Real Time Detection of Structural Breaks in GARCH Models

A sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks is proposed. Particle filtering techniques allow for fast and efficient updates of posterior quantities and forecasts in real-time. The method conveniently deals with the path dependence problem that arises in these type of models. The performance of the method is shown to work well using simulated data. Applied to daily NASDAQ returns, the evidence favors a partial structural break specification in which only the intercept of the conditional variance equation has breaks compared to the full structural break specification in which all parameters are subject to change. The empirical application underscores the importance of model assumptions when investigating breaks. A model with normal return innovations result in strong evidence of breaks; while more flexible return distributions such as t-innovations or a GARCH-jump mixture model still favor breaks but indicate much more uncertainty regarding the time and impact of them.particle filter, GARCH model, change point, sequential Monte Carlo

Real Time Detection of Structural Breaks in GARCH Models

A sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks is proposed. Particle filtering techniques allow for fast and efficient updates of posterior quantities and forecasts in real time. The method conveniently deals with the path dependence problem that arises in these type of models. The performance of the method is shown to work well using simulated data. Applied to daily NASDAQ returns, the evidence favors a partial structural break specification in which only the intercept of the conditional variance equation has breaks compared to the full structural break specification in which all parameters are subject to change. The empirical application underscores the importance of model assumptions when investigating breaks. A model with normal return innovations results in strong evidence of breaks; while more flexible return distributions such as t-innovations or a GARCH-jump mixture model still favors breaks but indicates much more uncertainty regarding the time and impact of them.Econometric and statistical methods; Financial markets

Understanding Systemic Risk: The Trade-Offs between Capital, Short-Term Funding and Liquid Asset Holdings

We offer a multi-period systemic risk assessment framework with which to assess recent liquidity and capital regulatory requirement proposals in a holistic way. Following Morris and Shin (2009), we introduce funding liquidity risk as an endogenous outcome of the interaction between market liquidity risk, solvency risk, and the funding structure of banks. To assess the overall impact of different mix of capital and liquidity, we simulate the framework under a severe but plausible macro scenario for different balance-sheet structures. Of particular interest, we find that (1) capital has a decreasing marginal effect on systemic risk, (2) increasing capital alone is much less effective in reducing liquidity risk than solvency risk, (3) high liquid asset holdings reduce the marginal effect of increasing short term liability on systemic risk, and (4) changing liquid asset holdings has little effect on systemic risk when short term liability is sufficiently low.Financial stability; Financial system regulation and policies

Forecasting output growth by the yield curve: the role of structural breaks

This paper proposes a new structural-break vector autoregressive (VAR) model for predicting real output growth by the nominal yield curve information. We allow for the possibility of both in-sample and out-of-sample breaks in parameter values and use information in historical regimes to make inference on out-of-sample breaks. A Bayesian estimation and forecasting procedure is provided which accounts for the uncertainty of structural breaks and model parameters. We discuss dynamic consistency when forecasting recursively with structural break models, which has been ignored in the existing literature, and provide a solution. Applied to monthly US data from 1964 to 2006, we find strong evidence of structural breaks in the predictive relation between the yield curve and output growth in late 1979 and early 1983. The short rate has more predictive power for output growth than the term spread before 1979 while the term spread becomes more significant since the breakof 1983. Incorporating the possibility of structural breaks improves out-of-sample forecasts of output growth from 1 to 12 months ahead.Vector Autoregressive Model; Structural Break; Forecast; Output Growth; Yield Curve, Chib Model, MCMC, Bayesian

Forecasting output growth by the yield curve: the role of structural breaks

This paper proposes a new structural-break vector autoregressive (VAR) model for predicting real output growth by the nominal yield curve information. We allow for the possibility of both in-sample and out-of-sample breaks in parameter values and use information in historical regimes to make inference on out-of-sample breaks. A Bayesian estimation and forecasting procedure is provided which accounts for the uncertainty of structural breaks and model parameters. We discuss dynamic consistency when forecasting recursively with structural break models, which has been ignored in the existing literature, and provide a solution. Applied to monthly US data from 1964 to 2006, we find strong evidence of structural breaks in the predictive relation between the yield curve and output growth in late 1979 and early 1983. The short rate has more predictive power for output growth than the term spread before 1979 while the term spread becomes more significant since the breakof 1983. Incorporating the possibility of structural breaks improves out-of-sample forecasts of output growth from 1 to 12 months ahead

Efficient estimation of extreme value-at-risks for standalone structural exchange rate risk

