StatisticalTools for Financial Research
StatisticalTools for Financial Research
Statisticaltools are developed for analyzing various types of data (Aït-Sahalia& Hansen, 2011).These methods vary in nature such that while some are simple whileothers are complicated and are designed for specific purposes.Analytical work entails the comparison of data to derive the levelsof errors or bias and the precision of the data. According to Siino,Fasola & Muggeo (2016), theimportance of statistics is that it can organize and simplify thedata, hence allow the users to derive some crucial information fromthe data set. The findings of the analysis process are recorded andare easy to retrieve. Any organization that wishes to detect andquantify the errors and other aspects of their financial records mustuse the statistics tools to analyze their data. While conducting theanalysis, some assumptions are made, which include the consistencyand the normality of the distribution of data. The basic parametersused are the mean and the standard deviation (Chatterjee,2014).
Thepublic finance records for a domestic organization can be analyzedusing the F-test statistics (Darwish,Samhan & Helmy, 2011).This method is used for comparing two sets of data that have a normaldistribution from the same or different populations. The procedurefor conducting this test involves the comparison of the differentstandard deviations and means respectively. The first step ofperforming the analysis comprises the construction of a hypothesis(Chatterjee,2014).The null hypothesis indicates that there are no significantdifferences between the sets of data. It implies that the differenceis so small such that it does not exceed the critical value in thetables (Siino,Fasola & Muggeo, 2016).
Consideringthe side of inclination of the standard deviations is important(Darwish,Al Samhan & Helmy, 2011).For instance, if the computation were testing on the differencebetween two data sets, then the test would be two-sided, but if itwas comparing the value of one data set against the other, then itbecomes a one-sided test. The two- tailed analysis is the most commoncase (Chatterjee,2014).While conducting the investigation of public finance records for adomestic organization, we can use the two-sided approach to determinethe difference between two data sets. However, if the statisticiansuspects that the mean and the deviation will move in one direction,for instance after the analytical procedure changes, then thesingle-tailed test is the most applicable.
Theconfidence interval of the two- tailed test is divided over the twotails of the normal distribution curve (Oleson,Cavanaugh, Tomblin, Walker, & Dunn, 2014).For instance, if the error alliance was at five percent, then eachrear accommodates 2.5% error allowance. For the one-tailed test, theerror adjustment remains at 5 percent for only one tail of theGaussian curve. The different probabilities in the tests arerepresented in the critical value tables, where a 95% confidenceinterval for a single-sided table is similar to 90% confidenceinterval of a two-sided table (Chatterjee,2014).
TheF-test is a comparison of two variances where the larger differenceis always the numerator (Siino,Fasola, & Muggeo, 2016). These variances are two independent Chi-square elements that aredivided by their degrees of freedom (Siino,Fasola & Muggeo, 2016).If the data has no significant differences, then their variancesshould not differ significantly, and their ratio should revolvearound a singularity. The calculated "F" is compared to thecritical "F" from the tables. It is necessary to computethe applicable degrees of freedom for the variances, to derive thecritical value. The degrees of freedom are calculated by eliminatinga single element from the total sample (j-1), where “j” is thecomplete number of items in the sample (Aït-Sahalia& Hansen, 2011).If the calculated "F" is less than the critical "F"at 95% confidence interval, then one can conclude that the differenceis insignificant and hence the null hypothesis is accepted. However,there is still a five percent chance that this conclusion iserroneous (Siino,Fasola & Muggeo, 2016).The confidence interval is not fixed at 95% it varies with thespecifications and the sensitivity of data being analyzed.
Anorganization may prefer to use the t-statistics. The main differencesbetween the t- statistics and the F-statistics are that t-test usesthe mean, while the F-test uses the standard deviation (Aït-Sahalia& Hansen, 2011).The t-statistics is majorly a measure of bias. Based on the nature ofthe data sets, the "means" can be compared to errors byseveral types of the test deviation (Chatterjee,2014).The common types of t-test include the student’s t-test used forthose data sets with similar standard deviations, the Cochran variantof the t-statistics, used when the standard deviations of the datasets are entirely different (Darwish,Samhan & Helmy, 2011).The other type of t-test is the paired test useful for the dependentsets of evidence. Just like the f- test, if the calculated "t"does not exceed the critical value, then there are no significantdifferences and the null hypothesis is accepted.
Accordingto Chatterjee(2014), themajor advantage of the F-test is that it is an omnibus analysis,which observes reasonable family wise error ratios while testing thehypothesis. On the other had t-tests increase the probability ofcommitting errors. The advantage of using the t-statistics is thatone does not require large sample sizes as every element takes partin all the tests. T-statistics is important as it allows adequatecontrol of individual differences as the random error is quite small.
BerkshireHathaway Inc. may choose to use the Ratio Analysis method to assessthe performance of the firm and assess the functioning of its vitalsectors. The Ratio Analysis is classified into liquidity ratios,market value ratios, asset ratios, credit rates and the profitmargins (Oleson,Cavanaugh, Tomblin, Walker, & Dunn, 2014).The calculation of rates allows the comparison of the firm to othercompanies in different performance aspects
TheClinton Foundation may apply the Common Size Ratios to analyze itsfinancial statements at various periods of time. Standardizedfinancial statements are created through classification of items intodifferent categories based on the same unit of measure (Siino,Fasola & Muggeo, 2016).The Common Size Ratios display the trends of the company performance,and can be used as a comparison tool for other businesses. Tocalculate the Common Size Ratio, one has to rate the item of interestagainst the object of reference. In many instances, the Common SizeStatements are prepared for the financial accounts and the balancesheet, and the values are expressed as a percentage of total revenueand cost respectively (Chatterjee,2014).
Themethods of accounting analysis encounter various limitations. Ratioanalysis has a shortcoming arising from its dependence on accountinginformation (Darwish,Samhan & Helmy, 2011).Distortions may occur in the financial statements due to such factorsas inflation and Historical Cost Accounting. Ratio analysis may omitsignificant aspects of the company’s progress, and if used alone itmay distil a lot of information into a series of numbers, giving theinstitution a simplistic view. Therefore, ratio analysis should beapplied in the initial financial assessment, aiming to compute thefirm’s performance and investigating areas that require furtherimprovements. Just like any financial statements, the Common SizeRatios are subjected to the limitations arising from the data used(Chatterjee,2014).Some of the data limitations include the difference in datacollection methods among the firms and the use of differentaccounting period.
Aït-Sahalia,Y. & Hansen, L. (2011). Handbookof financial econometrics tools and techniques.Amsterdam: North-Holland/Elsevier.
Chatterjee,R. (2014). Practicalmethods of financial engineering and risk management.[New York, N.Y.]: Apress.
Darwish,S., Al Samhan, A., & Helmy, H. (2011). Statistical Wear Model forAdhesively Bonded Tools.AMR, 264-265,1802-1811.http://dx.doi.org/10.4028/www.scientific.net/amr.264-265.1802
Oleson,J., Cavanaugh, J., Tomblin, J., Walker, E., & Dunn, C. (2014).Combining growth curves when a longitudinal study switchesmeasurement tools. StatisticalMethods In Medical Research.http://dx.doi.org/10.1177/0962280214534588
Siino,M., Fasola, S., & Muggeo, V. (2016). Inferential tools inpenalized logistic regression for small and sparse data: Acomparative study. StatisticalMethods In Medical Research.http://dx.doi.org/10.1177/0962280216661213