Time series plot

The first step in the analysis of time series x(t) is always to draw a plot  

Plotting gives a general idea about the shape of the time series. It may give visual information about any periodicity, trends, fluctuation, and outliers. It is, furthermore, 

The following time series analytical examinations will only deal with the time series at the feeder stream gauge at Lawitz and the drinking water reservoir at Weida. This is the only point of interest for practical conclusions in relation to the supply of humans with drinking water. 

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Time series plots give a useful overview of the processes studied. However, in order to compare different simulations to one another or to compare the simulation to experimental results it is necessary to calculate average values and measure fluctuations. The most common average is the root-mean-square (rms) average, which is given by the second moment of the distribution. 

When experimental data are collected over time or distance there is always a chance of having autocorrelated residuals. Box et al. (1994) provide an extensive treatment of correlated disturbances in discrete time models. The structure of the disturbance term is often moving average or autoregressive models. Detection of autocorrelation in the residuals can be established either from a time series plot of the residuals versus time (or experiment number) or from a lag plot. If we can see a pattern in the residuals over time, it probably means that there is correlation between the disturbances. 

Figure 12.29 Time-series plot of the y-residuals obtained from a PLS model developed using the process spectroscopy calibration data set (solid line), after removal of sample and variable outliers as discussed earlier. The measured y-values (dashed line) are also provided for reference.

Figure 12.33 shows a time-series plot of the reduced T and Q values of an analyzer-specific PCA health monitor for an actual PAT application, before and after a calibration update. There are several interesting... 

Figure 12.33 Time series plot of reduced V and Q statistics associated with the application of an analyzer-specific PCA model to on-line analyzer data - covering a period of approximately 4 months.

Comparison of the depositional fluxes shows that diatoms were the most important particle component transporting P to the sediment surface, accounting for 50-55% of the flux (Table II). Terrigenous material and calcite were also important transport vectors. Deposition varied markedly with season, as shown by the time series plot of the major particle components (Figure 13). The total P flux calculated by using the particle components model agreed with the flux measured by sediment traps (157-227 versus 185 mg/m2). The close agreement indicated that the major particle vectors were represented and associated P concentrations were accurately quantified. 

The time series plots of the nitrate concentrations of the feeder stream, the storage reservoir in Zeulenroda and the storage reservoir in Weida (Fig. 6-2) show periodic fluctuations with maxima near, or higher than, the limit of 50 mg L The time axes in all following figures are the x-axes with monthly scaling for every year. The notation 1.80 means January in the year 1980. 

Feeder stream —Zeulenroda storage reservoir —Weida storage reservoir Fig. 6-2. Time series plot of the feeder stream and the storage reservoirs at Zeulenroda and at Weida... 

Figure 12.6. Time-series plot of DOC concentrations in different hydrologic compartments of the two sites. Results are plotted within the same 12-month period only for illustrative purposes. Campina water was acmally monitored during the year following monitoring at Barro Branco. The annual occurrence of rainy and dry seasons is shown. Crosses mark sample dates. From McClain et al.(1997).

Fig. 4.8. A time series plot of the numerically estimated total potential energy Et of the spring-block system for...

Figure 4 Mg/Ca of different planktonic foraminifera from a Bermuda sediment trap time series, plotted versus calcification temperatures calculated from the oxygen isotopic composition of the shells (Anand et aL, 2003) (reproduced by permission of American Geophysical Union from Paleoceanography 2003, 18, 1050). The aggregate fit to all the data in the plot is Mg/Ca = 0.38 exp(0.09T), very similar to relationships derived from culturing and core-top studies.

Figure 4. Time-series plot of sea-salt aerosol concentration and local wind speed from Julian Day 41 to Julian Day 47, 1981.

Simple time-series plots of water or air quality can reveal a great deal of information (Ward and Loftis, 1986), such as ... 

Figure 15. Time-series plots of vent fluid variability at the Aa vent, 9-10°N EPR.

Spectrum Plots Time-Series Plots Converting Measured... 

Exhibit 19.11 presents Bloomberg s World Swap screen which presents swap spreads for various countries around the world for June 27, 2003. In this screen, the tenor of the swaps in this screen is five years as can be seen in the box labeled Maturity in the upper left-hand corner. Among the other choices available, a user can choose to display swap rates rather than spreads. Exhibit 19.12 is a time series plot obtained from Bloomberg for daily values of the 5-year euro swap spread (in basis points) for the period June 27, 2002 to June 27, 2003. 

To verify earlier observations and to serve as a base for the development of control methods, a correlation analysis was carried out with process data from one year of operation. Variables included were measurements of flow, temperature and pressure, origins of the concentrates in the feed mix, chemical analyses of feed and product compositions and grain size distribution of the product. In addition, some calculated quantities used in the furnace operation were also included. The study was carried out using linear correlation analysis and by time series plots of selected variables. Although the bed stability was the main focus of... 

Fig. 4.6 (Top) Normal probability plot of the residuals and (bottom) time series plot of the residuals with the different replicates clearly shown...

On the other hand, the time series plot of the residuals still seems to show some weird behaviour between the two different replicates. Now it seems to suggest that one replicate is different from the other. On the other hand, the coefficient of regression is now 0.91, and the model is significant given the F-test. On the whole, it would suggest that the model obtained by reducing... 

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 . 

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

The integrating model is often also called the random-walk model, since the time series plot of the data can resemble a person walking randomly along the... 

Fig. 5.5 (Left) Time series plot of the given moving-avtaage process and (right) autocorrelation plot for the same process...

Fig. 5.8 (Top) Time series plot, (middle) autocorrelation plot, and (bottom) partial autocorrelation plot for (left) integrating and (right) AR(1) with a = —0.98 processes...

Fig. 7.1 Linear regression example MATLAB plots of the (top, left) normal probability plot of the residuals, (top, centre) residuals as a function of y, (top, right) residuals as a function of the first regressor, Xj, (bottom, left) residuals as a function of x, (bottom, centre) residuals as a function of y, and (bottom, right) a time series plot of the residuals...

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