Forecast on Dow Jones Stock Price Index

Forecast on Dow Jones Stock Price Index

Abstract

It is hypothesized that price charts can be observationally categorized into two parts, namely random and non-random. The non-random segment, which can be treated as around customary conduct of the prices (trend) in an epoch, is a geometric line. Therefore, the random segment varies around the non-random portion with different amplitudes. Besides, the state of a trend in an epoch might be diverse in another epoch. It is further hypothesized that statistical evidence can be found for different relations between a few sorts of trends and the course of the following developments of the prices. These hypotheses are tried on the verifiable information of the DJIA (Dow) and affirmed. In addition, it is statistically demonstrated that various trends that have happened in the close past course of the Dow can be used to foretell the distant eventual fate of the index. Therefore, there is an upcoming recession in the DJIA, which may predict an overall monetary emergency.

In this thesis, the historical changes in the Dow Jones Industrial Normal index are analyzed. The distributions of index changes over short to direct length exchanging interims are found to have tails that are heavier and can be represented by a normal process. This distribution is better spoken to by a blend of normal distributions where the blending is concerning the index volatility. It is demonstrated that distinctions in distributional assumptions are adequate to clarify terrible showing of the Dark Scholes model and the presence of the volatility grin. The alternative evaluating model displayed here is less difficult than autoregressive models and is more qualified for useful applications.

Introduction

It is realized that the DJIA is the most established and most voluminous index of the NYSE, which is the most seasoned stock exchange. Therefore, the Dow can be viewed as an applicable agent of the world market. Subsequently, this index merits concentrating with the point of comprehension of the past, present and particularly, forecasting the fate of the world economy. Fortunately, various quantitative methods have been proposed and utilized in writing for statistical finance, likewise called econophysics, with the point of exploring different parts of value outlines.  However, the capacity of those methods to figure what’s to come costs isn’t checked logically. In addition, no scholarly accord is set up on the answer to the inquiry whether the arrangement of general values can be estimated, which has been a significant issue in the motivation of the researchers for about a century. The pursuer has alluded to the accompanying papers and books for far-reaching thinks about various econophysics methods, for example, the productive market theory and specialized examination. It ought to be noticed that a number of known methods and new ones will be utilized in this work.

Research objective

General objective

Establishment of linear regression analysis on Dow Jones stock price index.

Specific objective

To do a multiple linear regression analysis on the Dow Jones stock price index.

To establish a relationship between Dow jones stock price which at this point is the independent variable (Y) and the independent variables (X) which include real disposable income, the unemployment rate, the federal funds rate and finally the dummy variable.

Value of study

The study is essential to scholars by addition to the existing body of knowledge on leveraging knowledge on Dow Jones stock price index. It analyses two variables the dependent and the four independent variables.

Hypothesis

• There is no relationship between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable.
• There is no significant difference between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable.

Literature

Past research ponders analyzed stock index composition changes and battle that the index changes are identified with brief downward-sloping demand curves (value pressure), long-run downward-sloping demand curves (i.e., defective substitutes), liquidity costs, data content/condition, and financial specialist acknowledgement/shadow costs. The value pressure theory recommends that index composition changes are related to brief request irregular characteristics. Noteworthy request streams produced by a transient change in security demands can bring about brief stock value deviation from its harmony level. Be that as it may, in a semi-solid proficient stock market, the impact of such demand “stuns” ought to be ingested rapidly and ought not to cause long-term changes in the degree of the stock costs. Thus, the value pressure speculation predicts just short-run changes in share costs and exchanging volumes of included (erased) stocks. Thus, the price pressure hypothesis predicts just short-run changes in share prices and exchanging volumes included (erased) stocks.

Harris and Gurel (1986) and Lynch and Mendenhall (1997) archives proof indicating brief changes in stock prices following the S&P 500 List changes declarations. The adjustments in prices are non-changeless and return to pre-consideration (or pre-cancellation) levels.

Shleifer (1986) and Kaul, Mehrotra, and Morck (2000) find that the occasion time abundance returns related to index changes are not transitory. The abnormal returns reported after index component changes don’t return, and stock prices move to a higher (lower) level for index augmentations (erasures) on a lasting premise. Shleifer (1986) characteristics the long-term changes in security prices to perpetual changes in the interest for the stock once it enters or exists the S&P 500 Index.

