Top Chicago Style Essay Samples Choices

Top Chicago Style Essay Samples Choices The Lost Secret of Chicago Style Essay Samples Image links aren't great for search engine optimization. It's crucial because the info published on the site can change over a brief period. You've been redirected to our new website. There are sites offering several facts about how to present information associated with the formatting style. A Startling Fact about Chicago Style Essay Samples Uncovered On the flip side, it shouldn't be so broad that some resources would outweigh the info you could squeeze into one paper. Summary particulars of the source have to get decoded in the conclusion of each page. Author really isn't the source of info in table Authors commonly utilize statistics or a whole statistical table from another source. He is also the source of information in table The following models may be used when the author of the item you want to cite is also the source of the information in the table. In truth, it's better to s et the paper aside for a couple days between proofreading sessions. In any case, such assignments are rather intricate and frequently cause numerous stressful circumstances, confusion, and other issues. Before you even begin writing, make sure you are familiar with the data which you are working with. Over time, writing has been an important process of passing information from 1 person to the next all around the world. Adhering to the Chicago Manual of Style rules closely are a valuable part of making a thriving paper. Videos are put in quotations. A very good academic writing implies the use of quotations. Numerous writing styles have been made over time. Most often, a specific formatting style is used for a specific area of knowledge. There are a lot of key reference styles utilized in academic writing. You may use the references Tab then set the cursor in which you need to bring the foot and click insert footnote. Each style has different requirements in regards to its format. As an example, Chicago style employs the serial comma, sometimes referred to as the Oxford comma. Since you may see, the writing voice is extremely important. Your future writing assignment will appear a lot more correct and organized with a particular format applied. You place the number beside the author's name. If, but the title of a published work comprises abbreviated inclusive dates, the abbreviation needs to be retained. Based on the significance of the paper, you might want to employ someone to do some additional proofreading for you. If you're intimidated at the notion of making a book, there are various helpful sources out there to give you a hand. If you may take a rest from the paper for a couple days, you will be surprised how far better your proofreading sessions go with a fresh look at the paper. Simple writing isn't enjoy a part of furniture. There's a typical college essay writing format that you need to follow. Make it a practice of writing daily even when you have been writing for ten minutes. Writing is the kind of expressing your own personal freedom that's used to free us from mass identity spread around us. The titles of the majority of poems ought to be enclosed in double quotation marks, but the titles of quite long poems ought to be italicized. As previously mentioned, one well-known quality of Chicago style essay format is the usage of footnotes and endnotes. The Turabian style papers also incorporate footnotes or endnotes section that's single spaced. Every style gives you official citation guides. What's a persuasive essay. In addition, the readers might not even bother to read it. The bibliographic list must be completed in an alphabetical order that makes it simple for the readers to trace a source through the usage of the surnames of the authors. Whenever you have four or more authors, you will list all them in the bibliography utilizing exactly the same format as you would for one, a few authors.

