Business Forecasting
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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)
Naive
0.0079280
0.0000827
0.0082559
0.0000757
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.
Naive
0.00793
0.000082670
0.00826
0.000075706
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
0.9279
Naive Model
0.9154
SES (alpha 0.4)
0.9241
SES (alpha 0.399756)
0.9235
Table 1.23- See Appendix 1.1-1.4
iv) Evaluate the forecasting performance of all models between 25/03/08 to 28/03/08 using your forecasts from iii and the exchange rate data between 25th March and 28th March (Do not update the forecasts with the new data.
Summary
0.0102
0.00012046
SES(0.4)
0.0063
0.00005725
NAIVE
0.0043
0.00002297
SES(0.399756
0.0058
0.00005051
Table 1.4- see appendix 1.5
Evaluating the performance of the four models using two error criteria Mean Absolute Error (MAE) and Mean Squared Error (MSE) suggests that the naive model is superior to all three models, with the naive model having an MAE of 0.0043 and an MSE of 0.00002297. This is followed by the SES model (alpha 0.399756), then the SES (alpha 0.4) model and lastly the MA5 model as seen in table 1.4.
However, this is contradictory to what was found in the previous question where the MA5 was considered the best predictor. The new finding is due to the new data being introduced into the model and may be due to the observation found in Graph 1.2 that residuals are not random for the 5MA model.
v) Using all the available data (up until 28th March) and on the basis of your answers above comment on the adequacy of the above forecast models. Which method, if any of these, would you prefer to predict the exchange rate for Monday 31st. (You may if you wish, nominate other methods or modifications to the above models that you feel will lead to better forecasts)