This study investigates the econometrical principles of cross correlation analysis on the variables, Gold price in PKR and U.S. Dollar in PKR. The research consists of two major econometric analysis; Granger’s Causality Test and Cross- correlation test. In Granger’ Causality test, the study had created bilateral causal relationships between the variables. It showed a strong causal relation of Gold in PKR with U.S. Dollar in PKR and U.S. Dollar in PKR was found to had extensively significant causal relation with Gold Price in PKR. In cross-correlation investigation, the study identified the U.S. Dollar in PKR were significantly correlated overtime with Gold Price in PKR.
Gold was thought by many to be a currency without borders, being known around the world. While gold was influenced naturally by its supply and demand components, gold responds also to many macroeconomic factors including exchange rate and equity market. While gold provides diversification properties in a portfolio mix with equities, it also was alleged to act as a hedge against the U.S dollar as gold appears to had an inverse relationship with the currency (Ciner, Gurdgiev, & Lucey, 2010). Cross-correlation of the two series were in accordance with standard procedures for evaluation of the extent, so the main objective was to identify to which degree these two variables Gold Price in PKR and Exchange Rate (U.S. Dollar in PKR) were correlated.
Gold had provided a cushion against depreciation in the value of the dollar for two reasons. It firstly provides protection as it was a hedge against (U.S. originated) inflation and secondly it provides a hedge against depreciation. Therefore it was not surprising that gold historically had been considered a hedge against fluctuation in the U.S. Dollar. Any depreciation in the dollar may fuel increased interest in gold due to the dilution in dollar’s worth. Gold may then be considered to be the anti dollar (Capie, Mills and Wood, 2005).
Gold price had been in the centre of vivid discussions since the very beginning of economics as a science. Every recession since 1971 made these discussions severe (Ivan, 2009).
1.2 Problem Statement
The main objective of this paper was to investigate the cross-correlation between gold price fluctuation & Exchange Rate Dollar. This was estimated using econometric model of Cross correlation on yearly data from 1958-2009. Cross correlation was generally used when measuring information between two different time series. The range of the data was -1 to 1 such that the closer the cross-correlation value was to 1, the more closely the information sets were.
The U.S. dollar exchange rate in PKR was taken as this was observed closest to the gold price in PKR. This rate was chosen as this was one of the most important foreign exchange markets that were in operation for the complete sample period, which was a yearly data from1958 till 2009 on an annual basis, had been used in the study.
1.3 Outline of the Study
The main notion to the study was to identify the underlying principles of the cross-correlation function. The degree of extend to which fluctuation in gold price & U.S. Dollar was associated.
H1: There was a Cross Correlation between Gold Price in PKR & Exchange Rate (U.S. Dollar in PKR).
For commodities that were traded continuously in organized markets such as the Chicago Board of Trade, a change in any exchange rate will result in an immediate adjustment in the prices of those commodities in at least one currency and perhaps in both currencies if both countries were “large”. For example, when the dollar depreciated against the euro, dollar prices of commodities tend to rose (and euro prices fall) even though the fundamentals of the markets––all relevant factors other than exchange rates and price levels––remain unchanged (Sjaastad, 2008). This suggested that the there was a relationship between the commodity prices and exchange rate, as the dollar was depreciating, the prices of commodity increased, and other things remaining constant.
The potential importance of this phenomenon was not limited to the major currency countries. With several minor currencies of the world being directly or indirectly tied to one of the three major currencies (the dollar, the euro, and the yen) or a currency basket, shocks to major currency exchange rates were felt not only by producers and consumers of internationally-traded commodities in major currency countries but also by many of the smaller, commodity-exporting countries in the form of inflationary (or deflationary) shocks transmitted by fluctuations in the international prices of commodities. The idea of the Australian dollar as a “commodity currency” was an example (Sjaastad, 2008). This stated that not only the commodity prices of major currency countries were affected by the shocks to major currency but also the minor currency countries were affected.
Gold price had been in the centre of vivid discussions since the very beginning of economics as a science. Every recession since 1971 made these discussions severe (Ivan, 2009).
Gold was also identified as a hedge against fluctuations in the U.S. Dollar on average, both in distressed and in normal market conditions. The properties of safe asset and hedging capabilities suggested that the dollar price of gold should increase when the bilateral exchange of the U.S. Dollar against other currencies depreciates (Massimiliano & Paolo, 2010).
