Edmonton Weather Data Series Example

Consider the case of a chemical engineer who is involved in the optimisation of a plastics plant on Refinery Row in Edmonton, Alberta, Canada. After analysing the available data, it was determined that the summer temperature had an overall effect on profitability of the plant. For this reason, it was desired to model the mean summer temperature so as to be able to predict the temperature in the future. 

After examining all the available weather data, the data set presented in Table 5.3 for Edmonton was compiled using original data from Environment Canada. Further information regarding this data set, including all the original data points, can be found in Appendix A5. The challenge is to use this data set to develop a model of the mean summer temperature. 

A time series plot of the mean summer temperature is shown in Fig. 5.1. In this example, the autocorrelation of the mean summer temperature will be determined. Also, the cross-correlation between the mean summer temperature and the mean spring temperature will be examined. The methods used to compute these plots can be found in either Chap. 7 for MATLAB or Chap. 8 for Excel . 

The autocorrelation plot is shown in Fig. 5.2, the partial autocorrelation plot in Fig. 5.3, and the cross-correlation between the mean summer and spring temperatures in Edmonton in Fig. 5.4. For the autocorrelation plot shown in Fig. 5.2, there are some salient features that need to be considered. Firstly, it can be noted that at a lag of zero, the autocorrelation is, as expected, 1. Secondly, it can be seen that all of the autocorrelations are located above the 95% confidence interval for significance. Note that the confidence intervals are equal to 2/a/121 = 0.18. This suggests that all of the observed correlations are significant. Finally, there seems to be a weak, but noticeable, 8-lag oscillation. 

The partial autocorrelation plot for the mean summer temperature in Edmonton, shown in Eig. 5.3, has the same format as the autocorrelation plot. Unlike in the autocorrelation plot, here, there are values located both inside and outside of the confidence region. A similar pattern to that previously observed can be seen here, that is, the values are significant at multiples of some constant. In this case, the significant partial autocorrelation values are located at lags of 1, 2, 3, and 8. This suggests a potential 2-year seasonal component (with values at 2, 4, 6, and 8). 

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