Abstract: The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.
Abstract: The paper evaluates several hundred one-day-ahead
VaR forecasting models in the time period between the years 2004
and 2009 on data from six world stock indices - DJI, GSPC, IXIC,
FTSE, GDAXI and N225. The models model mean using the ARMA
processes with up to two lags and variance with one of GARCH,
EGARCH or TARCH processes with up to two lags. The models are
estimated on the data from the in-sample period and their forecasting
accuracy is evaluated on the out-of-sample data, which are more
volatile. The main aim of the paper is to test whether a model
estimated on data with lower volatility can be used in periods with
higher volatility. The evaluation is based on the conditional coverage
test and is performed on each stock index separately. The primary
result of the paper is that the volatility is best modelled using a
GARCH process and that an ARMA process pattern cannot be found
in analyzed time series.