The data provided consisted of the future closing prices of crude oil as expired on Jan, Feb & March 2006 respectively in three worksheets starting in Oct, Nov & Dec; the days it was introduced in the market. The assignment is to forecast the closing prices of these data using Time Series Forecasting (TSFS) for the next trading days.
Model Selection Criteria:
The model selection criteria used here is Root Mean Squared Error (RMSE) which is the squared sum of differences between the actual data and predicted data of regression; which is the default goodness-of-fit measure. For understanding the nature of the forecast, I have chosen here only the data for February to be run through TSFS.
The forecasts for February data set were written to output data set called WORK.FORECAST. This is a simple output format where the data set contains the time ID variable and the forecast variables and contains one observation per time period. Observations for earlier time periods contain actual values copied from the input data set; and the later observations contain the forecasts.
Figure 1 below shows the previous close price series which does not seem to have a trend. If you click on the high and low points, one sees that they occur randomly without indicating any nature of seasonality. Seasonality would have been observed had they occurred during particular week of the month, or during particular days of a week. If there were seasonality then, it can be modeled deterministically with seasonal dummies or via seasonal ARIMA models. Smoothing models can also incorporate trends and seasonality. There are 3 diagnostic tests that can be run for this:
• Log Transform Test
• Trend Test
• Seasonality Test
Figure 1: Previous Close Price – Damped Trend Exponential Model
The above model appears to be a good fit.
The p-value for unit root test results is as shown below in Figure 2:
Figure 2: Prediction error... [continues]
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