Further Wurgler and Zhuravskaya (2002) fight that security exchange chance is a significant factor that determines overabundance returns watched at the point when a stock is added to or erased from a market index. At the end of the day, a stock with a high exchange hazard.

Amihud and Mendelson (1986) fight that the necessary pace of return for a stock is diminished when the trading liquidity estimated by the bid-ask spreads of the stock becomes lower. The liquidity costs contention recommends a lasting stock cost expands (diminishes) for list augmentations (cancellations).

RESEARCH DESIGN, MATERIALS AND METHODOLOGY

Introduction

We discuss methods used on the collection of data and processes adopted in accomplishing study’s objectives. We also majorly look at research design used in conducting the study, the data collection techniques used and last and not least methods used in analyzing the data

Research design

The study used a correlational research design, which was longitudinal as the study covered sixty years. Its main importance was to ccc. This is consistent with other studies such as that of Shleifer (1986) and Kaul, Mehrotra, and Morck (2000). Quantitative research depends on numerical data used on statistical routine.

Sample and Sampling procedure

The research covered a period sixty years from 1959 and2019. Convenience sampling method selected twelve months for each year. This is a reasonable way to demonstrate the relationship between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable.

Research analysis

Descriptive Statistics

We dealt with a measure of central tendency. We calculated mean, variance, standard deviation, median, maximum and minimum.

Mean

Variance

Covariance

Coefficient covariance

Correlation and Regression 

Regression analysis was used as the statistical tool to test the relationship between the dependent and the independent variables. Regression quantifies the relationship between one or more predictor variables and that of the outcome thus showing the relative effects on the factors

With the models simple and multiple regression, we can establish the values of the parameter of Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable.

Under this two types coefficient were used which included

1.      Spearman’s coefficient:

This is a type of coefficient portraying a monotone relationship between the dependent variables. A monotone relationship alludes to a relationship where the dependent variable either rises or sinks consistently as the independent variable ascents.

2. Pearson’s correlation coefficient:

This is a type of coefficient portraying the straight relationship between the dependent variables. Correlation coefficients convey information on the quality and bearing of a relationship between two consistent variables. This suggests: if state r,

1. R = ± 1: this infers there is straight and monotone relationship.
2. R = 0: this concludes there is no straight or monotone relationship.

iii. R < 0: this concludes there is a negative relationship.

1. R> 0: this concludes there is a particular relationship.

The research model estimated was general multiple regression models as follows:

Where

Now taking y which denotes the independent variable which is linearly associated to k independent variable X₁, X₂,…X_K  alongside parameters

So, y= X₁+ X₂+……………. + X_K +

The model was linear since it was linear in parameters. In many cases,  or equivalently  should depend on any.

is a linear model as it is linear in parameters.

Which is a linear parameter  and, but nonlinear is variable.

DATA ANALYSIS, RESULTS AND INTERPRETATION

 Introduction

We discuss research findings on the relationship between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable. The study took data taken over 60 years from 1959 to 2019. The data was obtained from Dow Jones stock price index.

Data analysis

Descriptive statistics were used in analysing the data to find out the relationship between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate and dummy variable. Analysis of variance tables was also used to find the significant difference of variables in the study. Microsoft Excel facilitated data coding and tabulation. Excel enabled data analyzation through both descriptive and inferential statistics. Descriptive statistics embraced percentages besides measures of central tendency, i.e. mean, variance and standard deviation. Paired t-test facilitated trough developing inferential statistics. Tables and inferential statistics also assisted in presenting the analyzed data. This helped in bringing out the relationship between the variables under study.

Discrete statistic on variable analysis

We dealt with a measure of central tendency. We calculated sum, mean, variance, standard deviation, and this was the finding.

Microsoft excel analyses output

From the findings on descriptive analysis of various variables, the study found that mean for the logarithms of Dow Jones, Real Dispensable income, Federal Fund and Unemployment were 7.98736605, 8.7569501, 1.094465878 and 1.751354031 respectively.

