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Time travel
Humans’ perception of space has commonly been embodied in the three-dimensional model of length width and depth. However, a fourth aspect comes into play from an individual’s journey from the cradle to the grave. This aspect is time. Time has a great impact on the existence of humans in space and is considered to be the most precious yet most perishable resource in life. This has since time memorial, stirred desires to be able to manipulate this fourth aspect in order to increase the periodical dominance of man over space. In 1985 H.G Wells published a work of fiction titled “The Time Machine” which introduced the concept of time travel.( Morris, Richard) This concept proposes that it is possible for man to move between two different points in time. However, Albert Einstein’s special theory of relativity laid foundation for the theoretical possibility of travelling through time. (“How Time Travel Will Work”) With time, time travel has developed from a mere fantasy to an actual projection of future capabilities. This has been seen through hefty investment in numerous experiments designed and executed by different physicists and scientists in an attempt to explore any future prospects in the application of time travel. These experiments, though not fully successful, have provided significant breakthroughs in man’s understanding of time and space. This research paper highlights an experiment to justify the hypothesis that time travel will most likely be part of the future.
The experiment documented in this research paper is based on Albert Einstein’s theory of special relativity. This theory involves the physics of bodies moving at the speed of light. At these speeds, Newton’s laws of motion need to be modified. (“Einstein’s Theory Passes a Space ‘Laboratory’ Test.”) This theory suggests that if a man was to travel away from his twin at a speed that is a similar to that of light and then returns some time later still at the speed of light he will find that his twin has aged more than him. This difference in time in relation to special relativity is known as time dilation. This research paper highlights two experiments carried out by Ricky K. C. Au, Katsumi Watanabe and Fuminori Ono. These experiments prove their hypothesis that the time dilation induced by the motion of an object is based on spatiotopic positions rather than retinotopic positions. (Ricky K. C. Au) Retinotopic motion involves the motion of the retina with no physical motion while spatiotophic motion involves physical motion of observers with no motion of the retina. This paper focuses more on their first experiment to indicate why the reality of time travel seems probable in the near future.
Their first experiment investigated time dilation under the motion of an object without any movement of the eyes. This experiment involved eleven paid observers from the University of Tokyo; eight of whom were females. One of the researchers, authors also participated voluntarily making a total of 12 observers. All the observers had normal or corrected vision. The stimuli used in this experiment were programmed in MATLAB and viewed on a CRT monitor at a rate of 100 Hz. These monitors had a resolution of 800 × 600 pixels and were controlled by a Windows XP operating system. The observers were asked to view the stimuli from a quiet room that was dimly lit and which was 60 cm away from the stimuli. On the monitor, all stimuli appeared white against a black background. The target on the screen was circular.
In each experiment, there was a stimulus and another stimulus to compare to it. These two were presented to the observers at separate intervals of time. At the beginning of each trial, a fixation stimulus was constantly at the center of the screen. Observers were asked to start the observation of the stimulus by pressing the space bar on the keyboard of the computer. After 1000 ms, the target stimulus appeared 4.5330 below for the duration of 1000 ms. After this period, a comparison stimulus was then presented to the observers for a random duration of 800-1200 ms. In the static state, the stimulus used for comparison appeared at 4.5330 above the point of fixation without any movement. On the motion, the target circle appeared at the same vertical distance above the point of fixation but moved horizontally to the left or right of the point of fixation at a constant speed of 11.334 degrees per second. A random variation of -0.136 0, 00 and +0.136 0 for the starting and ending positions of the moving stimulus. This was done so that the observer being tested would not become accustomed to the identical stimulus within the same duration of time. As a result of this change in position, the starting distances appeared to shift to the right and left of the point of fixation with variation of time in milliseconds.
After the comparison stimulus had been presented, the observer was asked to judge whether the comparison or reference stimulus had appeared for a longer duration of time by pressing the right arrow key (for the comparison stimulus) and the left arrow key (for the reference stimulus) on the keyboard of the computer. In this experiment the duration conditions were tested three times, the motion conditions were tested two times and the Starting-ending positions were tested three times. These were presented in a pseudorandom order with a total of 6 repetitions. This totaled up to 108 trials. This experiment took an average of ten to fifteen minutes to complete.
