# The relationship between spot and futures prices of Ribbed Smoked Rubber Sheet traded on Agricultural Futures Exchange of Thailand.

INTRODUCTIONIn Thailand, the first Futures Exchange, Agricultural Futures Exchange of Thailand (AFET), has been established since 1999. The first trading, with Ribbed Smoked Rubber Sheet no. 3 (RSS3) as the first underlying asset, was on May 28, 2004. Ribbed smoked rubber sheet is considered to be the most liquid contract traded on AFET.

In 2002, about 2.61 million tons of natural rubber was produced in Thailand and more than 2.35 million tons were exported with the value of 76,400 million Baht. Natural Rubber is domestically used in tire industry, rubber stick, latex glove, and condom. Ribbed smoked rubber sheet is produced in Thai rubber production more than other kinds of rubber. Many smoked rubber factories have directly exported their products to overseas customers, with the important Thai rubber importers are the United States and Japan. AFET chose ribbed smoked rubber sheet as the underlying asset in the futures contract to help rubber farmers, processors, and exporter in managing their risk. And futures trading may help discover the price of rubber in the future which may help provide some information to the parties involved in making decision. (Retrieved November 17, 2008 from http://www.afet.or.th)

Price discovery from futures trading is one of the functions that Agricultural Futures Exchange of Thailand (AFET) has tried to achieve. Futures contract is the commitment to buy or sell the underlying asset in the future time at the futures price. Futures price is the price that is agreed today but will be used for settlement at maturity. Knowing futures price or its trend today for future delivery may then help forecast or discover the expected future spot price at maturity. Many previous studies found the long-run and short-run relationship between the spot price and the futures price of both commercial and financial products (i.e. Tse (1995), Alphonse (2000), McKenzie, Jiang, Djunaidi, Hoffman and Wailes (2002), and Pinjisakikool (2009)). In order to investigate whether futures trading on AFET helps discover the expected spot price in the future or not, this paper employs the spot and futures price of ribbed smoked rubber sheet no. 3 which is the most liquid underlying asset during May 2004 to August 2009. Objectives of this paper are to explore whether the futures price help discover the expected future spot price, to study lead-lag relationship, to explore the best model in forecasting the expected futures spot price, and to see how far from maturity the futures price contains most information about the expected future spot price. Benefits from being able to discover the expected future spot price will help all investors, whether hedgers or speculators, in making decision on their business or portfolio and especially in managing the risk.

LITERATURE REVIEW

Tse (1995) investigated the lead-lag relationship between the spot index and futures price of the Nikkei Stock Average employing the Error Correction Model during February 1993 through April 1993. He has found that the futures price leads the movements in the spot index, but not vice versa. French stock index (CAC 40) cash and futures prices were examined by Alphonse (2000). The long-run relationship and short-run relationship for some lags from January 1995 to March 1995 has been reported. Lead-lag relationship between the spot index and futures contract for the FTSE 100 traded at the LIFFEE was investigated by Brooks, Rew, and Ritson (2001) and Antoniou and Holmes (1996). Brooks et al (2001), using 10-min observations from June 1996-1997, has found that lagged changes in the futures price helps predicting changes in the spot price. Antoniou and Holmes (1996), covering the period from September 1984 to June 1993, has found significant long-term relationship for the four and five months prior to maturity of the futures contract, while no long-run and short-run relationship is detected for the one and two months prior to maturity of the futures contract. Ghosh (1993) used Standard and Poor's (S&P) 500 index spot and futures intra-day prices from the Chicago Mercantile Exchange (CME) from January 1988 to December 1988. He has found statistically significant coefficient on error correction terms for changes in spot and changes in futures prices. Barnhart and Szakmary (1991), using spot and forward exchange rates for the U.K., German, Japan and Canada, have found significant relationship between the two rates.

