Applied Forecasting Methods
It is possible to include a trend in the estimation process since we can visually inspect the data graphically and identify the presence of trends within the particular period under our study. The trend in the estimation can also be statistically significant and show a more fitted estimation to the actual data.
However, trends cannot be included in financial data if the estimation equation is to be used for producing forecasts. Due to financial considerations the exchange rates movement in financial markets should be closest to a random walk. Hence, if trend is included and the forecast is predictable and accurate, the model will turn to be a money making machine. Anticipating such forecasts all market participants will behave in the same rational manner in the best of their own interest and will soon eliminate the arbitrage opportunity. Therefore, it is recommended not to include trend in any forecasting model for financial time series data and avoid pre-determining the direction of the market direction.
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The automatic forecasting software provides benefits to forecasters in the sense that it will minimize the bias that occurs when people interfere with judgments on forecasting issues. When human intervention is present, different subjective opinions will be presented, which in turn increases the bias that will occur, also resulting in errors in forecasting. Therefore using the automatic forecasting software, this human judgment and likelihood of bias is minimized or even eliminated.
Even though the automatic forecasting software has its benefits of eliminating bias that might occur with forecasters, using this software also has its disadvantages or costs. When using this software, we, as humans, are depending fully on the software doing the work for us. This means that we miss out on the way the forecasting is done and on the logic used behind the forecasting method. Becoming fully dependant on software doing a job automatically for us can also create errors, even though minimal, and if they occur, forecasters might not be able to notice because it is done for them without knowing the method used behind the forecasting. In addition, technology is not always proving to be the right solution for every job or every problem.
Using the automatic forecasting software is most useful to use when forecasters need to conduct common forecasting on something specific many times and it just becomes a matter of repeating the forecast using this software automatically. Another situation where the automatic forecasting software can be used is when forecasters want to make sure that the logic or method they used to conduct a forecast helped them get to a proper forecast. They can use the software and allow it to conduct the forecast for them as a reassurance that what they performed was correct. As we mentioned earlier, even though minimal, however, this software doesn't necessarily give the forecaster the 100% correct forecast due to technological errors that might occur, but it can act as a strong tool for forecasters.
After reading Ord and Lowe (1996), we confirm our answer to part (c), in which we mentioned that using the automatic forecasting software is most useful when the forecaster has to conduct many forecasts on a specific model. Instead of manually forecasting repeatedly, using the automatic software makes it a much easier job. Ord and Lowe mention the example of having to forecast thousands of inventories at a manufacturing plant (Ord & Lowe, 1996).
In addition, Ord and Lowe mention an advantage in using the automatic software, therefore, we would probably add to part (a) that another benefit to using automatic software to do the forecasting is that a detailed print out of the method used in conducting the forecast is an option given to the forecaster after the forecast is done. Therefore, after reading this part, we would make a slight alteration to part (b) on the costs of using the automatic software. We mentioned that the forecaster would not know the method used behind the forecasting done by the software whereas, the article assures that the detailed print out of the methods used is an option given to forecasters (Ord & Lowe, 1996).
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When (1 - Ls) operates on yt:
(1 - Ls) yt = yt - ytLs
= yt - yt-1s
= yt - yt-s
By differencing the process is made stationary, in the multiplicative ARIMA modeling the reduction to stationarity is an integral part of the model fitting technique and seasonal differencing deals with cases where the seasonal effect is fairly regular from year to year, and hence it appears regularly in seasonal models.
Stochastic seasonality is identified with both AR and, moving average (MA) terms at seasonal lags. If the AR coefficients at seasonal multiples are significant, or if the MA terms at seasonal lags are significant, then the series exhibits significant stochastic seasonality. On the other hand, the time series exhibits deterministic seasonality in mean if the null hypothesis about the vector of seasonal dummies is jointly equal to zero is rejected.
Accordingly, the appearance of (1 - L) in the model is stochastic as it has a root of one on the unit circle. Similarly, the (1 - Ls) has all the seasonal lags on the unit circle, whether 4 lags for quarterly seasons or 12 lags for monthly seasons in the model.
By substituting the expressions for and we can rearrange the equation as shown below:
By subtracting from both sides of the equation mentioned in part a above, we can show that can be written as a regression of on and as illustrated below:
If , then from part b above, the coefficient of = 0 which indicates that AR(2) process is really an AR(1) process in first differences, the AR(2) process has a unit root.
· Ord K, Lowe S (1996). “Automatic forecasting." American Statistician, 50(1), 88-94.