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Correlation Case One
| In the following calculations, we all use data after taking natural logarithm except for interest rates. |
| |
| (a) | |
| Correlation of spot exchange rate and Aust. MS is: – (for example, this uses data of “log of S(AUD/NZD)” and “log of Aust. MS”, all the following means the same way) |
| 0.461763 | |
| |
| Correlation of spot exchange rate and NZ MS is: |
| 0.529167 | |
| |
| Correlation of spot exchange rate and Aust. GDP is: |
| 0.495649 | |
| |
| Correlation of spot exchange rate and NZ GDP is: |
| 0.509683 | |
| |
| Correlation of spot exchange rate and Aust. IR is: |
| -0.48547 | |
| |
| Correlation of spot exchange rate and NZ IR is: |
| -0.44792 | |
| |
| So we could see the strongest correlation is the one of spot exchange rate and NZ MS, which is 0.529167, a positive correlation. |
| So NZ MS is our “PREDICTOR”. |
(b)
| Mean of log of spot exchange rate: |
| -0.19909 |
| Median of log of spot exchange rate: |
| -0.20046 |
| Mode of log of spot exchange rate: |
| #N/A |
Mean is the arithmetic average of the data; and median is the number which positions in the middle of the data, which means 50% of the data are below median and another 50% of the data are higher than the median; and mode refers to the number which appears most frequently in the data. And there is no mode in this data set.
The value of mean is -0.19909, which is just a little higher than the median which is -0.20046. I think mean is the most appropriate measure of average here because there isn’t any extreme value in the data set.
(c)
The minimum of the log of spot exchange rate is -0.55644, and the maximum of the log of spot exchange rate is -0.04051, so I chose the range -0.56 to -0.01 to draw the histogram.
Histogram of log of spot exchange rate:
| Variance: |
| 0.008038205 |
| Skewness: |
| -0.99690259 |
| Kurtosis: |
| 2.28480724 |
As calculated in question (b), the mean is close but not equal to median, so this data is not symmetric. And this is further demonstrated by the value of skewness, which is -0.9969, and which is not equal to 0. This is because if the data is symmetric, its skewness should be equal to 0.
If the data follows a normal distribution, the value of its kurtosis must be equal to 3. But now the value of kurtosis is 2.2848, which indicates the data does not follow a normal distribution.
So based on the above results, the log of spot exchange rate does not have a normal distribution.
(d)
- The level of the New Zealand money supply is our “PREDICTOR” as it has the strongest correlation with spot exchange rate.
- And mean is the most appropriate average for the log of spot exchange rate.
- Also the log of spot exchange rate does not have a normal distribution.