Behaviorism the beginnings Free Essays

Behaviorism is one of the most influential schools of psychology, especially American psychology. The development of behaviorism was spurned as a reaction to structuralism and functionalism. Behaviorism was posited as a revolution in the methodology of the science of psychology (Hothersall, 1995), while structuralism and functionalism have argued that the rightful object of study of psychology is the mind and consciousness and have developed methods that congruently were subjective and enabled the psychologists of that time to study the mind and consciousness. We will write a custom essay sample on Behaviorism the beginnings or any similar topic only for you Order Now Although behaviorism has become established as a major force in psychology, in its earlier days it was not popular and embraced by many psychologists. However as behaviorism evolved and developed into a theoretically based and objective science many have found its assumptions practical and scientific. Western psychology’s history is short and colorful compared to other sciences, it started with structuralism from Germany with Wundt at the helm (Murphy, 1930). When psychology arrived in America it obviously followed structuralism, and since it was too philosophical for the American scholars. James developed his own paradigm and called it functionalism, which in essence focused on the function of consciousness in explaining behavior than in studying the structure of the mind. Functionalism held greater influence in American psychology but together with structuralism it still espoused that psychology is the study of the mind and consciousness. The zeitgeist of that period was that the focus of psychology is the understanding of the human mind and internal experiences (Hothersall, 1995). This inspired psychologists to devise methods of studying perception and consciousness in the attempt to discover the workings of the human mind. Research at that time was centered on identifying and describing physiological experiences and how it affected human behavior. Psychologists were comfortable with the notion that psychology is the study of the mind and most of them wrote about the self, attention, consciousness, perception and even mental processes that were believed to be the cause of human behavior. At this point, methods used to study the human mind were subjective and did not lend itself to replication and reliability which in turn questioned the veracity of psychological researches. Although functionalism stressed that the mind and consciousness were responsible for human actions, they viewed behavior as a product of mental processes and ignored its importance in the study of psychology. Functionalism however stressed the application of psychological knowledge to practical issues such as learning, education and organizational development. The pragmaticism of functionalism led it to the discovery that human behavior is as much important to study since it is directly related to the human mind. Functionalism also identified the shortcomings of structuralism and its methods and since it was heavily influenced by Darwin, functionalism also welcomed the idea of studying animals in laboratories to test psychological assumptions. While this new developments were gaining support, a new school of psychology emerged from the work and writings of Ivan Pavlov (Hothersall, 1995). Pavlov was able to demonstrate that a dog can be trained to salivate with just the sound of a bell intrigued some psychologists and became one of the most popular teachings in psychology; Pavlov called this process classical conditioning. In America, John B. Watson was impressed with the experiments of Pavlov that he embraced the idea that behavior is the mot important aspect of man that should be studied by psychology (Watson, 1913). John B. Watson was an influential person and he is conventionally credited to be the father of behaviorism as he strongly and eloquently articulated the new psychology of that time. Central to Watson’s argument was that he accepted that animal behavior is quite similar to human behavior and that they are legitimate subjects in the experimental study of behavior. Earlier, it was mentioned that behaviorism was revolutionary in the sense that it developed a methodology of study of psychology and that it held few theoretical explanations to human behavior. Watson (1913) posited that any behavior is a response to a stimuli and the relationship between the stimulus and the response should be the subject matter of psychology. Watson also erased the mental processes that the structuralism and functionalism was focused on, arguing that studying mental processes are futile and subjective and did not uphold the scientific and experimental tradition of the discipline. Watson became the editor of the Psychological Review, one of the earliest scientific journals in psychology and used his position in the paper to put forth his ideas and conceptualizations of psychology as the behaviorist would see it (Watson Evans, 1990). Watson was a radical behaviorist, he always referred to himself as â€Å"the behaviorist† and it implied that he renounced all mental processes as devoid of any psychological insight. He reasoned that structuralism and functionalism are limited perspectives and it did not offer objective and rational explanations of behavior. He was famous for his experiments with Little Albert, wherein he conditioned fear of white and flurry objects in a small child. He demonstrated that fear can be conditioned and that it is manifested in different objects that fit the original object used as a stimulus (Watson, 1928). Watson believed that every action is a product of conditioning and that genetics or cultural orientations does not have anything to do with it. When asked to explain thinking, he said that thinking was not a mental process per se; instead it is an act of speaking in symbolic form (Watson, 1913). Watson’s intense dedication to behaviorism led him to believe that he can train any child to become what he wants them to be by subjecting them to the environment and experiences that would support this personality (Watson, 1928). Watson was a true-blooded behaviorist and this actually was the main criticism leveled against him. Psychologists who were trained in the functionalist and structuralist traditions had difficulty accepting Watson’s theories since it took out the mind and consciousness in psychology. There were a number of supporters but they also believed that mental processes are as much important as behavior. another criticism of Watson was that behaviorism was too deterministic, it seemed that the person had no free will since he/she is controlled by his/her environment. It can be remembered that psychology was the child of philosophy and for those who were trained in philosophical logic stressed free will, choice and freedom. Support for Watson waned in the later part of his career since he became too caught up in his assumptions on behaviorism that his contentions became too radical and lacked scientific credence. Watson’s major contribution to psychology is his emphasis on objective methods of research and the use of rats and animals in the study of psychology. Behaviorism became one of the great schools of thought in psychology because it evolved and developed into what we now know as modern behaviorism (Hothersall, 1995), a theoretical perspective that still focuses on human behavior as the object of study but have come to acknowledge the importance of mental processes, genetics and environmental experiences, as well as using methods that not only seek to elicit behavior but also gives due attention to thinking, attention, emotions and consciousness. References Hothersall, D. (1995). History of Psychology. New York: McGraw-Hill. Murphy, G. (1930). A Historical Introduction to Modern Psychology. New York: Harcourt, Brace Company, Inc. Watson, J. (1913). Psychology as the behaviorist views it. Psychological Review, 20, 158-177. Watson, J. (1928). The Ways of Behaviorism. New York: Harper Brothers Publishing. Watson, R. Evans, R. (1990). The great psychologists: An intellectual history 5th ed. New York: HarperCollins. How to cite Behaviorism the beginnings, Papers

