1. UNR * STAT 758 * Fall 2014

4. William Playfair (1759-1823), a Scottish engineer and political economist, is generally viewed as the inventor of line plots, bar chart, and pie chart. His The Commercial and Political Atlas, published in 1786, contained a number of interesting time-series charts. Playfair: "On inspecting any one of these Charts attentively, a sufficiently distinct impression will be made, to remain unimpaired for a considerable time, and the idea which does remain will be simple and complete, at once including the duration and the amount." http://www.math.yorku.ca/SCS/Gallery/ Balance of Trade

5. William Playfair (1759-1823) http://www.math.yorku.ca/SCS/Gallery/

6. William Playfair (1759-1823), A Letter on our Agricultural Disaster, 1821. http://www.math.yorku.ca/SCS/Gallery/ Prices, wages, and reigns

8. Jan Ingenhousz (December 8, 1730 – September 7, 1799), a British physiologist, botanist and physicist. First observed BM, 1765. Robert Brown (December 21, 1773 – June 10, 1858), a British botanist. Observed and studied BM, 1828. Albert Einstein (March 14, 1879 – April 18, 1955), a German-born theoretical physicist. Mathematical and physical description of BM, 1900. Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 - April 28, 1946), a French mathematician. Mathematical description of BM, 1900. Thorvald Nicolai Thiele (December 24, 1838 – September 26, 1910), a Danish astronomer, actuary, and mathematician. First mathematical description of BM, 1880. Fat in milk

9. X Y X-coordinate of a chosen particle: 1-D Brownian motion 2-D Brownian motion

11. http://www.math.yorku.ca/SCS/Gallery/ Simple pendulum Oscillatory motion is widely observed in Astronomy Physics Mechanics Electricity Biology Human behavior Socio-economics Climate and geophysics

12. Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830), a French mathematician and physicist Fourier decomposition of a periodic identity function http://en.wikipedia.org/wiki/Fourier_series

13. Pure oscillations

14. Oscillations with superposed random fluctuations, sd=0.05

15. Oscillations with superposed random fluctuations, sd=0.1

16. Oscillations with superposed random fluctuations, sd=0.5

17. Oscillations with superposed random fluctuations, sd=2

18. Observations = + Up to 1925 or thereabouts, there was a common belief that…

20. George Udny Yule (18 Feb 1871, Scotland -- 26 June 1951, England)

21. G. Udny Yule, "On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers", Philosophical Transactions of the Royal Society of London, Ser. A, Vol. 226 (1927), pp. 267–298.

22. G. Udny Yule, "On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers", Philosophical Transactions of the Royal Society of London, Ser. A, Vol. 226 (1927), pp. 267–298. Observations can not be explained as oscillatory behavior plus noise; they are affected not by superposed fluctuations, but by true disturbances, which are incorporated into the future behavior of the system

23. http://www.junglephotos.com/galapagos/satimages/othersatimages/elnino.shtml

25. G. Udny Yule, "On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers", Philosophical Transactions of the Royal Society of London, Ser. A, Vol. 226 (1927), pp. 267–298. http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-56031

26. Describe behavior of the series (construct a mathematical model) Explain behavior of the system that produced the series (construct a physical model) Forecast (predict) the system behavior using its model Control the system using its forecast behavior

27. Norbert Wiener (1894-1964), USA Founder of cybernetics and information theory Andrei Kolmogorov (1903-1987), Russia Founder of modern theory of probability (1933)

28. Timet t+  Processis predicted by with forward lag 

29. Processis predicted by with forward lag  General solution: conditional expectation For Markov Gaussianconditional expectation is a linear function of

30. Andrei Andreyevich Markov (June 14, 1856 – July 20, 1922), a Russian mathematician. CandyLand Game: an example of Markov process Markov process: all information about the history of the process that will affect its future is included in the process current state.