Abstract
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.
Highlights
Empirical observation made in Econometrics and applied financial time series literature for long time horizons reveal that log-returns of various series of share prices, exchange-rates and interest rates depict unique stylized features
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 following proposition is our main result on weak convergence for our proposed change-point process Dnk (h) as specified in (6) for GARCH processes based on the point process theory
Summary
Empirical observation made in Econometrics and applied financial time series literature for long time horizons reveal that log-returns of various series of share prices, exchange-rates and interest rates depict unique stylized features. The log-return data cannot be modelled by one particular GARCH model over a long period of time [3] They observe that in real financial time series the effect of non-stationarity of log-return series can be seen by considering the sample autocorrelation function of moving blocks of the same length as the estimates seem to differ from block to block. They suggest the use of change-point analysis of financial time series modelled by GARCH processes with parameters varying with time. The limiting distribution of Dnk is derived for a stationary GARCH sequence
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