In commodity futures market, McKenzie, Jiang, Djunaidi, Hoffman and Wailes (2002) examined the short-run and long-run relationship within the U.S. rice futures markets. The result shows no relationship between U.S. long-grain rough rice spot and futures prices. On the other hand, Kenourgios and Samitas (2004) has found significant relationship between the spot and futures prices for the copper futures contract on the London Metal Exchange with maturity three months and fifteen months from January 1989 to April 2000. Beck (1994) tested five commodity markets at the eight and twenty-four week horizon. He finds significant relationship between the spot and futures price for all markets for cattle, orange juice, corn, copper and cocoa. Mattos and Garcia (2004) investigated the relationship between cash and futures prices in the Brazilian agricultural market for coffee (Arabica), corn, cotton, live cattle, soybeans and sugar. Their study shows mixed results. Spot and futures prices from four different agricultural commodities markets: live cattle, hogs, corn and soybean meal during September 1959 to October 2000 were analyzed by McKenzie and Holt (2002). They have found significant relationship for corn and soy meal but no relationship for live cattle and hogs. Pinjisakikool (2009) studied the relationship between spot and futures prices of ribbed smoked rubber sheet no.3, white rice 5%, and tapioca chip traded on Agricultural Futures Exchange of Thailand during May 2004 to June 2008, and found a long-run relationship for all three contracts.

Bigman, Goldfarb, and Schechtman (1983) analyzed "Futures Market Efficiency and the Time Content of the Information Set". They examined the predictive power of commodity futures prices of wheat, soybeans and corn, quoted at different dates for the same maturity of the contract, in predicting the expected future spot price. The results show higher R-squared for the shorter time between the quoted date of the futures price and the delivery dates.

Previous studies have shown mixed results for the relationship between the spot and futures prices with the underlying asset as index, foreign exchange and commodity products in different countries. The purpose of this paper is to investigate the relationship between the spot and futures price of Ribbed Smoked Rubber Sheet traded in Thailand.

DATA AND METHODOLOGY

This paper covers the daily period from May 2004 to August 2009. Data on the futures prices of Ribbed Smoked Rubber Sheet are taken from the website of Agricultural Futures Exchange of Thailand while Spot prices of Ribbed Smoked Rubber Sheet are reported by the Thai Rubber Association and compiled by CEIC Database. In-the-sample data covers May 2004 to June 2009. Out-of-sample data are used for testing the forecasting accuracy of the models from July to August 2009. Daily futures prices are the price of the nearest contract month. For example, On September 22, 2009, the futures contract available for trading are October contract, November contract, December contract, January contract, February contract, March contract, and April contract. Futures price of October contract, which is the nearest contract month, will be used. Risk-free rate is the average deposit rate of five large Thai banks, namely Bangkok Bank, K-Bank, Krungthai Bank, Siam Commercial Bank and Bank of Ayudhaya. In the first part of the paper, Error Correction Model (ECM) is employed, using the data from May 2004 to June 2009, to test the relationship between the spot prices and the futures prices of ribbed smoked rubber sheet no. 3. In the second part, the investigation is on how far from maturity the information in futures price can help forecast the spot price of the underlying asset at maturity.

To avoid spurious regression, natural log of spot prices and futures prices are tested for stationarity by employing the unit root test. Contemporaneous prices are used from May 2004 to August 2009. Details on the tests are adapted from Gujarati (2003, pp. 814-826) and Brooks (2008, pp. 387-391).

Unit Root Test

[Y.sub.t] = [rho][Y.sub.t-1] + [u.sub.t] -1 [less than or equal to][rho] [less than or equal to]+1 (1)

where [u.sub.t] is a white noise error term

For the nonstationary stochastic process, [rho] will be equal to +1, or the unit root case, and (1) becomes a random walk model without drift.

If [Y.sub.t-1] is substracted from both sides of (1), the following will be obtained: Y - [Y.sub.t-1] = [rho][Y.sub.t-1] - [Y.sub.t-1] + [u.sub.t] = ([rho] - 1)[Y.sub.t-1] + [u.sub.t] (2) or [DELTA][Y.sub.t] = [delta][Y.sub.t-1] + [u.sub.t] (3) where [delta] = [rho]-1) and [DELTA] is the first difference operator.

To test for stationarity is to test whether p equals 1. If the null hypothesis that [rho] equals 1 or [delta] equals 0 is not rejected, the time series data contains a unit root and is not stationary. The Augmented Dickey-Fuller (ADF) test (1979) is used, to find out whether the estimated coefficient of [Y.sub.t-1] in (3) is zero or not, by adding the lag values of the dependent variables [DELTA][Y.sub.t] so that the error term is serially uncorrelated, with the critical values taken from MacKinnon (1996). Lag length is determined by choosing the model with minimum value of Schwarz Information Criterion.

