Edmonton temperature

Consider the previously examined Edmonton temperature data series detailed in Sect. A5.1. For the purposes of this example, consider the problem of estimating a model for the mean summer temperature. The autocorrelation and the partial autocorrelation plots have already been shown and analysed previously (see Figs. 5.2 and 5.3). Using the results from there, obtain an initial model for the data. 

Consider the Edmonton temperature series that is fully described in Sect. A5.1. Plot the periodograms for the spring, summer, and winter mean temperature series. Also, plot the periodogram for the differenced summer temperature series. What are some of the salient features ... 

Fig. 5.19 Periodograms for (left) spring, middle) summer, and right) winter of the Edmonton temperature series...

Take the Edmonton temperature series and fit appropriate ARM A models to the winter, spring, fall, and annual mean temperatures. Be sure to examine the residuals and verify that the assumptions are met. 

Using the Kalman filter, develop a model for the Edmonton temperature series. 

Take the Edmonton temperature series from Sect. D.l Edmontrai Weather Data Series (1882-2002) and model the winter temperature as a function of the other available temperatures. Validate the model. 

The design of a multi-purpose plant for the continuous extraction of liquids with supercritical fluids is presented. To provide flexibility in order to treat different feedstocks, a modular concept was developed based on experience gained in the operation of bench-scale and pilot plants. Four test systems were chosen in order to determine the proper dimensions for the equipment. Based on experimental data, e.g. measurements of flooding points and maximum flows for various column internals, the design pressure and temperature and heat exchange requirements were determined. The plant was built by a German manufacturer and was operated successfully by a Canadian company in Edmonton, Alberta. 

Sexually mature male round gobies were collected by hook and line and bottom trawl between May and August in 1995 and 1996 from the St. Clair and Detroit Rivers (Windsor, Ontario). The fish were shipped by air to Edmonton (Alberta, Canada), where they were maintained under constant photoperiod (16L 8D) in 70L holding aquaria (3—5 fish per aquarium) provided with flowing dechlorinated tapwater at temperatures roughly equivalent to those in the field (9—18°C from winter to summer). Fish were fed a variety of live, frozen and flake food ad libitum. Aquaria contained gravel substrate, an airstone, artificial weed cover and plastic pipes for shelter. 

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. 

Fig. 5.1 Time series plot of the mean summer temperature in Edmonton...

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). 

Fig. 5.2 Autocorrelation plot for the mean summer temperature in Edmonton. The thick dashed lines show the 95% confidence intervals for the given data set...

Example 5.11 Modelling the Mean Summer Temperature in Edmonton... 

Example 5.12 Validating the Initial Mean Summer Temperature in Edmonton Model... 

Having considered multiple different methods and approaches to modelling time series, it is now necessary to apply these methods to the problem at hand estimating the mean summer temperature in Edmonton. The data set is described in Sect. 5.1.3 and preliminary results have already been presented (see Example 5.11, Example 5.12, and Example 5.15). 

From an initial attempt to model the mean summer temperature in Edmonton as an ARMA(8,8) process, the parameter estimates and their standard deviatimi were determined as... 

The raw data for the Edmonton Weather Data Series are presented in Table 5.3. This data set has been compiled using daily temperature values available from Environment Canada. The values are obtained by combining the daily temperature values from two nearby weather stations Edmonton (C3012195) from 1880 to 1943 and Edmonton City Centre (C3012208) from 1937 to 2002. Since both locations are close to each other, the two data series were combined into a single set with the change over year being 1940 up until that year, the data were taken from the Edmonton weather station, while from January 1st, 1940, the data were taken from... 

Fig. 5.4 Cross-correlation between the mean summer temperature (j) and the mean spring temperature (x) in Edmonton.

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