A control experiment was also set up to observe if the effect was as a result of novelty caused by the movement of the comparison stimulus. This control experiment involved a similar number of trials but the reference stimulus (at 1000 ms) was in constant motion across the monitor from 5.6670 to the left and right of the fixation. All of the observers performed the control or main experiment in a counter-balanced order with a 5-minute interval between the two experiments.
Results
The proportion of trials in which the duration of the target stimulus was thought to be longer than the duration of the reference stimulus was then analyzed for the moving and static condition, averaged for the dozen (observers) and plotted against the three durations tested.
Experiment 1 [(A) stationary reference; (B) moving reference control experiment]; error bars represent SEM. (Ricky K. C. Au)
INCLUDEPICTURE “http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3289113/bin/fpsyg-03-00058-g002.jpg” * MERGEFORMATINET
Duration at 800ms, 1000ms and 1200 ms and ANOVA with motion (static or moving) were each measured repeatedly within subject factors. This was done in reference to the stationary reference to study the effect of the motion of an object on the perceived duration of time. The results of this first experiment revealed significant main events of Duration [F (2, 22) =214.866, p<0.001] and motion [F (1, 11) = 15.939, p=0.002]. The overall product of motion and duration also produced a significant value [F (2, 22) = 6.149, p=0.008]
Post hoc paired sample tests for t revealed that the difference between the two conditions (static and motion) were significant at the time of the duration at 800 ms, but did not reach significant level at 1200 ms. The same ANOVA (motion ×duration) was also performed on the data of the moving control experiment. This showed significant main effects of duration and motion. The values for motion × duration for this data were also found to be significant. When Post hoc tests for t were conducted the result revealed significant differences between the static conditions and motion conditions at the presentation duration of 1200 ms but failed to produce significant values at less than 800 ms. There was marginally significant difference at the 1000ms duration of presentation.
Both the control and main experiments showed a similar trend of a longer perception of time when the object was in motion. The control experiment showed that the time dilation effect was based on change in motion without a play of novelty of the stimuli.
The scientists then conducted a second experiment to investigate time dilation under object motion with eye movement. Findings from this second experiment revealed that that the time dilation associated with the movement of an object depends on the motion of the object that has been perceived in the brain rather than the positional shift of the image that is projected in the retina of the observers.
Another concept that is being applied in present time travel experiment in Albert Einstein’s relation of physiology and physicality. Albert Einstein noted that when a boy sits next to a beautiful girl it feels like a minute but on his own it feels like an eternity. He proposed that this is some form of mental travel and that its physical application would mark real time travel. (Catalin V. Buhusi) Experiments are being designed based on this concept to acquire insight into time travel.
In conclusion, the experiments featured demonstrate that time dilation is dependent on spatial motion rather than retinal motion. They also ascertain the possibility of inducing time dilation on the acceleration of a particle in relation to a constant observation. This is based on Einstein’s theory of special relativity: the movement of an object (approaching the speed of light) analogous to that of another exhibits differences in aging between the two bodies. This aging is manifested in biological, chemical and physical aspects. When motions of the targets were accelerated, the observers saw a difference between the reference object and that of a similar object used for comparison. This suggests that if a discovery is made on how to accelerate the cells of living organisms without inflicting any harm to the individual then it would not be impossible to achieve time travel. This defiance of Newton’s laws of motion would only be achieved if the living cells travel at a speed close to that of light. Presently there is a lack of technology that can achieve the acceleration of living cells to this speed. Physicists and other scientists are working on realizing this. Their research has gained significant ground on the matter through numerous experiments. The experiment featured in this paper ascertains that time dilation, an aspect of time travel, exists in the world as of present. This discovery coupled with other similar ones e.g. mental time travel promise that it is only a matter of time before scientist find a stable method of facilitating time travel for humans. This is likely to be achieved in the near future based on the rapid rates of experiments investigating the fourth dimension. This justifies the hypothesis that time travel will be possible in the future.
Works cited
Ricky K. C. Au, Katsumi Watanabe. “Time Dilation Induced by Object Motion is Based on Spatiotopic but not Retinotopic Positions.” Frontiers in Psychology, 3. (2012): Web. 30 Nov 2013.
