GARCH models have been commonly used to capture volatility dynamics in financial time series. A key assumption utilized is that the series is stationary as this allows for model identifiability. This however violates the volatility clustering property exhibited by financial returns series. Existing methods attribute this phenomenon to parameter change. However, the assumption of fixed model order is too restrictive for long time series. This paper proposes a change-point estimator based on Manhattan distance. The estimator is applicable to GARCH model order change-point detection. Procedures are based on the sample autocorrelation function of squared series. The asymptotic consistency of the estimator is proven theoretically.

The limit theory of a change-point process which is based on the Manhattan distance of the sample autocorrelation function with applications to GARCH processes is examined. The general theory of the sample autocovariance and sample autocorrelation functions of a stationary GARCH process forms the basis of this study. Specifically the point processes theory is utilized to obtain their weak convergence limit at different lags. This is further extended to the change-point process. The limits are found to be generally random as a result of the infinite variance.

Poverty and its alleviation schemes remain to be of much concern to many countries in the world. In the Sub-Saharan Africa, 41% of the population live below the extreme poverty line and in Kenya, almost 80% of the population are deemed poor. The Kenyan rural sector has a contribution of 40% to this poverty levels despite agriculture being the backbone and the main source of livelihood in the rural areas. It is in this regard that the study evaluates the household characteristics effect on Poverty indices among Crop Farmer Households. The Beta and Dirichlet regression models were used in the analysis in which the Beta regression model gave a better fit to the poverty indices data. The standardized residuals, probability plots, Chi-square test of association and the Breusch Pagan test for heteroscedasticity were used as goodness of fit evaluation tests in which levels of deprivation had a significant effect on the poverty indices among the crop farmers. Data used in the study was secondary data obtained from the Kenya National Bureau of Statistics Survey Consumption Index in Uasin Gishu County for the period March 2018 to May 2018 in which a total of 489 households were employed in the survey.