Social Class and Education free essay sample

Education is essential in society for a number of reasons. Firstly, education is important for developing skills for employment and living. If we did not have basic education, it would severely impact on society. Subsequently, it is possible that society could break down due to the absence, or poor quality of communication and basic skills. The World is dependent upon communication, which is developed through education (Mortimore 1986). Furthermore, another important purpose of education in society is to control unconformity. Education is a way in which people are taught the social and ideological norms which are dominant in society. Consequently, with the absence of education, it could foresee a delinquent future for society. Mortimore (1986) stated that within society, it has always been evident that people fall into different categories termed as ‘Social Class’. This shorthand label could be defined in numerous ways, most prominently by the scale developed by the Registrars General. We will write a custom essay sample on Social Class and Education or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Categories are classified as a result of breadwinner occupation, which are managed into five categories: Social Class I and II, professional and managerial occupations; Social Class IIIa, would be other manual workers, Social Class IIIb, skilled manual workers; Social Class IV, semi-skilled occupations; Social Class V, unskilled occupations. This is a rather reductionist point of view to take when classifying people, as quality home, relationships, interests and lifestyles are not taken into account (Mortimore, 1986). A way in which children are categorised in school based on social class, is the eligibility of free school meals. Schools provide free school meals to children whose family receive any kind of income based support, such as jobseekers allowance (Direct Gov). Figures show that in 2006-2010 55. 8 percent of pupils eligible for free school meals achieved the national average level in English and Mathematics, compared to 77. 1 percent of pupils were not eligible (Department for education, National statistics). ‘Many pupils in disadvantaged communities are simply less intelligent than others in higher social classes, according to the Scottish chief medical officer. It is apparent that children placed in the lower class categories are under achieving in comparison with higher class children. Again National Statistics demonstrate that there is a 23. 7 percentage point gap between the most and least deprived areas, which are defined by the Income Deprivation Affecting Children Indices. ‘ reclaim social class as a central concern within education as a powerful and vital aspect of both learner and wider social identities. ’ (Diane Reay 2006) Reay stresses just how vital social class is within education. As attainment levels appear to be affected by the influence of social class, this certainly highlights the importance of understanding the relationship between social class and education; consequently making changes to reduce the gaps in attainment levels. Furthermore, Davies,J (1980) illustrated that Social Class can create differences in attendance patterns of pupils. Looking at percentage of absence, he found a 7. 1 percent difference between attendance of pupils with a non manual family background and pupils from social class 5. In addition to this, Davies discovered a range of 16. 1 percent between non manual and unemployed backgrounds. Mortimore (1986) states that attendance rates have been considerably influenced by social class. ‘Whether that is a direct influence (working class parents being less motivated to insist that their children attend school) or an indirect one (pupils with working class backgrounds been less successful in academic life and, therefore, being less committed to the value of schooling) has not yet been resolved satisfactorily. ’ (Mortimore, P and Mortimore, J 1986) Mortimore et al discuss how social class, attendance and attainment are closely linked. It is suggested that children from a working class background who are less successful in academic life have a tendency to value education less, subsequently not attending. However, could it not be argued that the reason the child is underachieving be the fact that they do not attend school enough? It is clear that social class, attendance and attainment are inextricably linked. School behaviour is also another factor that is linked to social class; however this issue is substantially more complex to monitor. To study school behaviour is extremely difficult as behaviour is influenced by a number of things, such as teacher behaviour and general school ethos. Research into social class and adjustment to school was monitored and evidently there was a higher percentage of pupils less successfully adjusted, who were in the lower classes, especially unemployed (EP 1982, Mortimore, P and Mortimore, J 1986). Many reasons for the relationship between social class and education have been debated. Hyman, H (1967) alleged that working class people compared to middle class people tended to lack ambition. He believed that working class attitudes emulated their experience of working class labour: A chance of promotion being slim, therefore their future reflects their present, resulting in no need to make long term plans. This attitude could be then acquired by the children of working class families, thus not valuing education and schooling. Poverty is an essential factor in the close relationship between social class and education. Less economically well off parents will have less disposable income to spend on their children and their education. Economical, social and cultural capitals are key in education (Bordieu). Bernstein argued that the linguistic codes in place favoured middle class children. He established that Middle Class people operated with elaborated code, whereas working class people use a restricted code. This posed a disadvantage to working class children as teachers usually operated the elaborated code. Could this manifest an explanation of lower attainment on behalf of working class children? (Bordieu). Other reasons that have been argued to create this relationship include Baxter et al’s (1981) study found that babies born into working class. Families boast a slimmer chance of developing into healthy children. In addition to this, school resources play a huge part in the quality of a school and the education they offer. A school in a low socio-economic area may not possess the right level of resources, subsequently affecting their pupils’ educational development (Mortimore et al). It is obvious that there are numerous reasons for the relationship between education and social class. Children’s patterns of performance at school, attainment, behaviour and attendance have been proved to be affected by social class. However, other important issues such as race and ethnicity and gender also have a great impact on education. The three social and cultural issues are inextricably linked and entwined amongst each other; therefore it is almost impossible to boldly state that social class is the only factor in play whilst analysing statistics and results of studies (Little, A). Nevertheless, we have come to a conclusion that Social Class does have a great affect on education, and research should continue to try and combat this.