The standalone structural exchange rate risk depends on the product of the future foreign currency earning and the change in the exchange rate. Its Value-at-Risk (VaR) implying an extremely high survival probability, usually exceeding 99.9%, is used in practice to determine its economic capital. This paper proposes a new conditional method to calculate such extreme VaRs that is shown to be more efficient than the conventional method of directly simulating from the joint distribution of the future foreign currency earning and the change in the exchange rate. The intuition of the proposed method is that, conditional on either the future foreign currency earning or the change in the exchange rate, the distribution of the structural exchange rate risk is usually analytically tractable. The proposed method can be implemented by solving a nonlinear equation via a simple one-dimensional numerical integration and is generally applicable under the distributional assumptions commonly employed in practice

Efficient estimation of extreme value-at-risks for standalone structural exchange rate risk

The standalone structural exchange rate risk depends on the product of the future foreign currency earning and the change in the exchange rate. Its Value-at-Risk (VaR) implying an extremely high survival probability, usually exceeding 99.9%, is used in practice to determine its economic capital. This paper proposes a new conditional method to calculate such extreme VaRs that is shown to be more efficient than the conventional method of directly simulating from the joint distribution of the future foreign currency earning and the change in the exchange rate. The intuition of the proposed method is that, conditional on either the future foreign currency earning or the change in the exchange rate, the distribution of the structural exchange rate risk is usually analytically tractable. The proposed method can be implemented by solving a nonlinear equation via a simple one-dimensional numerical integration and is generally applicable under the distributional assumptions commonly employed in practice

Forecasting output growth by the yield curve: the role of structural breaks

This paper proposes a new structural-break vector autoregressive (VAR) model for predicting real output growth by the nominal yield curve information. We allow for the possibility of both in-sample and out-of-sample breaks in parameter values and use information in historical regimes to make inference on out-of-sample breaks. A Bayesian estimation and forecasting procedure is provided which accounts for the uncertainty of structural breaks and model parameters. We discuss dynamic consistency when forecasting recursively with structural break models, which has been ignored in the existing literature, and provide a solution. Applied to monthly US data from 1964 to 2006, we find strong evidence of structural breaks in the predictive relation between the yield curve and output growth in late 1979 and early 1983. The short rate has more predictive power for output growth than the term spread before 1979 while the term spread becomes more significant since the breakof 1983. Incorporating the possibility of structural breaks improves out-of-sample forecasts of output growth from 1 to 12 months ahead

A Class of Generalized Dynamic Correlation Models

This paper proposes a class of parametric correlation models that apply a two-layer autoregressive-moving-average structure to the dynamics of correlation matrices. The proposed model contains the Dynamic Conditional Correlation model of Engle (2002) and the Varying Correlation model of Tse and Tsui (2002) as special cases and offers greater flexibility in a parsimonious way. Performance of the proposed model is illustrated in a simulation exercise and an application to the U.S. stock indices

Identification of inorganic and organic species of phosphorus and its bio-availability in nitrifying aerobic granular sludge

Phosphorus (P) recovery from sewage sludge is necessary for a sustainable development of the environment and thus the society due to gradual depletion of non-renewable P resources. Aerobic granular sludge is a promising biotechnology for wastewater treatment, which could achieve P-rich granules during simultaneous nitrification and denitrification processes. This study aimed to disclose the changes in inorganic and organic P species and their correlation with P mobility and bio-availability in aerobic granules. Two identical square reactors were used to cultivate aerobic granules, which were operated for 120 days with influent ammonia nitrogen (NH4–N) of 100 mg/L before day 60 and then increased to 200 mg/L during the subsequent 60 days (chemical oxygen demand (COD) was kept constant at 600 mg/L). The aerobic granules exhibited excellent COD removal and nitrification efficiency. Results showed that inorganic P (IP) was about 61.4–67.7% of total P (TP) and non-apatite inorganic P (NAIP) occupied 61.9–70.2% of IP in the granules. The enrichment amount of NAIP and apatite P (AP) in the granules had strongly positive relationship with the contents of metal ions, i.e. Fe and Ca, respectively accumulated in the granules. X-ray diffraction (XRD) analysis and solution index calculation demonstrated that hydroxyapatite (Ca5(PO4)3(OH)) and iron phosphate (Fe7(PO4)6) were the major P minerals in the granules. Organic P (OP) content maintained around 7.5 mg per gram of biomass in the aerobic granules during the 120 days\u27 operation. Monoester phosphate (21.8% of TP in extract), diester phosphate (1.8%) and phosphonate (0.1%) were identified as OP species by Phosphorus-31 nuclear magnetic resonance (31P NMR). The proportion of NAIP + OP to TP was about 80% in the granules, implying high potentially mobile and bio-available P was stored in the nitrifying aerobic granules. The present results provide a new insight into the characteristics of P species in aerobic granules, which could be helpful for developing P removal and recovery techniques through biological wastewater treatment