New Article Reveals the Low Down on Critical Essay Samples and Why You Must Take Action Today

<h1> New Article Reveals the Low Down on Critical Essay Samples and Why You Must Take Action Today </h1> <p>Bear as a main priority you ought to consistently apply basic speculation in such an exposition. It might even be helpful to have someone else read your article to make certain it is easy to grasp and locks in. You have to see how to urge perusers to continue perusing. The ability of incredible article composing is so as to fundamentally talk about and survey thoughts inside a set up word limit. </p> <p>For numerous understudies, it's more straightforward to make their own one of a kind crucial exposition should they have a prosperous model. Numerous understudies must make this sort of paper, yet a great deal of them have zero thought how to create an essential investigation article appropriately. 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Writing Children Essay Topics

<h1>Writing Children Essay Topics</h1><p>When it comes to composing kids' paper points, they ought to be about any subject that intrigues them. It doesn't make a difference on the off chance that they are in primary school or undergrads, they ought to have some enthusiasm for their point. It might appear as though the subject of the paper will be the most significant part of composing the task, however recall that the understudies may not feel that they are being engaged with the theme enough.</p><p></p><p>In request to help ensure that your kids exposition points are not exhausting, you might need to begin by narrowing down your choices. Do you realize what sort of books have your kid as an aficionado of? Do you realize what sort of magazines he has perused? These inquiries may assist with narrowing down your choices.</p><p></p><p>The next thing you need to do is compose a couple of short passages talking about what y our youngster considers the point. You may likewise need to give a few connects to sites where he can go to become familiar with the theme. In the event that your youngster is into computer games, at that point he may think that its simpler to relate the subject to video games.</p><p></p><p>When you ask your kid to clarify for what valid reason he feels a specific way, you might need to concentrate on his perspective and your perceptions about the world. Be that as it may, you would prefer not to confine the length of your exposition and simply give a ton of spellbinding words. Give fascinating realities about the subject and give a few stories as well.</p><p></p><p>Remember that the objective for your kids' paper points is to assist them with getting a thought regarding the point. They dislike the subject all that much however they might be keen on what they are perusing. The educator doesn't have to stress over them doing inadequatel y in the event that they simply read the paper and comprehend it.</p><p></p><p>Another thing you might need to recollect is that youngsters exposition points ought to be based on the inquiry. Attempt to think about an inquiry that your youngster may pose to himself as he peruses the paper. For instance, if your kid winds up inquiring as to for what reason does that bear has one arm?</p><p></p><p>The integral explanation behind the bear having one arm is on the grounds that it is the prevailing one, yet it can likewise be utilized to give him insurance from things that may hurt him if he somehow managed to get isolated from it. Moreover, on the off chance that he was assaulted by another bear, at that point he would in any case have the arm to safeguard himself. This is a generally excellent representation of how the paper point ought to be answered.</p><p></p><p>Once you have settled on the subject, it is essent ial to make way for composing youngsters' article themes. This implies you should explore the point altogether and afterward compose the exposition such that will make it simple for your youngster to comprehend. He should see the data obviously, however he won't need to stop and work to make sense of what you are saying.</p>

How to Choose The Best Essay Topics For Writing Papers

<h1>How to Choose The Best Essay Topics For Writing Papers</h1><p>Writing an article isn't generally a simple undertaking. It could be troublesome on the grounds that you need to invest the push to make sure that you think of successful and intriguing substance. In any case, it is as yet significant that you invest some energy to discover the best exposition points and afterward research on them. There are various sources that can assist you with discovering the best points for composing expositions so you don't come up short on subjects to compose about.</p><p></p><p>When it comes to composing papers, there are various article themes that you can look over. The most widely recognized subjects incorporate general and individual expositions, financial aspects, and promoting. You can likewise pick different subjects like wellbeing, religion, legislative issues, culture, and sentiment. Every theme has a reason and needs explicit composing styles and systems. Thus, contingent upon the topic, you can pick a point to suit your style.