If gold was quoted in currencies other than the U.S. dollar such as sterling, it was converted using the foreign exchange rate closing price on the same day. Therefore, gold reflected the relative strength of the currency in which it was quoted. Any depreciation in the dollar may fuel increased interest in gold due to the dilution in the dollar’s worth. Gold may then be considered to be the anti-dollar (Ciner, Gurdgiev, & Lucey, 2010).
Gold was a prime candidate for a study of the effects on commodity prices of fluctuations in major currency exchange rates. A highly homogeneous commodity, gold was traded almost continuously in well organized spot and future markets. Moreover, as annual production (and consumption) of gold was minuscule compared with the global stock, the gold producing countries, not all of whose currencies were traded in organized markets, were unlikely to dominate the world gold market (Sjaastad, 2008). This stated that gold was the important variable to be considered when studying the effects on commodity prices of fluctuation in exchange rates.
That does not mean that gold could no longer be a good store of value or protection against exchange rate change. But whether it was or not depends on different forces. It depended on whether, when currencies weaken, people switch to gold; and on when currencies strengthen; people became more confident about the value of currencies, and switch from gold. Even though gold no longer had any role in the monetary system of any major country, such behavior could still be sensible (Capie, Mills, & Wood, 2005).
In determining the extent to which gold acts as an exchange rate hedge, it was, therefore, well worth exploring the past, to see how well gold protected against currency fluctuations. That, in itself, was of interest, and it may also be of interest in the future (Capie, Mills, & Wood, 2005). The first was a hedge against changes in the internal or domestic purchasing power of the dollar. The second was gold was a hedge against changes in the external purchasing power of the dollar. If gold were a perfect internal hedge, its dollar (i.e., nominal) price would rise at the same rate and time as a domestic U.S. price index. If it were a perfect external hedge, its dollar (i.e., nominal) price would rise at exactly the same rate and time as the number of units of foreign currency per dollar fell (Capie, Mills, & Wood, 2005).
Gold as hedging asset or safe haven typically focuses on the pattern of correlation. A negative (conditional or unconditional) correlation was indicative of hedging capabilities. It was considered a more general approach, and shed light on properties of the relation between gold and the Dollar that had not been considered previously. In particular, we study the evolution of the pattern of contagion between the two assets across the turmoil (Massimiliano & Paolo, 2010).
The relation between gold prices and the U.S. Dollar exchange rate had been subject to intense scrutiny. In particular, a significant body of literature attributes a value to gold of safe haven or hedging capabilities against exchange rate fluctuations (Massimiliano & Paolo, 2010).
Our results suggest that gold generates stable co-movements with the Dollar that had indeed persisted during the recent phases of market disruption. We also show that exogenous volatility shocks tend to generate reactions of gold prices that were more stable than those of the U.S. Dollar (Massimiliano & Paolo, 2010).
Its importance was also stressed in some previous papers, in which the economist taken a retrospective view on the devaluation of the USD in 1933-34, i.e. the raising of the price of gold (Hoang, 2004).
For a given commodity, the authors started from an equilibrium situation between the world demand for imports (which depends only on the world price of the commodity in importers’ currency) and the world supply of exports (which depends only on the world price of the commodity in exporters’ country). In this study comparative static was performed to obtain the percentage change in the dollar (numeraire) price of the commodity as a weighted average of the percentage change in exporters’ and importers’ nominal exchange rates in terms of the numeraire currency. The authors did not explicitly consider real exchange rates or other supply and demand variables (Dupont & Juan-Ramon, 1996). This stated in previous paper that the effect of exchange rate changes on commodity prices were analyze by some authors in 1972, in which these formed an equilibrium b/w the world demand for imports and the world supply of exports.
In previous studies it was analyzed the effects of the bilateral real exchange rates among the major currencies on the real (dollar based) price of the commodity. In previous studies hypothesis was advanced that changes in the exchange rates among major currencies will cause commodity prices to fluctuate independently of the movements in the general price levels of the major countries (Dupont & Juan-Ramon, 1996). This stated that the studies were done on the effects of exchange rates among the major currencies on dollar price of commodity.