[DELTA][Y.sub.t] = [[beta].sub.1] + [[beta].sub.2]t + [delta][Y.sub.t-1] + [[alpha].sub.i] [[summation].sup.m.sub.i=1] [DELTA][Y.sub.t-i] + [[epsilon].sub.t] (4)

where [[beta].sub.1] is the drift, and t is the time or trend variable

If a time series has a unit root, or is integrated of order one, as denoted by the first differences of the time series with unit root will be taken to make it become stationary, or integrated of order zero, I(0).

After checking and correcting for the stationarity for both spot and futures prices, the next step is to test whether both have a long-term, or equilibrium, relationship using Cointegration Test.

Cointegration Test

If one nonstationary time series is regressed on another nonstationary time series, a spurious regression may occur because of stochastic trends from both data. However, if the residuals from such regression or linear combination are I(0) or stationary, implying that the linear combination cancels out the stochastic trends in the two series, two variables are then cointegrated and have a long-term, or equilibrium, relationship. That regression will be called a cointegrating regression and the slope parameter is known as the cointegrating parameter or long run parameter. Cointegrating regression will not be spurious, even though the two variables individually are nonstationary.

To test for cointegration, the ADF unit root test on the residuals estimated from two models of cointegrating regression will be used.

[F.sub.t,T] = [S.sub.t][e.sup.r(T-t)] (5)

where [F.sub.t,T] is the futures price at any time t of the contract matured at T

[S.sub.t] is the spot price at any time t

r is the continuously compounding risk-free rate

and T-t is the time to maturity

Taking natural log on both sides of (5), the following equations are obtained:

Ln([F.sub.t,T]) = Ln([S.sub.t]) + r (T-1) (6)

Model (6) will be estimated as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Contemporaneous model (without cost of carry)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where Ln([S.sub.t]) is natural log of spot price at time t

Ln([F.sub.t]) is natural log of futures price at time t

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Cost of Carry Model (ignoring storage cost and convenience yield)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

The next step is to test whether [[??].sub.t] or [[??].sub.t] is stationary or I(0), by testing whether the null hypothesis that [delta] equals 0 in (11) and (12) can be rejected or not. If the null hypothesis of unit root is rejected, it can be concluded that spot prices and futures price have long-term relationship, or they are cointegrated.

[DELTA][[??].sub.t] =[delta][[??].sub.t-1] (11)

[DELTA][[??].sub.t] =[delta][[??].sub.t-1] (12)

Since this is the test on residuals of a cointegrating model, then the critical values are changed compared to the test on a series of raw data. Engle and Granger (1987) have introduced a new set of critical values for this application; therefore, the test is known as the Engle-Granger (EG) test. This paper will use critical values, tabulated by Engle and Yoo (1987), which are larger in absolute value than the DF critical values.

When the time-series variables are integrated of order one or the first differences will be taken to correct for the nonstationarity, and will be used in the cointegrating regression. While this approach is statistically valid, problem of no long-run relationship between pure first-differences variables occurs. To overcome this problem, a model called an Error Correction Model or an Equilibrium Correction Model is introduced. The Granger representation theorem states that if two variables X and Y are cointegrated, the relationship between them can be expressed as Error Correction Model.

Error Correction Model (ECM)

If the time-series variables are cointegrated, there is a long-term, or equilibrium, relationship between them. However, there may be disequilibrium in the short run. The error term in (9) and (10) will be treated as the "equilibrium error" or "error correction term." This equilibrium error will then be used to tie the short-run behaviour to the long-run value. Error Correction Model (ECM) or Equilibrium Correction Model by Engle and Granger (1987) can be used to correct for disequilibrium by using combinations of first differenced and lagged level of cointegrated variables (or lagged level of the error correction term.)

[y.sub.t] = [gamma][x.sub.t] + [u.sub.t]

or [u.sub.t] = [y.sub.t]-[gamma][x.sub.t] (13)

Taking the lagged value of [u.sub.t], the error correction term will be obtained:

[u.sub.t-1] = [y.sub.t-1] - [gamma][x.sub.t-1] (14)

If [y.sub.t] and [x.sub.t] are cointegrated with cointegrating coefficient ([gamma]), then [u.sub.t-1] or [y.sub.t-1] - [gamma][x.sub.t-1] will be stationary or I(0.)