“Einstein’s Theory Passes a Space ‘Laboratory’ Test.” The Christian Science Monitor (pre-1997 Fulltext): 0. Jan 22 1992. ProQuest. Web. 30 Nov. 2013 .
Morris, Richard. “The Perils of Time Travel.” The Futurist 28.5 (1994): 60. ProQuest. Web. 1 Dec. 2013
Catalin V. Buhusi, Warren H. Meck. “Relativity Theory and Time Perception: Single or Multiple Clocks?.” PLoS ONE, 4. 7 (2009): Web. 1 Dec 2013.
“How Time Travel Will Work.” Bibliotecapleyades.net, 2013. Web. 1 Dec 2013. <http://www.bibliotecapleyades.net/ciencia/time_travel/esp_ciencia_timetravel25.htm>.
Time To End Exploitation Of Workers
Time To End Exploitation Of Workers
29th September, 2010
Time to End Exploitation of Workers
Dear Linda Chavez,
As much as immigration matters have always been controversial in the United States, the plight of people working as immigrant or undocumented workers cannot be ignored at all. You are a witness to the inhuman conditions immigrant workers are exposed to and I share with you my sympathies for these people whose only crime is being natives of another country. I condemn the idea that human beings have to be mistreated on the basis of race and capitalistic exploits. Ironically, all this happens under the watchful eye of the administration. I am writing this to expose and condemn the injustices immigrants are exposed to and to offer my opinion regarding measures to curb future exploitation of immigrants.
“Guest workers” is the term given to the people who leave their country in search of jobs in the United States. All those who have had the opportunity to toil in the cotton fields of the U.S have to agree that it is not a dance in the rain. This is occasioned by the insufficiency of the most basic welfare needs of the workers and low wages. Matters regarding health care have totally been neglected whilst this is an issue that deserves the highest priority. I fully agree with you when you state that when these workers were viewed “as units of production, employers worked them to their limit, knowing that the following season a fresh unsuspecting batch would arrive” (Chavez-Thompson).
Freedom and rights of the immigrant have also significantly been curtailed or denied altogether. This injustice has been put into effect through strange programs such as the one called ‘Bracero’. This is one program designed to control all the functions and operations of the persons who get an opportunity to live in the United States as immigrant workers. Bracero is a phenomenon that brings very painful memories to most people throughout the entire history of the world’s civilization. In spite of all this, the truth of the matter is that the exploitation that was experienced under the Bracero program still continues to exist in modern American today. This has manifested itself in fresh and more controlled immigrant worker programs such as the H2-A AND H2-B. Due to the existence of these newer programs, “guest workers” still continue to face so much trouble in fighting for their rights just as the undocumented workers did.
Those people who have worked under the H2 program have had to make great financial sacrifices just to get employment in the country of opportunity. It is common to meet some of them sourcing for financial assisting to cater for their transportation expenses as well as enticements to the authorities so that they can gain certain favors. This has always made such workers heavily bound with debts even before they start working. It is strange that much money is used to get low paying menial jobs. These are hard jobs mainly in agricultural and construction sectors. There are also some who work in the seafood industry. They are the kinds of jobs that do not deserve the huge investments that immigrants pay to get. It is pure manipulation of people who can not fight for their own rights in a foreign land.
Research conducted by the Southern Poverty Law Centre suggests that exorbitant fees are charged to those seeking for work opportunities in the United States. For example, it is common to encounter a Guatemalan parting with as much as $2,500 to get a temporary work opportunity. This is normally what an average worker in Guatemala earns in a full year. It was indeed surprising for me to learn that Thai worker pays “as much as $10,000 for the chance to harvest crops in the orchards of the Pacific Northwest” (Chavez-Thompson). Should the workers seek for loans from financial institutions they should be well prepared to pay back with very high interest rates. What is even more baffling is the fact that the collateral sought at times is too big for the small amounts that they receive. At times they have to part with their own cars and homes.
