Business Forecasting

i)

Graph1.1

ii)

The time series exhibits a fair degree of volatility or randomness.The underlying level of the series over the given time period appears to be well contained in an underlying band of 0.9250-0.9450. The level of this time series also appears constant over the entire time series and hence a horizontal data pattern is observed.

Since the time series is relatively horizontal with trend and seasonality not apparent in this time series, then moving average and simple exponential smoothing would be possible predictors for future days USD/AUD exchange rates. It is important to note that although it would appear that the data is not strictly horizontal, there is no systematic tendency to a change in level at least with the data that is presented.

Note: Trend, seasonality,cyclical- not apparent in this time series, more observations may be needed.

The factors which are likely to have influenced the pattern observed is the supply/demand for the AUD which is affected by rate of inflation in each country, interest rates, weather each country has run a current account deficit (imports/exports), public debt and finally political and economic predictability. The United State’s negative economic state have continued over the time series thereby making the pricing of the dollar relatively stable hence the horizontal pattern which is observed. 0.0000827 0.00694000

iii)

MAE MSE

Naive 0.0079280 0.0000827

SES 0.0082559 0.0000757

5MA 0.0069400 0.0000733

SESnew 0.0082183 0.0000754

Table 1.2

Looking at the MAE, MSE results, it appears that the 5 period moving average outperforms the Naive model and the SES model for this time series. The MAE and MSE criterion suggest that the 5 period MA is the “best” predictor, as it has the lowest error rate. See table 1.2

Graph 1.2

A quick analysis of the residuals for the MA5 model suggest that the residuals are not evenly spread out between 0 and 1 (not symmetric) and that the mean is not zero, which suggests that although the error functions for MA5 may give us the indication that this will be the best method to predict exchange rates, the analysis of residuals suggests that they are not random and hence the suitability of the 5MA is limited.

Graph 1.3

A quick analysis of the SES residuals reveals that there are 10 observations above zero and 9 below- which means the residuals are fairly symmetrical, with no pattern and that the mean (based on alpha of 0.4) is 0.00005, which is close to zero. Hence making it plausible to suggest that the data is unbiased and random.

Graph 1.4

Examination of the data suggests a constant level with random fluctuations around that level which suggest residuals are data and that this may be the right model to use despite 5MA having lower MAE and MSE scores.

Graph 1.5

However if we use SOLVER to find the optimum level of alpha for SES we come up with a new alpha level of 0.399756. The effect of this new alpha on the MSE for the SES model would be 0.000075441 hence indicating that whilst even using an optimised alpha for the SES model. The 5MA is at this stage still the one to be the best predictor of exchange rates. It is important to note that with the new optimised alpha the new forecast exchange rate will be 0.9235. The table 1.6 represents residuals are fairly symmetrical and appears unbiased and random.

MAE MSE

Naive 0.00793 0.000082670

SES 0.00826 0.000075706

5MA 0.00694 0.000073277

SESnew 0.00822 0.000075440

Table 1.3

In order the 5MA appears the best predictor who has the lowest MAE anbd MSE scores, followed by SES (0.399756) based on MSE score, then the SES (0.4) followed by the Naive model.

Forecasts for next 4 periods:

Model Forecasted Exchange Rate

MA5 0.9279

Naive