Error Correction Model is shown as:

[DELTA][y.sub.t] =[[beta].sub.1][DELTA][x.sub.t] + [[beta].sub.2]([y.sub.t-1]-[gamma][x.sub.t-1]) + [e.sub.t] or [DELTA][y.sub.t]=[[beta].sub.1][DELTA][x.sub.t]+ [[beta].sub.2][u.sub.t-1] + [e.sub.t] (15)

Even though [y.sub.t] and [x.sub.t] are individually not stationary or I(1), their first differences ([DELTA][y.sub.t] and [DELTA][x.sub.t]), as well as [u.sub.t-1] are stationary or I(0). It is then valid to use Ordinary Least Square and standard procedures for statistical inference on (15.)

ECM equation (15) may be interpreted that [DELTA][y.sub.t] depends on Axt and also on the equilibrium error term [u.sub.t-1]:-

--[gamma] defines the long-run relationship between x and y

--[[beta].sub.1] describes the short-run relationship between changes in x and changes in y

--[[beta].sub.2] describes the speed of adjustment back to equilibrium

--[e.sub.t] is the error term

The speed of adjustment ([[beta].sub.2]) measures the proportion of last period's equilibrium error that is corrected for, and it is expected to be negative value:-

--Suppose [DELTA][x.sub.t] is zero, and [u.sub.t-1] is positive, this means [y.sub.t-1] is above its equilibrium value. Since [[beta].sub.2] is expected to be negative and [u.sub.t-1] is positive, the term [[beta].sub.2] [u.sub.t-1] will be negative and therefore [DELTA][y.sub.t] will be negative. In conclusion, if [y.sub.t] is above its equilibrium value in this period, it will start falling in the next period to correct the equilibrium error.

--If [u.sub.t-1] is negative, this means [y.sub.t-1] is below its equilibrium value. Since [[beta].sub.2] is expected to be negative and [u.sub.t-1] is negative, the term [[beta].sub.2] [u.sub.t-1] will be positive and therefore [DELTA][y.sub.t] will be positive. To conclude, if [y.sub.t] is below its equilibrium value in this period, it will start increasing in the next period to correct the equilibrium error.

Including lagged periods based on Schwarz Information Criterion, this paper will investigate two models:-

Model 1: [DELTA] ln([S.sub.t]) = [[beta].sub.1] [DELTA]ln([F.sub.t]) + [[beta].sub.2][u.sub.t-1] +[[gamma].sub.i] [n.summation over (i=1)] [DELTA] ln([S.sub.t-i]) + [[delta].sub.i] [n.summation over (i=1)] [DELTA]([F.sub.t-i]) +[e.sub.t] (16.1)

Model 2: [DELTA] ln([F.sub.t]) = [[alpha].sub.1], [DELTA]ln([S.sub.t]) + [[alpha].sub.2][u.sub.t-1] + [[PHI].sub.i] [DELTA] ln([S.sub.t-i]) + [[lambda].sub.i] + [DELTA] ([F.sub.t-i]) +[e.sub.t] (16.2)

Out-of-sample data during July and August 2009 are used to test the forecasting accuracy of the various models. The first model is ECM for contemporaneous data, the second is ECM for cost of carry model, the third model is ARIMA model and the fourth one is VAR. Root Mean Square Error and Mean Absolute Error are used to determine the accuracy.

In the second part of the paper, the predictive power of the futures price in forecasting the expected future spot rate will be investigated. For the same delivery date of the futures contract, the hypothesis that the nearer the delivery date, the higher the predictive power of the futures price will be tested. The near-maturity contract should contain more information than the farmaturity contract and it should help in better forecasting of expected spot rate. R-squared will be used as the measurement of predictive power.

The Ordinary Least Square Regression will be employed:

[S.sub.T] = [[alpha].sub.0] +[a.sub.1] [F.sub.t,T] + [e.sub.t] (17)

Where,

[S.sub.T] stands for the spot price of ribbed smoked rubber sheet on the last business day of delivery month T

[F.sub.t,T] is the futures price at any time t of the futures contract that will mature at time T

t is set as i) the last trading day of the futures contract which is the third business day prior to the first business day of the delivery month, ii) one week before the last trading day, and iii) two weeks before the last trading day.