Square Root Using Sequential Cordic Essays

Square Root Using Sequential Cordic Essays Square Root Using Sequential Cordic Essay Square Root Using Sequential Cordic Essay Square root using Sequential Cordic Assignment-2 Submitted to: Dr. Sumam David Dept. of Electronics Communication Engineering NITK Surathkal Submitted by: Rakshith Sharma 10EC87 Vikas Majjagi 10EC107 Mullapudi Srinivas 10EC99 Algorithm: This is implemented for a range of input values 0. 75 since Xin should be less than 1 for the bit notation we used. Here we use the vectoring Mode of CORIC and its Hyperbolic subcase to calculate Xout=sqrt(xin2 -yin2 ) And yout= 0 Bit notation: [MSB(sign bit)] . (bit 1 to 15 for +ve fraction)] If we use xin=M+ ? and yin=M -1/4 we can compute xout=sqrt(M). The other equations of the cordic remain the same ie, X(i+1)=x(i)+d(i)*y(i)*2-i Y(i+1)=y(i)+d(i)*x(i)*2-i Z(i+1)= z(i) – d(i)*a(i) where a(i)=tan-1 (2-i) In this case we use 16bit fixed point notation with one sign bit and 15 bits in Q15 notation. A total of 12 iterations are used to reach the result where y(i) is sufficiently close to 0 and x(i) is approximately equal to sqrt(M). In case of hyperbolic, it is necessary to repeat shift iteration number for 4 th and 7th iterations in order to make the series to converge. The final obtained x(i) is to be multiplied by 1. 207534056 to get the result. The flow chart for the algorithm implement in the VHDL code is as shown in the following page. d(i)=1 if x(i)*y(i)0 Y(i) has gone to 0(apprx) input M=0. 63998413 output X(i)=0. 80035533 Y=0? sh ift12 Yes No Yes X(i)=sqrt(M) Yes Check iteration number Shift=4 or 7? Shiftrep= 0? No No Shiftrep+1 Shift+1 d(i)=-1 No x(i)*y(i)

Studying, Travels and Fun in Denmark!

