cardinal question remains the same as to whether investors focus more on indexes first and then the stocks or is it the other way round. REFERENCES 1. de faria, e., albuquerque, m.p., & gonzalez, j.l. (2009) predicting the brazilian stock market through neural networks and adaptive exponential smoothing methods. expert systems with applications, 36(10): ghosh, b & srinivasan, p. (2015) a statistical analysis of the stochastic drift between sensex & nifty- an in-depth study. international journal of innovative research and development, an-sing chen, leung,m.t. & daouk, h. application of neural networks to an emerging $nancial market: forecasting and trading the taiwan stock index. 4. gupta, n. & yuan, k. (2008) on the growth effect of stock market liberalizations 5. bekaert, g., harvey, c.r & lundblad, c. (2005) does financial liberalization spur growth? journal of financial economics,