Extracting a Common Stochastic Trend: Theories with Some Applications

This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by extracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.

Extracting a Common Stochastic Trend:Theories with Some Applications

This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of infer- ence is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by ex- tracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.state space model, Kalman filter, common stochastic trend, maximum likelihood estimation, stock price index, interest rates, return volatility and trading volume.

Extracting a Common Stochastic Trend: Theory with Some Applications

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models -- those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models we explicitly consider comprise a special -- yet useful -- class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices

Real-time hand printed character recognition on a DSP chip

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 119-120).by Christopher Isaac Chang.M.S

Mineralogical distribution of germanium, gallium and indium at the Mt Carlton high-sulfidation epithermal deposit, NE Australia, and comparison with similar deposits worldwide

Germanium, gallium and indium are in high demand due to their growing usage in high-tech and green-tech applications. However, the mineralogy and the mechanisms of concentration of these critical elements in different types of hydrothermal ore deposits remain poorly constrained. We investigated the mineralogical distribution of Ge, Ga and In at the Mt Carlton high-sulfidation epithermal deposit in NE Australia, using electron probe microanalysis and laser ablation inductively-coupled plasma mass spectrometry. Parageneses from which selected minerals were analyzed include: Stage 1 acid sulfate alteration (alunite), Stage 2A high-sulfidation enargite mineralization (enargite, argyrodite, sphalerite, pyrite, barite), Stage 2B intermediate-sulfidation sphalerite mineralization (sphalerite, pyrite, galena) and Stage 3 hydrothermal void fill (dickite). Moderate to locally high concentrations of Ga were measured in Stage 1 alunite (up to 339 ppm) and in Stage 3 dickite (up to 150 ppm). The Stage 2A ores show enrichment in Ge, which is primarily associated with argyrodite (up to 6.95 wt % Ge) and Ge-bearing enargite (up to 2189 ppm Ge). Co-existing sphalerite has comparatively low Ge content (up to 143 ppm), while Ga (up to 1181 ppm) and In (up to 571 ppm) are higher. Sphalerite in Stage 2B contains up to 611 ppm Ge, 2829 ppm Ga and 2169 ppm In, and locally exhibits fine colloform bands of an uncharacterized Zn-In mineral with compositions close to CuZn2(In,Ga)S4. Barite, pyrite and galena which occur in association with Stage 2 mineralization were found to play negligible roles as carriers of Ge, Ga and In at Mt Carlton. Analyzed reference samples of enargite from seven similar deposits worldwide have average Ge concentrations ranging from 12 to 717 ppm (maximum 2679 ppm). The deposits from which samples showed high enrichment in critical elements in this study are all hosted in stratigraphic sequences that locally contain carbonaceous sedimentary rocks. In addition to magmatic-hydrothermal processes, such rocks could potentially be important for the concentration of critical elements in high-sulfidation epithermal deposits