This mistreatment of workers deserves to be stopped. Why should undocumented workers face such tyranny their employers and the system that runs immigrant labor? Why do they have to suffer the consequences of their ignorance such as having to take up on loans that soon become a tall order to pay? What should really happen is an evaluation of the laws that protect the guest workers. This is because, in as much as these laws exist, they do little in protecting the rights of guest workers. The government has to be pressed to take up on its mandate and ensure the rights of immigrants are respected and upheld. Deportation is one of the worst fears for all guest workers and is always used as an intimidation tool to exploit them further. It causes them to fear fighting for their own rights. With the threat of deportation, employers continue asserting excessive force and dominion over their helpless workers. The final consequence is that the immigrant workers have no option than work in these very manipulative occupations.
It is important to come up with recommendations that will help solve these problems. If the problem continues to be neglected then such workers will continue to suffer in a modern society that should not thrive on exploiting other people. First, workers have to be allowed to form unions that would lobby for their rights without fear of intimidation. Employers who prohibit workers from joining unions deserve to be prosecuted. Secondly, the immigration department should stop deporting workers simply because they tried to fight for their rights. All non-governmental bodies working to stop the suffering of immigrant workers should be supported in totality. An example is the AFL-CIO that has strived for so long to bring to an end the abuse that guest and un-documented workers have had to endure for long. Perhaps the best way to achieve some of these goals would be by vetting and allowing such immigrants acquire citizenship. This will ensure that they get decent wages and enjoy their rights and freedoms.
Finally, one last suggestion to end these injustices is by the abolishment of the guest worker programs for good. This removes the burden of workers having to always depend on their bosses for livelihood at all times. Reconsideration of immigration rules and procedures is also urgently required. The ultimate goal should be the provision of permanent citizenry to everyone constructively involved in the labor market within the country. I fully concur with you in asking, “As a nation that prides itself on fair treatment and equality, how can we possibly settle for anything less?” (Chavez-Thompson).
Sincerely,
(Insert name)
Works Cited
Chavez-Thompson, Linda. It’s Time To End Worker Exploitation. 05 June, 2007. 29 Sept. 2010.< Commentaryhttp://www.forbes.com/2007/06/05/labor-immigrants-workers-opedcx_lct_0606labor.html>
Time Series Econometric Methods
Time Series Econometric Methods
Step 1
According to Enders, (2004), Purchasing Power Parity (PPP) measures how much money is required to buy same goods or services in between two countries. The PPP is then used to compute the exchange rate between these two countries. Considering the two countries; home country as Switzerland (country A) and foreign country as US (country B), then the Spot Exchange Rate between the two countries will be given by the following relationship;
EMBED Equation.3 :
Where St is the spot exchange between Switzerland and US, Pt is the price level in Switzerland, and Pt* is the price level in US. If the two countries produce tradable goods and there are no trade impediments to international trade, such as tariffs or transaction costs, then the law of one price should hold. Sometimes the PPP is taken as the law of one price if we are dealing with one commodity. This situation at most times is untenable because the possibility of “basket of goods” is almost impossible to get in both countries that are diverse economically. Differences between PPP and the actual rate frequently occur due to miss-measurement of the relevant price indices. If the price indices reflected only traded goods, then the discrepancy would not be so large. Another reason could be because investors have changed their preference from the dollar to non dollar assets (Dickey, & Fuller, 1979).
The PPP should mean that exchange rates should equate the price of goods and services across the countries. For example, 100 Swiss Francs should buy as much as 100 Swiss Francs exchanged into US dollars and used to purchase goods in America. Usually the spot exchange is expressed as EMBED Equation.3 , where lower case letters denotes a variable in logarithms.
Step 2
Using the Consumer Price Index; the prices in the US were slightly higher than Switzerland. Consumers tend to spend more for products and services in the US compared to Switzerland. The trend of the time series shows that there have been gradual increases for the forty observations taken (Wessa, 2010).