[e.sub.t] is the error term.

ANALYSIS

The descriptive statistics for natural log of daily spot and futures prices in Table 1 show that characteristics of both spot price and futures price are very similar. Mean for ln(spot) is 4.18 with the standard deviation of 0.2495 where mean for ln(futures) is 4.22 with the standard deviation of 0.2449. The distributions of both ln(spot) and ln(futures) have long left tails as evidenced from the negative skewness. Kurtosis of less than 3 shows that the distribution for both is platykurtic relative to the normal. And Jarque-Bera's reported probability shows that the null hypothesis of normal distribution for both prices is rejected.

The stationarity test for both spot and futures prices is done by using the unit root test. Results in Table 2 show that ln(spot) and ln(futures) both contain unit root, or both are not stationary. After taking the first differences on both prices, the null hypothesis of unit root is rejected for both prices. The result confirms that both spot and unit prices are not stationary at the level, but they become stationary after taking the first differences.

The next step is to examine whether the spot prices and the futures prices have any long-run relationship by using the cointegration test. Even though individually spot prices and futures prices are not stationary or integrated of order one denoted as I(1), both may have long-run relationship if the residual from the regression model is integrated of order zero or I(0). Contemporaneous model using the spot and futures prices at the same time and cost of carry model, where cost of carry is allowed in the model but ignoring storage cost and convenience yield, will be tested. Table 3 reports that residuals from both contemporaneous model and cost of carry model do not contain unit root which implies that spot and futures prices have long-run, or equilibrium, relationship and spot and futures prices are cointegrated. Two models will be cointegrating regression models, and will not be spurious, even though spot prices and futures prices individually are not stationary. Table 4 reports the results of both cointegrating regressions. Both regressions report cointegrating parameter or long-run parameter as one, and both also show the problem of serial correlation as evidenced from Durbin-Watson Statistics.

To investigate the short-run and long-run relationship between spot and futures prices and the lead-lag relationship between two prices, the error correction model (ECM) which allows for the lagged differences in spot prices and futures prices will be employed. Lag length is determined based on the minimum value of Schwarz Information Criterion. Only cost of carry model will be reported here (contemporaneous model obtains the similar result.)

Table 5 reports the result from Error Correction Model. In model 1, [[beta].sub.1] is positive and highly significant, indicating that change in spot price is related to change in futures price in the short-run. Speed of adjustment ([[beta].sub.2]) is negative and significant as expected, implying that in the long run, if spot price is higher than the equilibrium in the last period, it will be adjusted down in the next period to restore equilibrium, and vice versa. [[gamma].sub.i] is negative and highly significant, implying that on average, there is a negative serial correlation in spot prices.[[delta].sub.i] is positive and highly significant, showing that futures prices contain some information which lead the spot price, because lagged changes in futures prices lead to a positive change in the subsequent spot price. The long-run and short-run relationships are also found in model 2 where the dependent variable is natural log of futures price.

In conclusion, there is strong evidence showing that spot prices and futures prices both have short-run and long-run relationship to each other.

Table 6 reports the comparison of out-of-sample forecasting accuracy of Error Correction Model with contemporaneous data, Error Correction Model with Cost of Carry, ARIMA model, and VAR model. Based on the minimum Schwarz Information Criterion, ARIMA(3,1,3) is chosen, and 4 lags for spot and futures prices are used in VAR model. Forecasting accuracy is measured by Root Mean Square Error and Mean Absolute Error. Error Correction Model allowing cost of carry reports the lowest Root Mean Square Error while VAR gives the lowest value for Mean Absolute Error.

Finally, predictive power of information contained in futures price that will help predicting the expected spot price at maturity is tested. Ordinary Least Square is employed to test how far from maturity the futures prices predict the best expected spot prices on delivery date.