A key feature of previous study’s model was that the country that had the most influence in determining the world price of a commodity was not always the country in whose currency the commodity price was denominated. One can gain insight into this with an example from the financial markets (Dupont & Juan-Ramon, 1996).
In previous studies model was developed to analyze the gold market for the period 1982-90. Dynamic econometric specification was used to study the effect of fluctuations in the real exchange rate among the major currencies on fluctuations in the price of gold (Dupont & Juan-Ramon, 1996).
The empirical analysis focuses on three large financial markets (the U.S., the UK and Germany) with different currencies (U.S. dollar, UK pound and the euro) in order to examine the differences and similarities of the role of gold in these markets (Baur & Lucey, 2010).
The volatility of the exchange rates among the major currencies since the dissolution of the Bretton Woods international monetary system had been a major source of price instability in the gold market. Indeed, the instability of real exchange rates between major currencies was responsible for nearly half of the observed volatility in the spot price of gold during the 1982-90 periods (Dupont & Juan-Ramon, 1996).
In previous studies the role of gold as a hedge against the dollar was analyzed, finding evidence of the exchange-rate hedging potential of gold (Dirk & Thomas, 2009).
While gold was usually denominated in U.S. dollars, the dollar bloc had but a small influence on the international price of gold (Dupont & Juan-Ramon, 1996).
The major gold producers of the world (South Africa, the former U.S.S.R., and Australia) appear to had no significant influence on the world price of gold (Dupont & Juan-Ramon, 1996).
Moreover, gold was said to be uncorrelated with other types of assets which was an important feature in an era of globalization in which correlations increased dramatically among most asset types. These components might had contributed significantly to the role of gold (Baur & Lucey, 2010).
The world gold market was dominated by the European currency bloc who possesses approximately two-thirds of the ‘market power’ enjoyed by all participants in the market. Accordingly, real appreciations or depreciations of the European currencies had profound effects on the price of gold in all other currencies (Dupont & Juan-Ramon, 1996).
The diversification property of gold and gold’s relationship with the equity markets had been subject to significantly increased examination over the last number of years. Previous studies it was reported that gold, while risky in its own right, had the propensity to provide valuable diversification qualities. (Ciner, Gurdgiev, & Lucey, 2010)
While cross correlations gave a first hint at the time structure of the indicators with respect to developments in industrial production it did not necessarily imply causation in the sense of Granger. A more refined analysis to determine the lead of each indicator quantitatively can be performed with Granger causality tests. This test was used to see how much of the current variable Y can be explained by past values use of Y and then to see whether adding lagged values of X can improve the explanation. Thus, X was said to Granger-cause Y if the X variable was statistically significant in the equation and therefore improves the forecast of Y (Hüfner & Schröder, 2002).
In time series analysis one often used concept was Granger causality. Given a TSCM it could derive the Granger causality among the time series variables in the TSCM. Generally, Granger causality and the graphic causal models were two different concepts: while the Granger causality concerns the prediction power of one time series for the, a TSCM concerns the causal relation among time series variables at each time points (Chen, 2010).
The study of Time Series Analysis had been a subject of interest in multiple focuses throughout history from the early astronomical forecasting to the modern day economic and technological (Diebold, Kilian, & Nerlove, 2006). Time series had been an important source of analysis and forecast, Harmonic analysis had been considered one of the original most methods of forecasting time series overtime (Diebold, Kilian, & Nerlove, 2006). Time series analysis had evolved from various stages to the current automated analysis through econometrics. Automated discovery in science was a fairly recent phenomenon. It was commonly associated with the newfound capacity to collect, store and process vast amounts of data in extremely short periods of time. These capabilities come from sheer computational power and storage capability in conjunction with electronic communication, data processing and statistical analysis. Rapid information processing accelerates learning. It also enables algorithms to be implemented that automate judgments and scientific evaluations that would otherwise be made by human participants. The upshot was that empirical and experimental research could now be conducted in an automated fashion with much more limited human involvement than in the past (Phillips, 2004).
In particular, many authors argue that stock returns become positively cross-correlated in large samples, causing unspecified test statistics. Specifically, calendar clustering and overlapping returns were shown to represent two main sources of cross-sectional dependence (Antoniou, Arbour, & Zhao, 2006).