Descriptive statistics of the US CPI data
Anderson-Darling A-Squared 1.178
p 0.004
95% Critical Value 0.787
99% Critical Value 1.092
Mean 218.210
Mode #N/A
Standard Deviation 4.598
Variance 21.145
Skewedness 0.561
Kurtosis -0.639
N 48.000
Minimum 211.401
1st Quartile 214.740
Median 217.419
3rd Quartile 220.570
Maximum 227.033
Confidence Interval 1.335
for Mean (Mu) 216.875
0.95 219.546
For Stdev (sigma) 3.828
5.760
for Median 216.476
218.749
Descriptive statistics of the Swiss CPI data
Anderson-Darling A-Squared 1.129
p 0.005
95% Critical Value 0.787
99% Critical Value 1.092
Mean 218.209
Mode #N/A
Standard Deviation 4.687
Variance 21.969
Skewedness 0.438
Kurtosis -0.615
N 48.000
Minimum 210.228
1st Quartile 215.608
Median 217.987
3rd Quartile 220.029
Maximum 226.889
Confidence Interval 1.361
for Mean (Mu) 216.848
0.95 219.570
For Stdev (sigma) 3.902
5.871
for Median 216.177
218.783
F-Test Two-Sample for Variances 0.05 US Switzerland 218.2104 218.2085 21.14503 21.96906 48 48 47 47 0.96 0.448 0.896 Two-tail 1.62 1.78 Two-tail Accept Null Hypothesis because p > 0.05 (Variances are the same)
Accept Null Hypothesis because p > 0.05 (Variances are the same) Multivariate analysis
Step 3
Autocorrelation of the US and Swiss data
The US and Swiss data are autocorelated
US Switzerland 1 0.986169 0.986169 1
Step 4
Regression analysis of the US and Swiss CPI data
SUMMARY OUTPUT Force Constant to Zero FALSE Regression Statistics Multiple R 0.986 R Square 0.973 Goodness of Fit >= 0.80 Adjusted R Square 0.972 Standard Error 0.785 Observations 48 g
ANOVA df SS MS F P-value Regression 1 1004.180 1004.180 1628.486 0.000 Residual 46 28.36518 0.616634 Total 47 1032.545 0.95
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -1.136719056 5.436640586 -0.2090848 0.835 -12.080108 9.80667068
US 1.005200879 0.02490926 40.354505 0.000 0.955061 1.055340618
y = -1.137 +1.005*US Confidence Level
0.99
Lower 99% Upper 99%
-15.745 13.47161
0.938269 1.072132
y = -1.137 +1.005*US Observations Predicted Switzerland Residuals Standard Residuals Percentile Switzerland
1 212.16590 -1.08590 -1.39781 1.04167 210.228
2 212.59211 -0.89911 -1.15736 3.12500 211.08
3 213.41436 0.11364 0.14628 5.20833 211.143
4 213.94712 0.87588 1.12746 7.29167 211.693
5 215.18854 1.44346 1.85806 9.37500 212.193
6 217.46432 1.35068 1.73864 11.45833 212.425
7 219.09274 0.87126 1.12151 13.54167 212.709
8 218.74997 0.33603 0.43255 15.62500 213.24
9 218.87361 -0.09061 -0.11663 17.70833 213.528
10 216.95769 -0.38469 -0.49519 19.79167 213.856
11 213.04545 -0.62045 -0.79867 21.87500 214.823
12 211.36375 -1.13575 -1.46197 23.95833 215.351
13 211.92767 -0.78467 -1.01005 26.04167 215.693
14 212.79315 -0.60015 -0.77253 28.12500 215.834
15 212.52978 0.17922 0.23069 30.20833 215.949
16 212.67453 0.56547 0.72788 32.29167 215.969
17 212.94795 0.90805 1.16887 34.37500 216.177
18 214.72414 0.96886 1.24715 36.45833 216.33
19 214.70604 0.64496 0.83021 38.54167 216.573
20 215.46296 0.37104 0.47761 40.62500 216.632
21 215.86906 0.09994 0.12864 42.70833 216.687
22 216.46515 -0.28815 -0.37091 44.79167 216.741
23 217.10546 -0.77546 -0.99819 46.87500 217.631
24 217.32359 -1.37459 -1.76941 48.95833 217.965
25 217.46331 -0.77631 -0.99929 51.04167 218.009
26 217.39094 -0.64994 -0.83662 53.12500 218.011
27 217.43416 0.19684 0.25338 55.20833 218.178
28 217.36681 0.64219 0.82664 57.29167 218.312
29 217.17482 1.00318 1.29133 59.37500 218.439
30 217.19894 0.76606 0.98609 61.45833 218.711
31 217.64425 0.36675 0.47210 63.54167 218.783
32 218.05939 0.25261 0.32516 65.62500 218.803
33 218.36297 0.07603 0.09787 67.70833 218.815
34 219.02238 -0.31138 -0.40081 69.79167 219.086
35 219.44557 -0.64257 -0.82713 71.87500 219.179
36 220.42363 -1.24463 -1.60212 73.95833 219.964