</p><p></p><p>One of the things that makes an article theme for an organization or a business solid is its uniqueness. In the event that the subject has a special edge, it is bound to catch everyone's eye. The central matter is that it must stand apart from the remainder of the papers that are accessible. The uniqueness of the point must be the characterizing factor in picking a decent theme. On the off chance that you don't pick the correct point, you may think that its difficult to concoct a decent composing style.</p><p></p><p>Another approach to find the best article subjects is to look through the Internet. There are a lot of online destinations that offer subjects. It is significant that you experience the site and take a gander at the points first before picking one. It is significant that you see what individuals are expounding on when they d iscover that you have remembered a similar subject for the paper that you are submitting. This will give you a thought of how novel the theme is and in the event that it can stand apart among the numerous others that are out there. The most significant point to remember is that this composing is to engage just as educate. Consequently, it is significant that you incorporate data that individuals will need to know in their own articles. Your exposition should fill the two needs according to the reader.</p><p></p><p>When you locate the best article points to compose your examination papers, the assignment is simpler. The following stage is pick the best substance for your article. It would be a smart thought to initially compose the substance in a short exposition or even two. The subsequent stage is perused the substance and choose whether or not you concur with the tone, structure, and the key focuses. You may likewise need to remember your own musings for re quest to ensure that you comprehend the material properly.</p><p></p><p>Before you present your papers, make certain to check in the event that you have picked the best article themes and that you have remembered your own contemplations and feelings for your expositions. The exact opposite thing that you need to do is to let the understudy see that you are a novice. Ensure that your substance is special, intriguing, and has some good times to it. At that point, you should simply kick back and watch the papers to see whether your expositions are up to par.</p>

The Wilkie investment model - Free Essay Example

CHAPTER THREE METHODOLOGY 3.1 Research Design The ultimate purpose in this paper was to describe and compare a number of published models, to provide some comparison of the distributions that result from them, and to determine which best suit the Ghanaian economic data. This research focuses on the strategic asset allocation models. This is because these models have the tendency to capture several investment series in a single model development procedure. The data used for the empirical analysis in this paper were taken from the Bank of Ghana data base. Yearly data were considered because the stochastic asset models used in the study (Wilkie, 1986; 1995; Whitten Thomas, 1999) used similar data frequency. The selection of the models is purely purposive and convenience. Modelsà ¢Ã¢â€š ¬Ã¢â€ž ¢ parameters are calculated using the Ghanaian economic data. Subsequently, some statistics are investigated for easy comparison of the models. This helped in identifying the best model for the Ghanaian economic data. The models considered were; (a) The Wilkie model, as described in Wilkie (1995); (b) The ARCH variation of the Wilkie model, also described in Wilkie (1995) (c) The Whitten Thomas model, as described in Whitten Thomas (1999). Before the models comparison, I also looked at the characteristics of the data in other to understand and present the nature of the Ghanaian economic variables. Statistical univariate time serie s analysis were conducted, also, basic assumptions for stochastic modelling were checked. Actuarial stochastic modelling usually follow the standard assumption that the model errors are independent and identically distributed (i.i.d.) normal random variables and that, in practice the variables used in the actuarial applications, such as the inflation or interest rate, are assumed to be autoregressive and have constant unconditional means (Sherris, 1997). The existence of unit roots in the series for models show the nature of the trends in the series. If a series contains a unit root then the trend in the series is stochastic and shocks to the series will be permanent and this can be an accumulation of past random shocks otherwise, the series is termed as à ¢Ã¢â€š ¬Ã…“trend stationaryà ¢Ã¢â€š ¬Ã‚ . An investigation concerning the unit root and stationarity of the series were also conducted. This is because trend stationary has major implications for investment models in actua rial applications (Sherris et al. 1999). The Dickey and Fuller (1979) test is employed for this purpose. 