In previous studies that examined the cross-correlation effects on the post-merger stock performance of U.S. acquirers. In that study, however, excluded were the all overlapping observations (i.e., multiple bids). But it was known that overlapping returns represent a major source of cross-sectional dependence and that multiple bids constitute a large part of the overall merger population (Antoniou, Arbour, & Zhao, 2006).
Using cross correlations and Granger causality estimates it was determined which of the indicators had the longest lead with regard to the year-on-year growth rates of industrial production. Additionally, it was analyzed lead/lag structures among the indicators, taking into account differences in the publication schedule (Hüfner & Schröder, 2002).
According to some previous studies, a (weakly) stationary stochastic variable X can be said to cause another (weakly) stationary stochastic variable Y if and only if the information contained in the history of X helps improve the prediction of Y when the prediction model already contains the history of Y and all other relevant information (Atuker, 2010).
3.1 Method of Data Collection
The secondary source of data was used for data collection. Data of gold price (per ounce) in PKR & U.S. Dollar in PKR for 52 years (from 1957 – 2009) had been collected through various websites. It was collected from the Commodity Traders of National commodities Exchange Ltd (NCEL), www.Kitco.com, Daily Business Recorder, & Pacific Exchange Rate Service, www.exchange-rates.org, www.forex.pk.
3.2 Sample Size
Annual observations of Gold price & U.S. Dollar of Pakistan was collected for 52 years starting from 1957 to 2009 had been included in the sample size. This was considered a sufficient sample size for running econometric cross correlation test.
Findings and Interpretation of the results
Grangers Causality Test
Before performing the cross correlation test, granger’s causality test was run on the variables to test the casual relation between the variables amongst each other’s. This had resulted with the evidence of a bilateral relation between variables used in the study.
Granger’s definition of causality was a pragmatic one – defined in terms of predictability.1 In the bivariate case, Granger causality from ‘X’ to ‘Y’ (both as defined above) can be operationalised and tested as follows (Atuker, 2010)
where:”a” was the constant term; “b’s” and “g’s” were parameters to be estimated; p and q were lag lengths; and et was a well-behaved error term. X does not Granger-cause Y if (Atuker, 2010)
The granger causality model was based on keeping a 3.5 F-statistic threshold to find out the casual relationship among variables. That was if any variable with a higher than 3.5 F-statistic in regards to the other variable was considered to had a casual relation of the variable in opposition with the other variable.
Following outcome were generated using e-views
Granger Causality Tests
Based on the granger’s causality test, variables (Gold Price in PKR & Exchange Rate: U.S. dollar in PKR) were found with bilateral relationship, this had been noticed in this paper’s results and many previous papers. Gold price in PKR had a strong causal relation with Exchange Rate: U.S. Dollar in PKR. Also there was a strong causal relation of U.S. Dollar in PKR with Gold Price in PKR. Both had threshold higher than 3.5F- Statistic, when Granger test was run, it showed 16.7913 F-Statistic which shows a strong causal relation of Gold in PKR with U.S. Dollar in PKR and it had even more strong causal relation for U.S. Dollar in PKR with Gold Price in PKR, which was 19.2676 F-Statistic.
Cross correlation Function
After Granger test was run, Cross correlation function was applied using SPPSS. Cross correlation of two series correlate the level of assessment was a specific way. Consider two sets ‘x’ (i) and ‘y’ (i) where i=0, 1, 2…N-1. Cross correlation ‘R’ was defined as a delay of
Where “mx” and “my” were the resources of the matching sequence, if the above was calculated for every delays d=0, 1, 2,…N-1 then it outcome in a cross correlation series of two times the span as the original series (Bourke, 1996)
Index was less than 0 or concerns about the series was supposed to be run was equal to or greater than the number of points (i-d < 0 or i-d >= N). The most common method, or a series of these problems was to ignore the notion of ‘x’ and ‘y’ were zero for i < 0 and i >= N. In various signal processing applications the series was understood to be rounded in which case the out of range indexes were “wrapped” back within series, i.e.: x(-1) = x(N-1), x(N+5) = x(5) etc (Bourke, 1996)
The range of delays‘d’ and thus the length of the cross correlation series can be less than N, for example the aim may be to test correlation at short delays only. The denominator in the expression above serves to normalize the correlation coefficients such that -1 <= r(d) <= 1, the bounds indicating maximum correlation and 0 indicating no correlation. A high negative correlation indicates a high correlation but of the inverse of one of the series (Bourke, 1996).
