The analysis of volatility of gold coin price fluctuations in Iran using ARCH & VAR models

Article history: Received June 28, 2013 Received in revised format 19 October 2013 Accepted 2 January 2014 Available online January 4 2014 The aim of this study is to investigate the changes in gold price and modeling of its return volatility and conditional variance model. The study gathers daily prices of gold coins as the dependent variable and the price of gold in world market, the price of oil in OPEC, exchange rate USD to IRR and index of Tehran Stock Exchange from March 2007 to July 2013 and using ARCH family models and VAR methods, the study analysis the data. The study first examines whether the data are stationary or not and then it reviews the household stability, Arch and Garch models. The proposed study investigates the causality among variables, selects different factors, which could be blamed of uncertainty in the coin return. The results indicate that the effect of sudden changes of standard deviation and after a 14-day period disappears and gold price goes back to its initial position. In addition, in this study we observe the so-called leverage effect in Iran’s Gold coin market, which means the good news leads to more volatility in futures market than bad news in an equal size. Finally, the result of analysis of variance implies that in the short-term, a large percentage change in uncertainty of the coin return is due to changes in the same factors and volatility of stock returns in the medium term, global gold output, oil price and exchange rate fluctuation to some extent will show the impact. In the long run, the effects of parameters are more evident. 2014 Growing Science Ltd. All rights reserved.


Introduction
The first decades of the new millennium has witnessed different world's challenges such as infamous September 11 incident, Iraq and Afghanistan war, etc.These incidents have created tremendous uncertainties and many investors moved to safe side in order to protect their investment, switching to gold from stock exchange.The world gold price went up from 600$ level to a historical record of 1900$ (Lawrence, 2003).Melvin and Sultan (1990) investigated South African political unrest, oil prices, and the time varying risk premium in the gold futures market and reported that while gold prices did not have any relationship with oil price but fluctuations on oil and stock exchange both influence on gold price, significantly.Bollerslev (1986) presented a natural generalization of the Autoregressive Conditional Heteroskedastic (ARCH) process to show for past conditional variances in the current conditional variance equation is proposed.Cai et al. (2001) provided a comprehensive characterization of the intraday return volatility in gold futures contracts traded on the COMEX division of the New York Mercantile Exchange.They detected employment reports, gross domestic product, consumer price index, and personal income as having the biggest impact.They also detected that the high-frequency returns disclosed long-memory volatility dependencies in the gold market, which had important implications on the pricing of long-term gold options and the determination of optimal hedge ratios.Tully and Lucey (2007) investigates macroeconomic influences on gold using the asymmetric power GARCH model (APGARCH) of Ding et al. (1993).They investigated both cash and futures prices of gold and substantial economic variables over the period 1983-2003, with special concentration on two periods, around the 1987 and 2001 equity market crashes.Their results indicated that APGARCH model could provide the most sufficient description for the data, with the inclusion of a GARCH term, free power term and unrestricted leverage impact term.Glosten et al. (1993) detected some support for a negative relationship between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model.Using the modified GARCH-M model, they also demonstrated that monthly conditional volatility could not be as persistent as was thought.Positive unanticipated returns seemed to result in a downward revision of the conditional volatility whereas negative unanticipated returns yield in an upward revision of conditional volatility.Ivanova and Ausloos (1999) presented a forecast of the low q-moment values of the assumed multifractal spectrum of Gold price, Dow Jones Industrial Average (DJIA) and Bulgarian Lev -USA Dollar (BGL-USD) exchange rate.The analysis demonstrated that these three financial data were not likely fractal but rather multifractal indeed.

The proposed model
The aim of this study is to investigate the changes in gold price and modeling of its return volatility and conditional variance model.There are two main hypotheses associated with the proposed study of this paper as follows, 1.The change on gold coin is a function of macro-economic factors and there are some meaningful relationships among them.2. The change on gold coin is a function of micro-economic factors and there are some meaningful relationships among them.
The study also considers whether there is some causality among various factors and whether the effects of positive and negative pulses are equal or not.The study gathers daily prices of gold coins as the dependent variable and the price of gold in world market, the price of oil in OPEC, exchange rate USD to IRR and index of Tehran Stock Exchange from March 2007 to July 2013 and using ARCH family models and VAR methods, the study analysis the data.The study first examines whether the data are stationary or not and then it reviews the household stability, ARCH and GARCH models (Engle et al., 1987;Engle & Kroner, 1995).

