Analysis of Time Series

3 Analysis of Time Series In the period from 1720 to 2005, the Baltic Sea was completely covered by ice for 16 winter seasons 4 times in the eighteenth century (1740, 

Looking at the period from 1720 to 2005, we observed a trend toward milder ice coverage seasons. In 1756-1805, the average maximum extent of ice coverage was 247 000 km , in 1856-1905 it was 297 000 krir, and in 1956-2005 it was 186 000 km. The average maximum extent of ice coverage thus has decreased by 61 000 km in two hundred years and is now only 75% of what it used to be two hundred years ago. The same trend was also found in air temperatures the average air temperature from December to March in Stockholm in the period from 1756 to 1805 was —4°C, from 1856 to 1905 was —2.5°C, and from 1956 to 2005 was — 1.3°C. In two hundred years, the mean temperature has risen by 2.1 °C. 

Looking closely at the 50-year periods, we found that on average the ice seasons became milder until the first part of the twentieth century. However, there has been no major change in the average ice extent in the course of the twentieth century (Fig. 8.13). 

The mildest decadal averages in the period from 1720 to 1990 were found for the 1930s and 1990s, with an ice coverage of 150 000 km. This was followed by a group of eight 

FIGURE 8.13 Average maximum extent of ice coverage in the Baltic Sea in 50-year averages, and average air temperature from December to March in Stockholm, 1756-2005. 

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Chatfield C (1989) The analysis of time series. An introduction. Chapman Hill, London, 4 th edn... 

Single value charts are only used for special purposes, e.g. as original value chard for the determination of warning and control limits or, for data analysis of time series (Shumway [1988] Montgomery et al. [1990]). All the other types of charts are used relatively often and have their special advantages (Besterfield [1979] Montgomery [1985] Wheeler and Chambers [1990]). 

Anderson, T.W. (1971). The Statistical Analysis of Time Series. Wiley, New York. 

Bloomfield, P. Fourier Analysis of Time Series. An Introduction, John Wiley and Sons, New York 1976... 

Garcia-Barron L. and Pita M. F. (2004). Stochastic analysis of time series of temperatures in the south-west of the Iberian Peninsula. Atmosfera, 17(4), 225-244. 

Chatfield, C. Analyse von Zeitreihen, BSB B.G. Teubner Verlagsges., Leipzig, 1982 Chatfield, C. The Analysis of Time Series An Introduction, 4th Ed., Chapman and Hall, London, 1989 Fomby, T.B., Hill, R.C., Johnson, R. Advanced Econometric Methods, Springer, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1984... 

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

Chatfield, C. The Analysis of Time Series An Introduction, 4th Ed., Chapman and Hall, London, 1989... 

Stieb DM, Judek S, Burnett RT (2002) Meta-analysis of time-series studies of air pollution and mortality Effects of gases and particles and the influence of causes of death, age, and season. J Air Waste Manage Assoc, 52 470-484. 

In a fashion similar to the discussion presented on organic chemicals, Baas et al. (2007) applied the 1-compartment model without TK interactions for the analysis of-time series survival data for the springtail Folsomia Candida exposed to binary mixtures of heavy metals. It must be stressed that no internal concentrations were measured in these experiments instead, the toxicokinetics parameters were solely determined from the survival pattern in time. In this case, the toxicity data were well described without assuming interactions, which stresses that even though we know that interactions on toxicokinetics can occur, this does not mean that they will significantly influence toxicity for every metal mixture in each organism. 

J. R. Mansfield et al., Fuzzy C-Means Clustering and Principal Component Analysis of Time Series from Near-Infrared Imaging of Forearm Ischemia, Computerized Med. Imaging and Graphics, 21(5), 299 (1997). 

N. Scafetta and B.J. West, Multiscale Comparative Analysis of Time Series and a Discussion on Earthquake Conversations in California. Phys. Rev. Lett. 92, 138501 (2004). 

The convolution defined in (4.2.1) is a linear operation applied to the input function x(t). Nonlinear systems transform the input signal into the output signal in a nonlinear fashion. A general nonlinear transformation can be described by the Volterra series. It forms the basis for the theory of weakly nonlinear and time-invariant systems [Marl, Schl] and for general analysis of time series [Kanl, Pril]. In quantum mechanics, the Volterra series corresponds to time-dependent perturbation theory, and in optics it leads to the definition of nonlinear susceptibilities [Bliil]. 

Ruelle D. (1989). Chaotic evolution and strange attractors the statistical analysis of time series for deterministic nonlinear systems. Cambridge University Press, Cambridge, U.K. 

D. Permann and I. Hamilton, Wavelet Analysis of Time Series for the Duffing Oscillator The Detection of Order Within Chaos, Physical Review Letters, 69 (1992), 2607-2610. 

Tukey, J. W. In Spectral Analysis of Time Series Harris, B., Ed. John Wiley and Sons New York, 1967 p 25. 

Bloomfield, P. Fourier Analysis of Time Series An Introduction John Wiley and Sons New York, 1976 Chapter 6. Chambers, J. M. Cleveland, W. S. Kleiner, B. Tukey, P. A. Graphical Methods for Data Analysis Wadsworth International Group Belmont, California, 1983 Chapter 3. 

Chatfield, C. (1975). The Analysis of Time Series Theory and Practice, 2nd ed. Halsted Press, New York. 

Anderson HR, Atkinson RW, Peacock J et al (2004) Meta-analysis of time-series studies and panel studies of particulate matter (PM) and ozone (O3). Report of a WHO task group. WHO Regional Office for Europe, Copenhagen... 

The residts of the phase-space analysis of time-series data for capillary pressure for one of the tests show that the time intervals (x) between pressure spikes (pulses) can be described using a sinq>le exponential equation, given as a difference equation by ... 

Aldiough direct measurements of variables characterizing (he individual flow and chemical transport processes under field condidons are not technically feasible, their cumulative effect can be characterized by the phase-space analysis of time-series data for the infiltration and outflow rates, capillary pressure, and dripping-water frequency. The tune-series of low-frequency fluctuadons (assumed to represent intrafracture flow) are described by three-dimensional attractors similar to those fi m die sohidon of the Kuramoto-Sivashinsky equadon. These attractoia demonstrate die stretching and folding of fluid elements, followed by diffusion. 

Chatfield C (2004) The analysis of time series an introduction, 6th edn. Chapman and Hall/CRC,... 

Semi-automatic software These are moderately priced but they require the user to have some basic knowledge of forecasting principles and fechniques. Here, fhe user has to select an appropriate forecasting technique based on the analysis of time series data. The software will then compute the optimal parameters for the chosen method using some measure of forecasf error. It also gives the forecasts and all the statistics, such as MAD, MAPE, MSE, Bias, etc. The software makes no recommendation as to which forecasting technique is appropriate for the given data. 

For the analysis of time series models, two concepts need to be introduced causality and invertibility. A process is said to be causal, if and only if, the current value of the process can be determined solely using past or current values of the process. This means that no unavailable, future values of the process are required. A process is said to be causal if and only if all roots of the denominator (i.e. the A-polynomials) lie inside the unit circle in the complex domain, that is, z < 1. Under such circumstances, a causal process is also stationary. Furthermore, for a causal process, the infinite-order moving-average model will converge to a finite value. 

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