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This chapter proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. It proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method that demonstrates the ability to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is implemented in order to analyze a real-time series, namely, the foreign exchange rate between the Australian dollar and the South Korean won.

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Based on surface temperature and the normalized difference vegetation index (NDVI), we calculated the temperature vegetation dryness index (TVDI). Using the relationship between TVDI and NDVI, we established a vegetation-soil moisture response model that captures the sensitivity of NDVI's response to changes in TVDI using a linear unmixing approach, and validated the model using Landsat Thematic Mapper (TM) images acquired in 1997, 2004 and 2006 and a Landsat Enhanced Thematic Mapper Plus (ETM+) image acquired in 2000. We determined the correlations between TVDI and field-measured soil moisture in 2006. TVDI was correlated significantly with soil moisture at depths of 0 to 10 cm and 10 to 20 cm, so TVDI can be used as an index that captures changes in soil moisture at these depths. By using fractional vegetation cover (FVC) data measured in the field to validate the estimated values, we estimated mean absolute errors of 0.043 and 0.137 for shrub and grassland vegetation coverage, respectively, demonstrating acceptable estimation accuracy. Based on these results, it is possible to estimate a region's FVC using the linear unmixing model. The results show bare land coverage values distributed similarly to TVDI values. In mountain areas, grassland coverage mostly ranged from 0.4 to 0.6. Shrub coverage mostly ranged from 0.4 to 0.6. Forest coverage was zero in most parts of the study area.