The effects of TARCH model on gold price
The proposed study investigates the causality among variables, selects different factors, which could be blamed of uncertainty in the coin return.Table 1 demonstrates the summary of some basic statistics.

Table 1
The summary of some basic statistics on gold price In this paper, we have performed Dickey Fuller test to see whether the data are stationary or not and Table 2 demonstrates the results of our investigation on price of gold (PCOIN).
The results of Table 2 clearly specify that Y is a stationary variable.The proposed study of this paper uses ARCH method with GARCH(1,1) as follows, Table 3 shows details of our results of the TARCH model for gold price.

Table 3
The results of TARCH model on gold price

The effect of TARCH model on oil price
Table 4 demonstrates the summary of some basic statistics.In addition, we have performed Dickey Fuller test to see whether the oil prices are stationary or not and Table 5 demonstrates the results of our investigation on price of oil (PROIL).
Table 6 shows details of our results of the TARCH model for oil price.

Table 6
The results of TARCH model on oil price

The effects of nonlinear EGARCH model on currency
The proposed study investigates the causality among variables, selects different factors, which could be blamed of uncertainty in the coin return.Table 7 demonstrates the summary of some basic statistics on currency data.Besides, we have performed Dickey Fuller test to see whether the oil prices are stationary or not and the proposed model find the following two equations as appropriate models, Table 8 shows details of our results of the EGARCH model for currency changes.

Table 8
The results of EGARCH model on currency changes Finally, we have performed augmented Dickey Fuller (ADF) to verify whether time series of gold price, oil price and currency are stationary or not and Table 9 shows details of our findings.The results of Table 9 specify that all data are stationary when the level of significance is one or five percent.

The VAR method
In this section, we present details of the implementation of VAR method.The proposed method uses the following time series equation, Table 10 demonstrates the results to find the optimum number of Inertia.

Table 10
The results of regression analysis According to Table 10, the best lag is determined as one based on Schwartz Baysian criterion.In addition, Fig. 1 demonstrates the stability of the VAR method.Res pons e of GARCHCOIN to PGOP Res pons e of GARCHCOIN to GARCHOIL Res pons e of GARCHCOIN to GARCHDR2 Response to Cholesky One S.D. Innovations ± 2 S.E.
As we can observe from the results of Fig. 2, the changes on local currency, world gold price, oil price have instance effects on gold coin.Next, we present details of analysis of variance for fluctuation of gold coin prices in different periods.Table 11 summarizes the results of our findings.As we can observe from the results of Table 11, during the first period, nearly all changes on gold coin fluctuations are associated with the gold coin price itself and world gold price as well as oil price did not influence on gold price, significantly.However, in other periods, other parameters such as world gold price, currency de-evaluation and stock exchange start influencing the gold price.

Conclusion
In this paper, we have presented an empirical investigation to study the effects of different factors such as world gold price, stock exchange, oil price and currency exchange on Iranian gold coin price.
The proposed study has gathered the historical information from March 2007 to July 2013 and using ARCH family models and VAR methods, the study analysis the data.The results have indicated that the effect of sudden changes of standard deviation and after a 14-day period disappears and gold price goes back to its initial position.In addition, in this study we have observed the so-called leverage effect in Iran's Gold coin market, which means the good news leads to more volatility in futures market than bad news in an equal size.Finally, the result of analysis of variance implied that in the short-term, a large percentage change in uncertainty of the coin return was due to changes in the same factors and volatility of stock returns in the medium term, global gold output, oil price and exchange rate fluctuation to some extent will show the impact.In the long run, the effects of parameters are more evident.

Fig. 1 .Fig. 2 .
Fig. 1.The results of inverse roots of AR characteristics polynomialThe results of Fig.1clearly show that the VAR model preserve sufficient stability.We now consider the effects of a shock on price of gold and these effects are shown in Fig.2as follows,

Table 2
The summary of Dickey Fuller test

Table 4
The summary of some basic statistics on oil price

Table 5
The summary of Dickey Fuller testThe results of Table5indicate that oil data become stationary after taking one difference.Here TARCH model for oil price is studied through the following relationship.

Table 7
The summary of some basic statistics on currency

Table 9
The results ADF test

Table 11
The summary of analysis of variance