Studying, Travels and Fun in Denmark! We continue discussing the topic of studying abroad, as there is so much yet to say. Today our interviewee is Ally Flessel. She studies Biology and English at Bucknell University and went for a semester abroad to Denmark, Copenhagen. Did she get some other impressions from this country than our previous interviewees Judy Su and Ellen Wall? Lets find that out! Ally, you decided to aply for DIS program. Why? What major benefits of studying abroad did you see for yourself? Studying abroad is an amazing experience that I would not give up for anything else in my college career. First, it taught me how to adapt to new culture and new people. Such programs are filled with students from all over the US, so you need to learn how to step up and meet new people, even if they are American. Secondly, studying abroad motivated me to come back to college for my senior year with a level of energy many of my friends are missing. I was excited to be back at school and in a familiar environment with my friends I have not seen for over a year. I think it is also important for students to face real world problems away from the comforts of friends and family. Independence is one of the things I gained the most of abroad. I feel confident in my ability to take care of myself no matter what challenged I may face. By the way, Ally had a different situation with accomodation from the two previously interviewed students. She didnt rent a flat or live with a host family. Instead, she was living in  the largest DIS Residential Community with 110 other DIS students. Due to a roommate mix up she was living all by herself, so probably, she didnt face that annoying-roommate-makes-noise-and-I-cant-concentrate-on-studying kind of problem. Lets move on straight to your studying. What courses did you take in Denmark? I had Immunology (for my Biology major at Bucknell), Hans Christian Anderson Literature, Sociology of the Family, and Danish Language. I was also in the Medical Practices and Policies (MPP) Core. So you took a challenge to learn Danish? Did you have a chance to practice in live conversations with Danes? Danish classes were great and absolutely enhanced my experience. However, everyone in Copenhagen speaks English! For example, when my classmates and I would try to practice our Danish and order coffee the baristas would always respond in English. Danes are not accustomed to foreigners trying to learn their language so they are not very good at understanding accents and typically switch to English if they encounter this. And you didnt feel the language barrier? There were only two times when not knowing Danish was burdensome. First, when I was with my Danish visiting family. I would not be able to follow along in conversations they were having; usually they spoke English because I was around, but once in a while I had to follow stories based off of body language. And second was eading the signs.All of them are in Danish and asking someone to meet you at a location you cannot pronounce is pretty tricky. What kind of writing assignments did you get? What were the most interesting topics? I had an English course on Hans Christian Andersen so I wrote a paper about his works. I also took a course called Sociology of the Family and wrote a paper about different family structures. Have you noticed the difference between US and Danish education systems? Of course, there are some differences. In Denmark, taxes cover education costs, and once turning 18 students are actually paid to attend school. Teenagers attend â€Å"high school† until approximately age 19. Often students take a gap year (or two) before starting at University. The biggest difference I learned about was the specificity of education in University. While I attend a liberal arts college and could have any major before applying to medical school, in Denmark students apply to university as medical students and begin studying to be a doctor right away. The students stressed that it is important to know what one wants to do prior to starting University because the education is very specific compared to the US norm. Another big difference is the language requirement. Students begin taking English in the 2nd grade and continue taking it throughout their â€Å"undergraduate† career. They also pick up either French or German around 7th grade. And what about free time? How do Danish students spend it? The Danish students I knew spent their time at school, after school activities, such as sports, and at jobs. They were all really busy during the week and did not have much free time. When they did they usually hung out with their friends and went out to clubs or parties. What about your free time? Did you lack it as well when studying in Denmark? Very much the other way, a major challenge for me was having a lot of free time and not knowing how to use it. My housing was outside of the center of Copenhagen, so as I got more comfortable with the city I began exploring my local area after classes. It is challenging to meet new people and ask them to explore with you when you first arrive in a new place. The most memorable moments of your Denmark life period The most memorable moment of my time in Denmark was with my visiting family. The youngest son had turned 13 and I went to an amusement park with their family for the day to celebrate. After visiting the park we went to their cousin’s house for dinner. There were three different families with children of all ages, so after dinner we sat down and watched a movie on netflix. I picked out White Chicks because no one had seen it and I thought the teenagers would enjoy it. What was most memorable was how we actually watched the movie: A few minutes into the movie I realized that although the older children were all fluent in English, and the film had Danish subtitles, the youngest children did not yet know how to read, or at least read quickly enough to watch a movie via subtitles. The 16 year old daughter read the subtitles out loud for the entire film so that her younger cousins could understand what was happening. I realized how lucky I am to have movies readily available to me and easily accessible to all English speakers. I was amazed at how complex watching a movie as a family could be. Your advice for the students who want to study abroad I would advise trying to immerse yourself into the culture as much as possible. I was nervous about doing a homestay and never really pursued meeting Danes my age. Taking Danish and meeting with my visiting family once a week completely made my experience, so I can only imagine how much more I would have gotten out of my experience had I dug slightly deeper into the culture. Are you ready to follow the advice of our charming interviewee and consider studying abroad? Or maybe you have any questions to ask? Write comments and share your opinions here!