37 221.04886 -0.82586 -1.06307 76.04167 220.223
38 222.02592 -0.71692 -0.92284 78.12500 221.309
39 223.21708 0.24992 0.32170 80.20833 223.467
40 224.05843 0.84757 1.09101 82.29167 224.906
41 224.66558 1.29842 1.67137 84.37500 225.672
42 224.86963 0.85237 1.09719 86.45833 225.722
43 225.55116 0.37084 0.47736 88.54167 225.922
44 226.30606 0.23894 0.30757 90.62500 225.964
45 226.91320 -0.02420 -0.03116 92.70833 226.23
46 226.84686 -0.42586 -0.54818 94.79167 226.421
47 227.05795 -0.82795 -1.06577 96.87500 226.545
48 227.07705 -1.40505 -1.80863 98.95833 226.889
The estimated error correlation (ECM) model will be as bellow
The process starts by estimating the long run relationship between the variables in the yt and xt yt = β0 + β1xt + ut, however, with cointetegration, it is healthy to be confident that the variables in β0 and β1 may never be biased evening when dealing with large samples like 40 in our case. Therefore both β0 and β1 are extremely consistent. Because the two are also super consistent, it is also healthy to ignore all the dynamic terms and use all the residuals that arise from the co integrating regression in order to test for consitegration. This can provide us with the results for testing variables for the existence of long-term equilibrium associations. The test can use the DF/ADF statistics irrespective of the nature of
U (stationary or dynamic)
HYPERLINK “http://3.bp.blogspot.com/-UQ58H-0noqI/TVaC4Heft2I/AAAAAAAAAGE/sWH1DpzZ3eA/s1600/cointegration+and+ecm1.JPG”
INCLUDEPICTURE “http://upload.wikimedia.org/wikipedia/en/math/c/7/d/c7dafde3c8b029f02b3192a4acd1cc85.png” * MERGEFORMATINET
In this equation, the components of the dickey fuller test are as shown below:
α =is a constant, β=coefficient, p =the lag order
From our original results, we can conclude that the two series have extremely co integrated because the residuals are stationary.
The CPI Data
US Data from U.S. Department of Labour: Bureau of Labour Statistics
Period US Switzerland
2008-01-01 212.199 211.08 0.99
2008-02-01 212.623 211.693 1.00
2008-03-01 213.441 213.528 1.00
2008-04-01 213.971 214.823 1.00
2008-05-01 215.206 216.632 1.01
2008-06-01 217.470 218.815 1.01
2008-07-01 219.090 219.964 1.00
2008-08-01 218.749 219.086 1.00
2008-09-01 218.872 218.783 1.00
2008-10-01 216.966 216.573 1.00
2008-11-01 213.074 212.425 1.00
2008-12-01 211.401 210.228 0.99
2009-01-01 211.962 211.143 1.00
2009-02-01 212.823 212.193 1.00
2009-03-01 212.561 212.709 1.00
2009-04-01 212.705 213.24 1.00
2009-05-01 212.977 213.856 1.00
2009-06-01 214.744 215.693 1.00
2009-07-01 214.726 215.351 1.00
2009-08-01 215.479 215.834 1.00
2009-09-01 215.883 215.969 1.00
2009-10-01 216.476 216.177 1.00
2009-11-01 217.113 216.33 1.00
2009-12-01 217.330 215.949 0.99
2010-01-01 217.469 216.687 1.00
2010-02-01 217.397 216.741 1.00
2010-03-01 217.440 217.631 1.00
2010-04-01 217.373 218.009 1.00
2010-05-01 217.182 218.178 1.00
2010-06-01 217.206 217.965 1.00
2010-07-01 217.649 218.011 1.00
2010-08-01 218.062 218.312 1.00
2010-09-01 218.364 218.439 1.00
2010-10-01 219.020 218.711 1.00
2010-11-01 219.441 218.803 1.00
2010-12-01 220.414 219.179 0.99
2011-01-01 221.036 220.223 1.00
2011-02-01 222.008 221.309 1.00
2011-03-01 223.193 223.467 1.00
2011-04-01 224.030 224.906 1.00
2011-05-01 224.634 225.964 1.01
2011-06-01 224.837 225.722 1.00
2011-07-01 225.515 225.922 1.00
2011-08-01 226.266 226.545 1.00
2011-09-01 226.870 226.889 1.00
2011-10-01 226.804 226.421 1.00
2011-11-01 227.014 226.23 1.00
2011-12-01 227.033 225.672 0.99
References
Wessa P., (2010). Autocorrelation Function (v1.0.9) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_autocorrelation.wasp/
Dickey, D. & A. Fuller (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, 74, p. 427–431.
