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Statistical Analysis with t-test and f-test

In this Case Study, you will look at modelling the Australian dollar vis-á-vis the US dollar exchange rate, using a conventional monetary model. The data you will use is in the file called “The Monetary Model.xls”. This contains the following data: ‘S(AUD/USD)’ , which is the Australian dollar per US dollar exchange rate; ‘Aust. MS’ , which is the level of the Australian money supply; ‘US MS’ , which is the level of the US money supply; ‘Aust. GDP’ , which is a measure of Australian gross domestic product (GDP); ‘US GDP’ , which is a measure of US gross domestic product (GDP); ‘Aust. IR’ , which is a measure of short-term Australian interest rates, and ‘US IR’ , which is a measure of short-term US interest rates. Data on these variables were collected from the IMF’s International Financial Statistics database, and from the Reserve Bank of Australia’s website.

To begin the empirical analysis, make sure you take the natural logarithm of S(AUD/USD), Aust. MS, US MS, Aust. GDP, and US GDP. Leave the interest rate variables, Aust. IR and US IR, in their raw form. Also, use a level of significance of  = 0.05 for all tests in this study.

(a) Calculate the correlation between the spot exchange rate and all the other variables. Which variable has the strongest correlation with the exchange rate? I will call this variable “PREDICTOR” in the questions that follow.

(b) Calculate the mean, median and mode of the spot exchange rate. What is the difference between these types of “averages”? State what you think is the most appropriate average for this set of data, giving brief reasons for your answer.

(c) Draw a histogram of the spot exchange rate. Calculate the variance, measure of skewness and kurtosis. Compare the values of the median and mean. Do they indicate the data is symmetric, and is this confirmed by the value of the skewness? Comment on the value of kurtosis. Based on these results, say why you believe that the spot exchange rate does, or does not, have a normal distribution.

(d) Calculate the mean and variance of the PREDICTOR for the time period 1984:1 to 1992:4, and then for the period 1993:1 to 2013:4 separately. Using these figures, calculate the variance of the difference between the sample means for the period 1984:1 to 1992:4, and then for the period 1993:1 to 2013:4 (You can assume that the covariance is zero). In the first quarter of 1993, the Reserve Bank of Australia adopted an inflation targeting regime. Test to see whether the adoption of an inflation targeting regime has had any impact on PREDICTOR, that is, test to see whether the difference is significantly different from zero. Under the conditions discussed in part (e), the standardised value of the difference will have a Student’s-t distribution with n-2 degrees of freedom (Subtract 1 for each sample mean calculated).

(e) The test in part (d) is only reliable if both samples are large, or if a sample is small, it has a normal distribution. Do you think the test in part (d) is reliable? Give brief reasons for your answer.

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Category: Sample Questions