ARGUMENTATIVE Essay Example | Topics and Well Written Essays - 500 words

ARGUMENTATIVE - Essay Example Recently a man took out a billboard saying his ex-girlfriend was a murderer for aborting his child. The man had no legal recourse to make his ex-girlfriend to carry his child to term. Fathers have no say in whether a child can be born or aborted. If a woman decides to have a child, the man is stuck paying child support. This is considered to be his responsibility for creating a child. Men that do not want a child cannot request for their mate to have an abortion. They are stuck with the child. It is considered that the man played he should pay. Women are not held to the same standard. If a woman plays, she can abort the child and not pay. This does not seem fair. Another aspect of this issue is because a woman can decide what to do with her body she can drink, take drugs, or have an unhealthy lifestyle. If a baby is born on crack, has birth a defect due to drugs or alcohol, or other problems, the man still has to pay. A man with a good job, health insurance, or money will have to fund the child for life. The woman’s decision will dictate the man’s finances and time without his input. The baby will also either go directly into the man’s custody or state custody. The man will have no choice in the matter. Birth defects can also be another issue. If a woman wants to abort a Down syndrome baby, a baby with heart problems, or other defects the man has no choice. However, if the woman decides to have the baby, the man once again has to pay. A woman choses whether or not to bring an afflicted baby into the world. One way to rectify this injustice is to allow men to have an input on abortions. This solution is not viable. The Supreme Court ruling in ‘Roe vs. Wade’ made clear that a woman’s body is her own. A man cannot force a woman to carry his child. This is not medieval times. A man having input into an abortion is not legal under the law. It probably would not become legal. This solution would not work. Another solution would be to

Pricing of derivatives on mean-reverting assets. Are stock prices and Essay

Pricing of derivatives on mean-reverting assets. Are stock prices and returns are mean reverting or not - Essay Example 15 3.6 Data Analysis Methods †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 16 3.7 Summary †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 16 CHAPTER 4 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.†¦Ã¢â‚¬ ¦. 17 FIGURES †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦...†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 17 4.1 Definition of mean reversion stock prices †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.†¦Ã¢â‚¬ ¦.. 17 4.2 Permanent and transitory price com ponents †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 17 4.3 Properties of multi-period returns †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.†¦Ã¢â‚¬ ¦... 18 4.4 One-period returns †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦....†¦..†¦. 19 4.5 Multi-period returns †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 20 4.6 Higher-order AR model †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.... 22 4.7 The relation between mean reversion and covariance stationary †¦...†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 23 CHAPTER 5 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 25 5. Mean reversion and mean-variance efficient portfolios †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 25 5.1 Outline †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 25 5.1.1 Expected returns and volatilities of stocks and bonds †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦... 25 5.1.2 Correlation between stock and bond returns †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 26 5.1.3 Risk-free yield curve †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 26 5.1.4 Variance ratio of permanent and transitory returns †¦Ã ¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.†¦Ã¢â‚¬ ¦.. 26 5.2 The role of the variance ratio... Although the mean-reverting price process defined later by Equations (1), (2), and (3) may seem restrictive, they are more general than is apparent at first sight. This generality explains the model’s suitability as a tool for describing the mean reverting behavior of stock prices. To allow the price process to be consistent with the efficient market hypothesis, the random walk should lie nested in the specification for the stock price (Frankel, 1995, 140). This explains why the permanent price component in the first equation lies chosen to be a random walk. The price process in Equation (1) follows a random walk for à ¸= one, but deviates from the efficient market hypothesis for zero A seemingly more general specification defines zt with regard to the first equation as a covariance-stationary, mean-reverting process with mean 0.But every covariance stationary series can stand written as a moving average (MA) process of infinite order. If the MA process is invertible, it can be written as an AR process of infinite order, which brings us one-step closer to our AR (1) process. The only restrictive aspect of the first-order AR process is its order. We may therefore want to consider a generalization of the previously considered mean reverting price process by relaxing the assumption of a first order AR process for the transitory price component. Instead of an AR (1) process we could assume an AR (p) process as approximation of an AR process of infinite order, for any p= one, 2†¦ (Bekaert, 1999, 65).