3.2 DATA Stochastic modeling requires the use of data from the past to combine with the present to model the future. For a good model, the structure should be consistent with validated or widely accepted economic and financial theory. These theories and the developed models depend on empirical data for validation. Statistically analysing the historical data provides a better insights into the features of past experience inherent in the variable that the model must capture. Good models are consistent with historical data since the parameter estimations are usually based on the historical data. The data considered were: Consumer Price Index (CPI); Ghana Stock Exchange All Share Index (ASI); Share dividend yield The 90 day bank bill yields; One year note yield Logarithms and differences of the logarithms are used in the analysis of the CPI, ASI, and dividends. The difference in the logarithms of the level of a series is the continuously compounded equivalent growth rate of the series. The time series plots are used to show the pictorial behavior of the series used in this research. 3.3 ANALYTICAL TOOLS the descriptive statistics and graph were obtained (Talk about R) Normality Test UNIT ROOTS AND STATIONARY SERIES Stationarity When we want to estimate a VAR model, an important assumption is that the historical data is stationary. This means that the properties of the process such as the mean and the autocovariances are _xed and do not depend on time t (strictly speaking the process is covariance stationary under these conditions). Stationarity is a crucial assumption for being able to describe the stochastic behavior of some variable by a single model and to be able to estimate the parameters of such a model on one sample of data. Otherwise each point in time would require another model and only one observation would be available to estimate 3.4 THE MODELS The models are explained below showing the formulae and consider the nature of the variables as modelled by the respective Authors. The formulae define how each variable is simulated and each model requires certain parameters. All the models have been calibrated from past data and the authors have generally given the values of the parameters from their fitted model, but by fitting different economic data, it requires re-calibration to derive the parameter set that are useful to the study. In order to compare the models in certain respects I shall use the same data set for the parameter estimation. 3.4.1 THE WILKIE MODEL THE WILKIE MODEL The Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s model is a cascade structure encompassing various investment series. In Wilkie (1986, 1995), the inflation series is assumed to be the driving force for the other investment series. The investment series are linked together through a vigorous study and analysis based on a mixture of statistical evidence and economic assumptions. The cascade structure of the Wilkie model and the outline are given below. Fig 3.1: Structure of Wilkie model Figure 2.1. The Cascade Structure of the Wilkie model. The parts of the Wilkie Model development in the UK included four fundamental variables, and these are: Retail price index (Q) Share dividends index (D) Dividend yield (Y) on share price index (P) Consols yield or longà ¢Ã¢â€š ¬Ã¢â‚¬Å"term government interest rate (C). Each of the variables are modeled within a cascade structure such that they are ordered from the top level to the lower levels. The values of the lower level variables depend on the lagged value of themselves and the values of the variables in the upper levels (Chao, 2007). Chao (2007) explains that the inflation rate, which is calculated from the change of retail price index, depends on its own lagged values and is placed on the top layer of the structure. The forecast of this variable depends on its historical evidence. Chao (2007) describes the dividend yield as being in the second layer, and that its prediction is based on both the historical evidence and that of inflation rate; and finally, the third layer includes dividend and consols, whose forecast are based on the historical data, that of dividend yield, and that of inflation rate. The variables of the Wilkie (1986, 1995) were modeled under the following procedures: Step one, the variables were modeled by the regression on the upper level variables. Then, the modelsà ¢Ã¢â€š ¬Ã¢â€ž ¢ residuals were tested and constructed through the standard Boxà ¢Ã¢â€š ¬Ã¢â‚¬Å"Jenkins univariate time series modeling method. Next, he tested other methods such as Vector Autoregressive (VAR) modeling of two correlated variables, and GARCH modeling for the variance of residuals. Formulae a. The Price Inflation Model. Inflation, as measured by the retail prices index (CPI), is modelled by a first order auto regressive (AR (l)) process. Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s AR (1) price inflation model is of the form: Where is the force of inflation over year (t-1) to (t) and it is given as: Hence: That is is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where QMU, QA and QSD are parameters to be estimated. This model is described as that, each year the force of inflation is equal to its mean rate (QMU), plus a percentage of last years deviation from the mean (QA), plus a random innovation which has zero mean and a standard deviation of QSD (Wilkie, 1986). The assumption is that, inflation, being the factor of economic uncertainty, depends only on past values of itself. There is significant autocorrelation at lag 1, which provides stati stical justification for inclusion of the variable, and no other economically plausible autocorrelation or partial autocorrelation is significant at 95% (Whitten Thomas, 1995). The AR (1) model of the force of inflation is a statistically stationary series (i.e. in the long run the mean and variance are constant), of a b. Share Yields