Previous studies considered an internationally-traded homogeneous commodity, the price of which obeys the law of one price. It was assumed that worldwide there were N trading blocs, that the numeraire currency, the dollar, was the currency of bloc 1, and that each bloc’s commodity excess demand depends on the commodity price deflated by the general price level and on other supply and demand variables. World market clearing condition closed the model, which yields the following reduced form equation (Dupont & Juan-Ramon, 1996).
where pt was the logarithm of the real (dollar based) commodity price, ejt was the logarithm of the bilateral real exchange rate between blocs 1 and j , Kt groups together other supply and demand variables and 0j was the elasticity of the real commodity price with respect to the bilateral real exchange rate between blocs 1 and j . Note that the 0js were between zero and one (Dupont & Juan-Ramon, 1996).
Cross Correlation Tests
Series Pair: Exchange_rate_RS with Gold_Price_RS
Cross Correlation Function when testing U.S. Dollar in PKR with Gold Price in PKR shows different behavior at different lags. Lag 0 shows that cross correlation was 0.621 which was significant and it showed that there was association between gold price in PKR of current year and U.S. Dollar in PKR in current year. Lag 1 showed that Current year (year 0) exchange rates: U.S. Dollar in PKR had an association with year 1 gold price in PKR. Lag 2 showed that current year U.S. Dollar in PKR had no association with year 2 gold prices in PKR. Lag 3 showed that current year U.S. Dollar in PKR had again no association with Gold prices in PKR. Lag 4 showed that current year U.S. Dollar in PKR had again no association with Gold prices in PKR of 4th year. Lag 5 showed that current year U.S. Dollar in PKR had negligible or no association with Gold prices in PKR of 5th year. Lag 6 showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 6th year. Lag 6 showed that current year U.S. Dollar in PKR had again no association with Gold prices in PKR. Lag 7 which had cross correlation 0.267 showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 7th year. Lag 8 which had cross correlation 0.468 showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 8th year. Lag 9 which had cross correlation 0.327 showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 9th year. Lag 10 which had cross correlation 0.34 showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 10th year.
Lag -1 which had 0.403 cross correlation showed that year 0 (current year) U.S. Dollar in PKR had an association with Gold prices in PKR of last year. Lag -2 which had 0.23 cross correlation showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 2nd last year. Lag -3 which had 0.244 cross correlation showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 3rd last year. Lag -4 which had 0.056 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 4th last year. Lag -5 which had 0.092 cross correlation showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 5th last year. Lag -6 which had 0.403 cross correlation showed that current year U.S. Dollar in PKR had an association with Gold prices in PKR of 6th last year. Lag -7 which had 0.07 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 7th last year. Lag -8 which had 0.022 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 8th last year. Lag -8 which had 0.022 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 9th last year. Lag -9 which had -0.03 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 9th last year. Lag -10 which had 0.0 cross correlation showed that current year U.S. Dollar in PKR had no association with Gold prices in PKR of 10th last year.
If it was to summed up then the Current year at lag 0, the U.S. Dollar in PKR had an association with Gold price in PKR at 1 year after (lag 1), 1 year back (lag -1), 2 year back (lag -2), and 3 year back (lag -3), and then no association till lag 6 and then positive association till lag 10.
CONCLUSION AND DISCUSSIONS
The study investigated cross correlation analysis on the U.S. Dollar in PKR and Gold Price in PKR. The Granger’s Causality Test was used to see the causal relation between the variable among each other and the Cross Correlations test was used to check the degree to which both the variable were correlated. The purpose of the study was to investigate the cross correlation between gold price and U.S. Dollar. The study encompassed data for 5 decades (i.e. 1957 – 2009).
Grangers Causality Tests suggested that variables (Gold Price in PKR & Exchange Rate: U.S. dollar in PKR) were found with strong bilateral relationship which means that the variables both caused each other.
Cross Correlation suggested that U.S. Dollar in PKR were significantly correlated overtime with Gold Price in PKR. And considering previous year it was found non-significantly associated. A close relationship exist between U.S. dollar in PKR and Gold price in PKR, as there was no such lag in which these were negatively associated.
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