Enders, W., (2004). Applied Econometric Time Series: Second Edition. John Wiley & Sons: United States.
Elder, J. & Kennedy, E. (2001) “Testing for Unit Roots: What Should Students Be Taught?”. Journal of Economic Education, 32(2): 137-146
Appendix
Period US
2008-01-01 212.199
2008-02-01 212.623
2008-03-01 213.441
2008-04-01 213.971
2008-05-01 215.206
2008-06-01 217.470
2008-07-01 219.090
2008-08-01 218.749
2008-09-01 218.872
2008-10-01 216.966
2008-11-01 213.074
2008-12-01 211.401
2009-01-01 211.962
2009-02-01 212.823
2009-03-01 212.561
2009-04-01 212.705
2009-05-01 212.977
2009-06-01 214.744
2009-07-01 214.726
2009-08-01 215.479
2009-09-01 215.883
2009-10-01 216.476
2009-11-01 217.113
2009-12-01 217.330
2010-01-01 217.469
2010-02-01 217.397
2010-03-01 217.440
2010-04-01 217.373
2010-05-01 217.182
2010-06-01 217.206
2010-07-01 217.649
2010-08-01 218.062
2010-09-01 218.364
2010-10-01 219.020
2010-11-01 219.441
2010-12-01 220.414
2011-01-01 221.036
2011-02-01 222.008
2011-03-01 223.193
2011-04-01 224.030
2011-05-01 224.634
2011-06-01 224.837
2011-07-01 225.515
2011-08-01 226.266
2011-09-01 226.870
2011-10-01 226.804
2011-11-01 227.014
2011-12-01 227.033
Swiss CPI data
Period Swiss CPI data
2008-01-01 211.08
2008-02-01 211.693
2008-03-01 213.528
2008-04-01 214.823
2008-05-01 216.632
2008-06-01 218.815
2008-07-01 219.964
2008-08-01 219.086
2008-09-01 218.783
2008-10-01 216.573
2008-11-01 212.425
2008-12-01 210.228
2009-01-01 211.143
2009-02-01 212.193
2009-03-01 212.709
2009-04-01 213.24
2009-05-01 213.856
2009-06-01 215.693
2009-07-01 215.351
2009-08-01 215.834
2009-09-01 215.969
2009-10-01 216.177
2009-11-01 216.33
2009-12-01 215.949
2010-01-01 216.687
2010-02-01 216.741
2010-03-01 217.631
2010-04-01 218.009
2010-05-01 218.178
2010-06-01 217.965
2010-07-01 218.011
2010-08-01 218.312
2010-09-01 218.439
2010-10-01 218.711
2010-11-01 218.803
2010-12-01 219.179
2011-01-01 220.223
2011-02-01 221.309
2011-03-01 223.467
2011-04-01 224.906
2011-05-01 225.964
2011-06-01 225.722
2011-07-01 225.922
2011-08-01 226.545
2011-09-01 226.889
2011-10-01 226.421
2011-11-01 226.23
2011-12-01 225.672