model Share yields are modelled as a function of the current inflation rate and the history of their past trends. The Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s AR (1) model of the share dividend yield is given as: That is, is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, YMU, YA, YW and YSD are parameters to be estimated. This model uses logarithmic transformed dividend yield, as the response variable. Wilkie (1995) described the model as that, at any date the logarithm of the dividend yield is equal to its mean value (ln YMU), plus a pe rcentage of its deviation a year ago (YA) from the mean, plus an additional influence from inflation (YW) times the force of inflation in the previous year, plus a random innovation which has zero mean and a standard deviation of YSD. c. The Dividends model The model for share dividends, where is the value of a dividend index on ordinary shares at time t, is give as: Defining as the logarithm of the increase in the share dividends index from year to year , the Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s MA(1) dividend yield model can also be represented as: Where, . Hence, Wilkie (1985,1995) modeled for P(t), the value of a price index of ordinary shares at time t as: Or . That is, is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, DMU, DB, DW, DX, DSD, DY and DD are parameters to be estimated. Wilkie (195) described the model in words as: à ¢Ã¢â€ š ¬Ã…“in each year the change in the logarithm of the dividend index is equal to a function of current and past values of inflation, plus a mean real dividend growth (which is taken as zero), plus an influence from last years dividend yield innovation, plus an influence from last years dividend innovation, plus a random innovation which has zero mean and a standard deviation ( DSD).à ¢Ã¢â€š ¬Ã‚  d. Long Term Interest Rate The long term interest rate model is for the Consols yield The model is based on , which is adjusted the long memory effect of inflation rate. The Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s AR(1) consols yield model is presented as: This part is an exponentially weighted average of current and past price inflation, standing the expected future inflation over the life of the bond. This is a zero-mean AR (1) process which is independent of price inflation, and controls the long-term real interest rate. That is, is a series of independent, identica lly distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, CMU, CW, CA, CSD, and CD are parameters to be estimated. The model is composed of two parts: an expected future inflation and a real yield (Sahin, et tal.). The portion representing the inflation part is modelled as a weighted moving average whiles the real part is modelled is an AR (1) with a contribution from the dividend yield. The parameter, CW = 1, which implies that, the model takes into account, the à ¢Ã¢â€š ¬Ã…“Fisher effectà ¢Ã¢â€š ¬Ã‚ , in which the nominal yield on bonds reflects both expected inflation over the life of the bond and a à ¢Ã¢â€š ¬Ã¢â€ž ¢realà ¢Ã¢â€š ¬Ã¢â€ž ¢ rate of interest Sahin, et tal.). Wilkie (1995) defines the logarithm of the real interest component as a linear autoregressive order one or three AR (1) or AR (3) but preferred the AR (1) model. e. Short Term Interest Rate (Bank Rate) Aside the fundamental parts of the Wilkie model, I consider one of the subsequent variables modelled by wilkie (1995). Wilkie used bank rate or bank base rate series to model short-term interest rates. Short-term interest rates are clearly connected with long-term ones. Wilkieà ¢Ã¢â€š ¬Ã¢â€ž ¢s approach was to model the difference between the logarithms of the difference of these series where is the value of bank rate at time t. That is, is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, BMU, BA, and BSD, are parameters to be estimated. 3.4.2 THE ARCH MODEL The Wilkie ARCH Model The initial model developed by Wilkie (1986) assumed that the residuals of the inflation model were normally distributed. In 1995, he re-examined his own model and observed that the residuals were much fatter tailed than a normal distribution. In Statistics and Econometrics, one of the ways to model these fat ta iled distributions is using an Autoregressive Conditional Heteroscedastic (ARCH) model (Engle, 1982). In an Autoregressive Conditional Heteroschedastic (ARCH) model, the variance of the innovation term is modelled as a separate process (rather than assumed to be constant) (Wright, 2004). After the re-examination of the historical data, Wilkie (1995) proposed an ARCH model for the standard deviation of the inflation model. The ARCH model was seen to describe the data better than the original model by Huber (1997) and was suggested that, it should generally be used in applications of the model, unless the ARCH effect is not significant for those particular applications. In this ARCH model the varying value of the standard deviation, QSD(t), is made to depend on the previously observed value of the principal variable, I(tà ¢Ã‹â€ Ã¢â‚¬â„¢1), which itself is modelled by an autoregressive series. The suggested model (with a slight alteration in the notation) was: That is, is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, QMU, QA QSA QSB, and QSC, are parameters to be estimated. This implies that the variation depends on how far away last yearà ¢Ã¢â€š ¬Ã¢â€ž ¢s rate of inflation, , was from some middle level, QSC (similar to the mean, QMU), but with the deviation squared, so that extreme values of inflation in either direction would increase the variance (Sahin, 2010). Comparing the ARCH model to the initial autoregressive model showed that, the distribution of the force of price inflation) exhibits fatter tails and a greater concentration around the long-term mean value (Wright, 2004). The ARCH variation was incorporated in only the price inflation model. Therefore, the remainder of the series follow the modelling as in the initial Wilkie model since Wilkie (1995) found no basses to re-model them as ARCH models. The ARCH mod el appears to give a better representation of inflation than the models assuming constant variance. 