Principles of Statistics In-Module Assessment - Coursework Example

The period over which the exchange rate is observed is January, 1973 to January 2013. Annual observations are used; for each year, a single value of the exchange rate is observed. Thus, there are 43 annual observations on the exchange rate in the sample of data. Before turning to the specific characteristics of the series, it may be useful to note the significance of forecasting foreign exchange rates. For any economy that is open to international trade, the foreign exchange rates play important roles in deciding policies governing most of the important macro-economic variables in the economy.

Particularly since the settlement of most international transactions occur within a short future horizon, the exchange rates likely to be applicable at the time of settlement assumes importance. The magnitude of the associated cash flows in terms of the domestic currency are evaluated by using foreign currency conversions. And these conversions are obtained by denominating the domestic currency by the foreign currency of the trade partner through the foreign exchange rate for the pair of countries (Taylor 1995). . Since the natural logarithm is a monotonic transformation, all dynamic properties of the series are preserved, only the scale of the magnitude is smaller.

Figure 1: The exchange rate between the Japanese Yen and the US Dollar The first and foremost point to be noted is that the price of the Dollar has exhibited a downward trend over the time horizon under consideration. Starting at slightly above 5.8 in 1971, the value of the series has ended at around 4.6 in 2013. However, the series has not continuously declined. It has exhibited periods of upward movements as well as downward movements. The length and magnitude of the downward movements however, dominate the trend.

As a result, the overall trend of the series is that of a decline. A closer look reveals that the series exhibits a particular persistence: a downward movement continues for a few years as does an upward movement. That is, once a dip starts, it persists for a few years. Similarly, once an upward swing starts, it seems to persist for a few years. This pattern of persistence will become important in the forecasting phase. It should also be noted that the average length of the persistence of upswings is visibly smaller than the average length of the downswings.

This pattern is particularly clear for the years after 1985. The other pattern worthy of note is that the overall magnitude of increases in the exchange rate over periods of appreciation is smaller than the observed magnitudes of decline in the exchange rate during periods of decreases. Barring the years between 1977 and 1983, this holds true for every period of decline and period of increase. Therefore, the observed pattern of decline in the Japanese price of the US dollar is explained by two