[S.sub.T] = [[alpha].sub.0] + [[alpha].sub.1] [F.sub.t,T] + [e.sub.t] (17)

where [S.sub.T] stands for the spot price at maturity or delivery date, and [F.sub.t,T] is the futures price at time t. Any time t is defined in 3 cases: the first case t is on the last trading day of the futures contract which is the third business day prior to the first business day of the delivery month, the second case is one week before the last trading day, and the third case is two weeks before the last trading day. Table 7 reports the result of predictive power, proxied by R-squared of the regression, of futures price in forecasting the expected future spot price. It is clearly shown that the nearest-contract month can predict the future spot price better than the far-from-maturity contract. Futures price on last trading day of the futures contract which is the nearest-to-delivery contract (about 4 weeks) reports the highest R-squared of 77.05%, while one week before the last trading day, or about 5 weeks before the delivery date shows R-squared of 67.66%, and R-squared of the model with the futures price at two weeks before the last trading day, or about 6 weeks before the delivery date is only at 55.95%.

LIMITATION OF THIS STUDY

Unlike the stocks listed on Stock Exchange of Thailand where trading prices are reported publicly and instantaneously, the prices of Ribbed Smoked Rubber Sheet are through the auction at the main rubber market i.e. Rubber Center in Had-Yai, Songkhla Province and are reported either on the website or in the newspaper in the evening. The movement of intra-day price volatility, therefore, cannot be observed. Though Futures contracts on Ribbed Smoked Rubber Sheet No.3 is the first contract traded in Thailand, it is still considered very young. The result of long-term relationship using daily data from May 2004 to August 2009 may be limited.

CONCLUSION

Consistent with the studies done by Tse(1995), Alphonse(2000) and Brooks, Rew, and Ritson (2001), Pinjisakikool (2009), test of Cointegration and Error Correction Model (ECM) reports that both short-run and long-run relationships between the spot and futures prices of ribbed smoked rubber sheet no. 3 traded on Agricultural Futures Exchange of Thailand can be detected significantly, and futures prices leads the movements in the spot prices. The Error Correction Model which allows for cost of carry reports the highest forecasting accuracy as evidenced by the lowest root mean square error. And the nearest-to-maturity futures contract gives the highest predictive power of futures price in predicting the future spot price which is consistent with the study done by Bigman, Goldfarb, and Schechtman (1983).

In conclusion, spot prices and futures price of Ribbed Smoked Rubber Sheet No.3 contract traded on AFET have both short-run and long-run relationship and the nearer-the maturity contact, the higher the predictive power of futures price in forecasting the future spot price.

Acknowledgements

Wiyada Nittayagasetwat acknowledges a research Grant from Assumption University, and Aekkachai Nittayagasetwat acknowledges a research Grant from National Institute of Development Administration. Comments from two anonymous referees are also acknowledged.

REFERENCES

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Wiyada Nittayagasetwat

Assumption University, Thailand

Aekkachai Nittayagasetwat

National Institute of Development Administration, Thailand

Wiyada Nittayagasetwat is currently served as a Program Director, Master of Science Program in Financial Economics at Assumption University, Thailand.

Aekkachai Nittayagasetwat is currently an Associate Professor in Finance at National Institute of Development Administration, Thailand.

