Markov Switching

Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent stochastic process with limited memory. More specifically, the current value of the state indicator is determined only by the value of the state indicator from the previous period, thus the Markov property, and the transition matrix. The latter characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period, given the state in the current period. This setup decides on the two main advantages of the Markov switching models. Namely, the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for improved interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities, as well as for improved forecasting performance based on persistent regimes and parameters characterizing them.Comment: Keywords: Transition Probabilities, Exogenous Markov Switching, Infinite Hidden Markov Model, Endogenous Markov Switching, Markov Process, Finite Mixture Model, Change-point Model, Non-homogeneous Markov Switching, Time Series Analysis, Business Cycle Analysi

Markov Switching

Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent stochastic process with limited memory. More specifically, the current value of the state indicator is determined only by the value of the state indicator from the previous period, thus the Markov property, and the transition matrix. The latter characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period, given the state in the current period. This setup decides on the two main advantages of the Markov switching models. Namely, the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for improved interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities, as well as for improved forecasting performance based on persistent regimes and parameters characterizing them.Comment: Keywords: Transition Probabilities, Exogenous Markov Switching, Infinite Hidden Markov Model, Endogenous Markov Switching, Markov Process, Finite Mixture Model, Change-point Model, Non-homogeneous Markov Switching, Time Series Analysis, Business Cycle Analysi

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure

Temporal and Spatial Data Mining with Second-Order Hidden Models

In the frame of designing a knowledge discovery system, we have developed stochastic models based on high-order hidden Markov models. These models are capable to map sequences of data into a Markov chain in which the transitions between the states depend on the \texttt{n} previous states according to the order of the model. We study the process of achieving information extraction fromspatial and temporal data by means of an unsupervised classification. We use therefore a French national database related to the land use of a region, named Teruti, which describes the land use both in the spatial and temporal domain. Land-use categories (wheat, corn, forest, ...) are logged every year on each site regularly spaced in the region. They constitute a temporal sequence of images in which we look for spatial and temporal dependencies. The temporal segmentation of the data is done by means of a second-order Hidden Markov Model (\hmmd) that appears to have very good capabilities to locate stationary segments, as shown in our previous work in speech recognition. Thespatial classification is performed by defining a fractal scanning ofthe images with the help of a Hilbert-Peano curve that introduces atotal order on the sites, preserving the relation ofneighborhood between the sites. We show that the \hmmd performs aclassification that is meaningful for the agronomists.Spatial and temporal classification may be achieved simultaneously by means of a 2 levels \hmmd that measures the \aposteriori probability to map a temporal sequence of images onto a set of hidden classes

A Classifying Procedure for Signaling Turning Points

A Hidden Markov Model (HMM) is used to classify an out of sample observation vector into either of two regimes. This leads to a procedure for making probability forecasts for changes of regimes in a time series, i.e. for turning points. Instead o maximizing a likelihood, the model is estimated with respect to known past regimes. This makes it possible to perform feature extraction and estimation for different forecasting horizons. The inference aspect is emphasized by including a penalty for a wrong decision in the cost function. The method is tested by forecasting turning points in the Swedish and US economies, using leading data. Clear and early turning point signals are obtained, contrasting favourable with earlier HMM studies. Some theoretical arguments for this are given.Business Cycle; Feature Extraction; Hidden Markov Switching-Regime Model; Leading Indicator; Probability Forecast.

Characterization of time-varying regimes in remote sensing time series: application to the forecasting of satellite-derived suspended matter concentrations

International audienceSatellite data, with their spatial and temporal coverage, are particularly well suited for the analysis and characterization of space-time-varying relationships between geophysical processes. We investigate here the forecasting of a geophysical variable using both satellite observations and model outputs. As example we study the daily concentration of mineral suspended particulate matters estimated from satellite-derived datasets, in coastal waters adjacent to the French Gironde River mouth. We forecast this high resolution dataset using environmental data (wave height, wind strength and direction, tides and river outflow) and four multi-latent-regime models: homogeneous and non-homogeneous Markov-switching models, with and without an autoregressive term, i.e. the suspended matter concentration observed the day before. We clearly show, using a validation dataset, significant improvements with multi-regime models compared to a classical multi-regression and a state-of-the-art non-linear model (Support Vector Regression (SVR) model). The best results are reported for a mixture of 3 regimes for autoregressive model using non-homogeneous transitions. With the autoregressive models, we obtain at day+1 forecasting performances of 93% of the explained variance for the mixture model compared to 83% for a standard linear model and 85% using a SVR. These improvements are even more important for the non-autoregressive models. These results stress the potential of the identification of geophysical regimes to improve the forecasting or the inversion. We also show that for short periods of lack of observations (typically lesser than 15 days), non-homogeneous transition probabilities and estimated autoregressive term, the observation of the previous day not being available, help to enhance forecasting performances