3.4.3 THE WHITTEN AND THOMAS MODEL Whitten and Thomas model The main underpinning belief for this model is that, à ¢Ã¢â€š ¬Ã…“the economy behaves differently in times of hyperinflation, than it does in times of normal inflation levelsà ¢Ã¢â€š ¬Ã‚  Whitten Thomas (1999). This belief is non-linear in nature and hence could not have been modelled linearly. After vigorous exploration of several alternative, Whitten Thomas (1999) adapted the Wilkie model (linear model) to incorporate their non-linearity assumption, rather than fundamentally changing the whole formulation. Whitten Thomas (1999) did not model the heteroscedastic nature of the price inflation using the ARCH model as in Wilkie (1995) due to the challenges in estimating the model since and that it can give rise to troubling results from simulation. Whitten Thoma (1999) employed the threshold modelling techn ique since threshold models are also capable of representing conditional variance, and moreover, exhibit short-term changes in mean. They proposed two regimes for each of the variables. The processes in each regime are similar to those defined by Wilkie (1986;1995). Following the same cascade structure above, the formulae for the models are given below: The Price Inflation Model Inflation is assumed to be represented as a SETAR (self-exciting threshold autoregressive) model, with delay 1, and a threshold that differentiates between normal and high inflation. They fitted many different threshold models. Due to the paucity of data partitioned into the upper regime, it was difficult to postulate any sort of autocorrelation structure in the hyperinflation regime Whiten Thomas (1999). The final suitable for threshold model for the price inflation is SETAR (2; 1, 0), thus: That is is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where QMU1, QA1, QSD1, QMU2, and QSD2 are parameters to be estimated. The model is described as that if the inflation in the previous year was below a certain threshold (QR), then the expected force of inflation () is equal to its mean (QMU1), plus a percentage of last yearà ¢Ã¢â€š ¬Ã¢â€ž ¢s deviation from the mean (QA1) plus a random innovation which has zero mean and standard deviation QSD1. Conversely if the inflation in the previous year was above the threshold, then the expected force of inflation presently is equal to its mean (QMU2), plus a random innovation which has zero mean and standard deviation QSD2. The model is able to control heteroscedasticity in a way because the expected variance of inflation when it is in its excited phase is greater than when it is in its quiescent phase Whitten Thomas (1999). The dividend model Following Wilkie (1986, 1995), Whitten Thomas (1999) also represented the share d ivided series as moving average of order one (MA (1)). Defining as in the Wilkie model as the logarithm of the increase in the share dividends index from year t-1 to t, this model is similar to the Wilkie model but with the introduction of a normal and a high inflation regimes. In economic sense, dividends do better in times of normal inflation, than in times of high inflation therefore, the model employs the condition that The model for is of the form: Where, That is is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where Where, DMU1 DMU2, DB, DW, DX, DSD, DY and DD are parameters to be estimated. The share yield model Our share yield model is different to Wilkie.s lnY(t) in that we include a transfer effect from à ¢Ã‹â€ Ã¢â‚¬ ¡lnC(t) to YN(t). lnY(t) was re-estimated a TAR model, with extra parameters YY1 and YY2, to include this transfer, i.e. where, That is, is a series of independent, identically distributed unit normal variates, (the assumption is that, they have zero mean and unit standard deviation). Where, YMU, YA, YW and YSD are parameters to be estimated. consol It is not easy to estimate the exponential smoothing parameter, CD, for each regime in C(t). There are problems when using a more sensitive smoothing parameter, in that {C(t) . CM(t)} 0, i.e. we cannot allow a negative real interest rate. It seemed a necessary simplification to have the allowance for expected future inflation over the life of the bond (CM(t)), and hence the parameter CD, defined the same for each regime. It therefore follows that, like the Wilkie model, our model gives a unit gain between inflation and interest rates. 4.4.6 C(t) was then re-estimated as a TAR model, i.e. short term interest rate BD(t) was re-estimated as a TAR model, i.e. 3.5 COMPARISON OF T HE MODELS 3.6 Parameter estimation 3.7 Simulation procedure