Table 1 Descriptive Statistics for Natural Log of Daily Spot Prices and Futures Prices from May 2004 to August 2009 LOGSPOT LOGFUTURES Mean 4.181936 4.222954 Median 4.204693 4.237001 Maximum 4.701752 4.708178 Minimum 3.511545 3.659708 Std. Dev. 0.249526 0.244895 Skewness -0.013094 -0.002044 Kurtosis 2.134368 1.964413 Jarque-Bera 39.68778 56.75083 Probability 0.000000 0.000000 Observations 1270 1270 Table 2 Unit Root Test for Natural Log of Spot and Futures at Level and at the First Differences Null Hypothesis: LOGSPOT has a unit root Lag Length: 2 (Automatic based on SIC) t-Statistics Prob. * Augmented Dickey-Fuller test statistic -1.8872 0.6605 Null Hypothesis: DIFF(LOGSPOT) has a unit root Lag Length: 1 (Automatic based on SIC) t-Statistics Prob. * Augmented Dickey-Fuller test statistic -21.9056 0.0000 ** Null Hypothesis: LOGFUTURES has a unit root Lag Length: 4 (Automatic based on SIC) t-Statistics Prob. * Augmented Dickey-Fuller test statistic -1.8357 0.6868 Null Hypothesis: DIFF(LOGFUTURES) has a unit root Lag Length: 4 (Automatic based on SIC) t-Statistics Prob. * Augmented Dickey-Fuller test statistic -13.9758 0.0000 ** Test critical values: 1 % level -3.9653 5 % level -3.4134 10 % level -3.1287 * MacKinnon (1996) one-sided p-values. ** stands for 1% significance level Table 3 Unit Root Test on the Residual (1) Contemporaneous model (without cost of carry) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where Ln([S.sub.t]) is natural log of spot price at time t Ln([F.sub.t]) is natural log of futures price at time t (2) Cost of Carry model (ignoring storage cost and convenience yield) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Null Hypothesis: Residual from (1) has a unit root Lag Length: 3 (Automatic based on SIC) t-Statistics Prob * Augmented Dickey-Fuller test statistic -7.6090 0.0000 ** Null Hypothesis: Residual from (2) has a unit root Lag Length: 3 (Automatic based on SIC) t-Statistics Prob * Augmented Dickey-Fuller test statistic -8.0743 0.0000 ** Test critical values: 1% level -4.32 5% level -3.67 10% level -2.5679 * Engle and Yoo (1987) ** stands for 1% significance level. Table 4 Results of Cointegrating Regression Models (1) Contemporaneous model (without cost of carry) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where Ln([S.sub.t]) is natural log of spot price at time t Ln([F.sub.t]) is natural log of futures price at time t Dependent Variable: LOGSPOT Method: Least Squares Included observations: 1228 Variable Coefficient Std. Error t-Statistic Prob. C -0.075975 0.01736 -4.376448 0.0000 ** LOGFUTURES 1.008332 0.004099 246.0233 0.0000 ** R-squared 0.980147 Mean dependent 4.187714 var Adjusted 0.980131 S.D. dependent 0.251637 R-squared var S.E. of 0.035470 Akaike info -3.838607 regression criterion Sum squared 1.542494 Schwarz -3.830280 resid criterion Log likelihood 2358.905 F-statistic 60527.45 Durbin-Watson 0.416023 Prob 0.000000 stat (F-statistic) Note: ** stands for 1% significance level (2) Cost of Carry model (ignoring storage cost and convenience yield) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Variable Coefficient Std. Error t-Statistic Prob. C -0.110161 0.01763 -6.248566 0.0000 ** LOGFUTURES 1.010173 0.004021 251.2055 0.0000 ** -(RAWRT) -0.268302 0.036666 -7.317381 0.0000 ** R-squared 0.980978 Mean dependent 4.187714 var Adjusted 0.980947 S.D. dependent 0.251637 R-squared var S.E. of 0.034734 Akaike info -3.879760 regression criterion Sum squared 1.477896 Schwarz -3.867268 resid criterion Log likelihood 2385.172 F-statistic 31587.54 Durbin-Watson 0.448421 Prob 0.000000 stat (F-statistic) Note: ** stands for 1% significance level Table 5 Result of Error Correction Model Model 1: [DELTA]ln[S.sub.t] [[beta].sub.1] [DELTA]ln ([F.sub.t])+ [[beta].sub.2][u.sub.t-1]+ [[gamma].sub.i][n.summation over (i=1)] [DELTA]ln ([S.sub.t-i]) + [[delta].sub.i] [n.summation