Regression Model (Multiple Linear Regressions Results)

Multiple Regression (Output)

ANOVA

ANOVA Analysis enabled us to determine the significance of the model, From the ANOVA statistics in figure 4.6, the processed data, which is the population parameters, had a significance level of 0% which shows that the data is ideal for concluding the population’s parameter as the value of significance (p-value) is less than 5%.

Regression Coefficients

From the findings, the following regression model was established

From the regression coefficient finding, Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate there was a significance indifference. Secondly, equating the regression model equation to zero, then.

• Dow Jones stock price index
• A unit increase in real disposable income return would lead to a decrease in Dow Jones stock price index by a factor of. A unit increase in the unemployment rate would lead to an increase in Dow Jones stock price index . A unit increase in federal funds rate would lead to the rise in Dow Jones stock price index

So clearly, it further revealed that all the variable was statistically significant as their p-value were less than 0.05

Residual output

Interpretation of Findings

It was established that variability of the Dow Jones stock price index had an average of 7. 98736605. This was clearly due to the effects of other factors which were independent. These factors included real disposable income, unemployment rate, federal funds rate. This implied that there was a relationship between the dependent variable and the independent variables. Increase or decrease of the independent variable affected the dependent variable, either positive or negatively.

There was also a significant difference between the Dow Jones stock price index and real disposable income, unemployment rate, federal funds rate.

Conclusion

In this examination, we analyzed the price pressure hypothesis using a far-reaching rundown of the Dow Jones Modern Average (DJIA) List augmentations and cancellations. We performed occasion study on stock prices and exchanging volumes encompassing the declaration and viable dates of the File part changes. Our study endeavoured to shed extra light on the effect of list exchanging methodologies (for example program exchanging, list assets, ETFs and file alternatives/prospects contracts) on the organizations that enter and leave the DJIA List. Our empirical analysis centred around the timespan (post-1959period) adhering to the Standard and Poor’s/DJ Organization’s ‘pre-declaration’ arrangement on file creation changes. This specific timespan moreover compares to the considerable development of list exchanging systems and related speculation items. It permits us to decide how financial specialists react to DJIA File options and cancellations, considering these extra-record exchanging and exchanges. Our outcomes show that record increases (erasures) experience brief expands (diminishes) in stock prices following the declaration. The abnormal returns encompassing the declarations are financially noteworthy. The two considerations and expulsions lead to brief abnormal exchanging volume increments in the post-declaration period. Truth be told, the stock prices and exchanging volumes return inside a couple of exchanging days. Our discoveries were steady with the value pressure hypothesis as the reported abnormal returns and exchanging volumes are not changeless. Future research may broaden the effect of price pressure on list considerations and evacuations by consolidating intra-day information to decide the elements of the market reaction. In light of the development in high-recurrence exchanging, the ‘second-by-second’ prices and exchanging volumes of the organizations added to and erased from the DJIA may yield extra bits of knowledge about how markets act and how new data are joined into share prices in a product market. Such research would hold any importance with both individual and institutional financial specialists.

Limitation of study

During data collection through mining, there was a limitation on the degree of accuracy of the data obtained from the secondary source. However, data was valid since it came from continuous Dow Jones Stock price index; despite this, there was still prone to these shortcomings.

The model may not be dependable due to some shortcoming of the regression models. Considering this shortcoming then, other models used to explain the various relationships between the variables.

There are also other factors Dow Jones Stock price index and even the Multiple regression model that may therefore not measurable that need to be fused with the above model to improve the research finding.

Reference

Lynch, A. W., & Mendenhall, R. R. (1997). New evidence on stock price effects associated with changes in the S&P 500 index. The Journal of Business, 70(3), 351-383.

Kaul, A., Mehrotra, V., & Morck, R. (2000). Demand curves for stocks do slope down: New evidence from an index weights adjustment. The Journal of Finance, 55(2), 893-912.

Wurgler, J., & Zhuravskaya, E. (2002). Does arbitrage flatten demand curves for stocks?. The Journal of Business, 75(4), 583-608.

Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid-ask spread. Journal of Financial Economics, 17(2), 223-249.

Amihud, Y., & Mendelson, H. (1986). Liquidity and stock returns. Financial Analysts Journal, 42(3), 43-48