As mentioned in the study, there have been so many studies for understanding the relationship between gold and USD. Here in this study, we will try to find the correlation of USD and gold by using their TL based values. These studies should be also conducted regarding the time series studies but here we will be focused on standard regression analysis.
Aim of the Reserach
The aim of the research is finding the relationship between the prices of gold and USD in order to lead the investors to better financial decisions on these investment instruments.
Scope of the Reserach
The data set has been extracted for the period covering 1990 to 2009.
Data of the Reserach
The data have been extracted from TCMB (Central Bank of Turkey) website.
The Methodology and the Software Used
Correlations analysis and the simple regression analysis have been used to determine the relation between two variables.
SPSS 15.0 has been used to analyse the data.
We have assumed that the dependent variable is gold (y) and the independent variable is USD (x). The linear regression equation is supposed to be:
y = a + b x
We will try to show if gold prices have been affected from USD prices. The data have been entered to
SPSS with linear regression method. The following assumptions of linear regression have been analysed:
- Independence of Error Terms: Successive residuals are not correlated. If they are correlated, it is known as autocorrelation.
- Homoscedasticity: The variance of the error terms is constant for each value of x,
- Multicollinearity: There is no relation between the independent variables (applicaple only in the multi linear regression models)
- Normally Distributed Error Terms: The error terms follow the normal distribution
For autocorrelation we have analysed the durbin watson statistics from the following output. The relevant statistics is should be around 1.5-2.5 in order to show that there is no autocorrelation however, it is very much smaller then the lower cap. This shows that there is autocorrelation. If we had only looked at the R value (correlation coefficient) we wolud have concluded that the correlations is high between these variables. But due to the high autocorrelation the R is not reflecting the true correlation.
The following figure also shows the autocorrelation. As the value of the gold increases the values of the residuals increase.
Therefore, we need to make transformations on y (gold) and x (USD) variables by using the following methodology.
ytrans = yt – ρ yt-1
xtrans = xt – ρ xt-1
ρ has been calculated to be 1 (very strong autocorrelation) and after all of these transformations the following table is handed.
After understanding that there will not be autocorrelation in the following linear regression equation, we will try to analyse Homoscedasticity.
Trans_y = a + b Trans_x
For understanding homoscedasticity, we need to look at the spearman correlation between the independent variable and the absolute value of the error terms. According to the following table, the spearman correlation is very small which tells us that there is no correlation between the absolute value of the errors and the independent variable (trans_x)
The third assumption is that there is no multicollinearity but since this is applicaple only in the multi linear regression models we don’t need to analyse this.
The last assumption is the normal distribution of the errors. We will try to calculate the skewness and kurtosis values in order to measure the normality. The figures are showsn as follows:
Std. Error of Skewness
Std. Error of Kurtosis
The ratios of Skewness to its standard error and Kurtosis to its standard error are analysed. The ratios are 2.32 and 33.12 respectively. Since both of them are higher than 2 we can say that the distribution is not normal. Therefore another transformation should be applied on the data.
After making different transformations we have concluded on the logarithmic transformation. The transformed variables have been transformed again by logarithma. Then the equation becomes:
Log(Trans_y) = a + b log(Trans_x)
Afterwards, the normality again was not satisfied. Due to this we have put some of the data (outliers) out of the analysis since they were increasing the kurtosis and skewness. These data are as follows: July97, Aug00, Feb01, Jan03, Jun04, Sep04, Apr05, Nov05, Nov06, Feb08, Marc09 and Oct09.
Afterwards, the distribution becomes more normal.
The other tables are as follows for the equaiton Log(Trans_y) = a + b log(Trans_x)
Very high and positive correlation (92.2%) has been found as follows.
According to the following table the durbin watson stat seems to be fine. Furthermore, the following polts sho that there is no autocorrelation.
According to the following table the significance level is 0% which shows that the model explains the relation between two variables.
Sum of Squares
a Predictors: (Constant), logtransX
b Dependent Variable: logtransY
The coefficients show that the equaiton should be:
Log(Trans_y) = 0.844 + 0.910 log(Trans_x)
The significance of the coefficients are good enough.