over (i=1)] [DELTA]ln ([F.sub.t-i]) +n [e.sub.t] Dependent Variable: D(LOGSPOT) Variable Coefficient Std. Error C -5.00E-05 0.000516 D(LOGFUTURES) 0.362405 0.033599 RESID (-1) -0.129784 0.017330 D(LOGSPOT(-1)) -0.106672 0.028960 D(LOGSPOT(-2)) -0.072264 0.027334 D(LOGSPOT(-3)) -0.115049 0.025795 D(LOGFUTURES(-1)) 0.302478 0.037620 D(LOGFUTURES(-2)) 0.357726 0.038037 D(LOGFUTURES(-3)) 0.289639 0.038691 R-squared 0.332302 Mean dependent var Adjusted R-squared 0.327906 S.D. dependent var S.E. of regression 0.018063 Akaike info criterion Sum squared resid 0.396438 Schwarz criterion Log likelihood 3180.710 F-statistic Durbin-Watson stat 2.005383 Prob(F-statistic) Model 2: [DELTA]ln([F.sub.t])=[alpha]ln ([S.sub.t]) + [[alpha].sub.2] [u.sub.t-1] + [[PHI].sub.i] [n.summation over (i=1)] [DELTA]ln ([S.sub.t-i])+ [[lambda].sub.i] [n.summation over (i=1)] [DELTA]ln ([F.sub.t-i])+ [e.sub.t] Dependent Variable: D(LOGFUTURES) Variable Coefficient Std. Error C 7.68E-05 0.000421 RESID(-1) -0.048627 0.014617 D(LOGSPOT) 0.241488 0.022309 D(LOGSPOT(-1)) 0.089111 0.023564 D(LOGSPOT(-2)) 0.061233 0.022247 D(LOGSPOT(-3)) 0.064700 0.021035 D(LOGFUTURES(-1)) 0.062602 0.031391 D(LOGFUTURES(-2)) -0.021792 0.032112 D(LOGFUTURES(-3)) -0.131404 0.031961 R-squared 0.146528 Mean dependent var Adjusted R-squared 0.140913 S.D. dependent var S.E. of regression 0.014723 Akaike info criterion Sum squared resid 0.263577 Schwarz criterion Log likelihood 3433.814 F-statistic Durbin-Watson stat 1.988948 Prob(F-statistic) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Variable t-Statistic Prob. C -0.096771 0.9229 D(LOGFUTURES) 10.78631 0.0000 ** RESID (-1) -7.488821 0.0000 ** D(LOGSPOT(-1)) -3.683368 0.0002 ** D(LOGSPOT(-2)) -2.643722 0.0083 ** D(LOGSPOT(-3)) -4.460202 0.0000 ** D(LOGFUTURES(-1)) 8.040447 0.0000 ** D(LOGFUTURES(-2)) 9.404581 0.0000 ** D(LOGFUTURES(-3)) 7.485969 0.0000 ** R-squared 3.63E-05 Adjusted R-squared 0.022034 S.E. of regression -5.182532 Sum squared resid -5.144959 Log likelihood 75.58569 Durbin-Watson stat 0.000000 Dependent Variable: D(LOGFUTURES) Variable t-Statistic Prob. C 0.182590 0.8552 RESID(-1) -3.326747 0.0009 ** D(LOGSPOT) 10.82447 0.0000 ** D(LOGSPOT(-1)) 3.781732 0.0002 ** D(LOGSPOT(-2)) 2.752450 0.0060 ** D(LOGSPOT(-3)) 3.075762 0.0021 ** D(LOGFUTURES(-1)) 1.994258 0.0463 ** D(LOGFUTURES(-2)) -0.678628 0.4975 D(LOGFUTURES(-3)) -4.111327 0.0000 ** R-squared 8.72E-05 Adjusted R-squared 0.015884 S.E. of regression -5.591533 Sum squared resid -5.553985 Log likelihood 26.09599 Durbin-Watson stat 0.000000 Note: ** stands for 1% significance level Table 6 Comparison of Out-of-Sample Forecasting Accuracy ECM ECM-COC ARIMA VAR RMSE 0.011147 0.009242 0.062934 0.010724 MAE 0.011147 0.009242 0.051893 0.008580 Table 7 Predictive Power of Futures Price [S.sub.T] + [[alpha].sub.0]+ [[alpha].sub.1][F.sub.t,T] + [e.sub.t] where [S.sub.T] stands for the spot price of ribbed smoked rubber sheet on the last business day of delivery month T [F.sub.t,T] is the futures price at any time t of the futures contract that will mature at time T t is set as i) the last trading day of the futures contract which is the third business day prior to the first business day of the delivery month, ii) one week before the last trading day, and iii) two weeks before the last trading day. [e.sub.t] is the error term. Last Trading One week before Two weeks before Day last trading day last trading day R-Squared 77.05% 67.66% 55.95%

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Author: | Nittayagasetwat, Wiyada; Nittayagasetwat, Aekkachai |
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Publication: | International Journal of Business and Economics Perspectives (IJBEP) |

Article Type: | Abstract |

Geographic Code: | 9THAI |

Date: | Sep 22, 2010 |

Words: | 6284 |

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