On the Kaiser-Meier-Olkin’s Measure of Sampling Adequacy

The paper examines the suitability of the Kaiser-Meier Olkin’s Measure of Sampling Adequacy (KMO) as a measure of suitability for factor analysis for a number of selected multivariate datasets. It first explores a systematic approach that determines the initial dimensionality of the dataset. It then identifies two sets of indicators that could create distortions in assessing factor-suitability: variables that do not influence any dimension; and those that influence multiple dimensions. Dimensionality is also affected by negatively correlated indicators leading to a small suitability measure, which portrays such datasets as unsuitable for factor analysis. It is found that for KMO to be high, the zero- and first-order partial correlations must be almost the same for indicators that influence the same dimension. It follows that generally, a KMO value within the range 0.6 – 0.7 is a typically good measure of factor-suitability. The results show that the overall KMO generally reflects factor-suitability. The study does not find the expected intuitive relation that should exist between the individual KMO value and the communality for a suitably selected factor solution. A high variable KMO appears to be associated with moderate value of coefficient of multiple determination of its model in terms of the others. A reasonable assessment of the KMO should therefore be made only by a good understanding of the correlation structure of the indicator variables. Keywords: KMO, Factor-suitability, Factor analysis, Dimensionalit

Generalized Autocorrelation Function of Stationary Higher Order ARMA Processes: Application to Pandemic Data

The Autocorrelation Function (ACF) of a time series process reveals inherent characteristics of the series that may not be visible from the original series. The ACF of the ARMA(p, q) process has been presented in a few studies in understandably rigorous and laborious manner with no explicit form of the function. In this study, the approach of autocovariance generating functions (acvgf) is used to obtain an explicit expression for a series that follows a linear process under condition of distinct real roots of the AR(p) lag operator polynomial. The technique is used to derive ACFs of processes as far as ARMA(2, q) for any value of q and subsequently states results for specific ARMA(3, q) processes. The procedure has shown a clear connection among autocovariances at consecutive lags of the respective process as well as among consecutive orders of the process at particular lags. The derived approach which is applied to daily new Covid-19 cases for countries with stationary series obtains the same results of damp exponential decay in each case as that based on "ARIMAfit" function in R. The results provide useful relations that may be utilized as diagnostic tests for determining whether a given data follows a specified linear process.Keywords: Autocovariance generating function, linear process, theoretical autocorrelatio

On the Exponential Power Distribution

The paper examines the nature of the exponential power distribution (EPD) in terms of its location, µ, scale, β and shape, σ, parameters. It establishes conditions under which the distribution is legitimate and reliable. It derives among others the moment and kurtosis of the distribution as well as the maximum likelihood estimators of the parameters. It then uses data on health to assess the departure of the distribution from normality. Three main softwares are used, namely; EasyFit, MATLAB and Minitab. In the application, we find that the EPD, for some values of , significantly fits Weight, Height and Body Mass Index out of seven variables covered. We deduce that the EPD would be inappropriate for fitting asymmetrical datasets, since the variables which are not significant are found to be highly skewed. Keywords: Exponential power distribution, Kurtosis, Legitimacy, Statistical Distribution

Empirical Similarity-Based Approach for Selection of Unit Root Test

The existence of unit roots in time series processes can impair the choice of techniques for analysis and forecasting time series data. It is of much importance in econometric modelling to determine the integration number of analyzed time series based on unit root tests. Though statistical theory provides broad range of unit root tests in standard softwares, the choice of an appropriate test highly depends on subjective assessment of the analyst. This paper considers similarity-based scoring approach for selecting the most appropriate unit root test for specific type of time series observations based on Chi-square statistic and which is able to reduce subjectivity. Six unit root tests are studied. The utility of the proposed method is illustrated in simulation. The most reliable test, which is found is applied to a real time series of some selected macroeconomic variables. Keywords: Time series, Stationarity, Unit root, Integration order, Chi square statisti