A local dynamic conditional correlation model

This paper introduces the idea that the variances or correlations in financial returns may all change conditionally and slowly over time. A multi-step local dynamic conditional correlation model is proposed for simultaneously modelling these components. In particular, the local and conditional correlations are jointly estimated by multivariate kernel regression. A multivariate k-NN method with variable bandwidths is developed to solve the curse of dimension problem. Asymptotic properties of the estimators are discussed in detail. Practical performance of the model is illustrated by applications to foreign exchange rates.Local and conditional correlations; multivariate nonparametric ARCH; multivariate kernel regression; multivariate k-NN method

Data-driven estimation of diurnal duration patterns

This paper proposes a local linear estimator for diurnal patterns of transaction durations under a special nonparametric regression model, whose asymptotics are different to any known results. An iterative plug-in algorithm is developed for selecting the bandwidth. The ACD model is then applied to analyze the standardized durations. Data examples show that the proposals work well in practice.Autoregressive conditional duration, diurnal duration patterns, local linear estimator, bandwidth selection, iterative plug-in.

Kernel Dependent Functions in Nonparametric Regression with Fractional Time Series Errors kernel dependent function, bandwidth selection.

Nonparametric regression, long memory, antipersistence, fractional difference

An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method

We propose a fast data-driven procedure for decomposing seasonal time series using the Berlin Method, the software used by the German Federal Statistical Office in this context. Formula of the asymptotic optimal bandwidth h_A is obtained. Meth- ods for estimating the unknowns in h_A are proposed. The algorithm is developed by adapting the well known iterative plug-in idea to time series decomposition. Asymptotic behaviour of the proposal is investigated. Some computational aspects are discussed in detail. Data example show that the proposal works very well in the practice and that data-driven bandwidth selection is a very useful tool to improve the Berlin Method. Deep insights into the iterative plug-in rule are also provided.Time series decomposition, Berlin Method, local regression, bandwidth selection, iterative plug-in

Filtered Log-periodogram Regression of long memory processes

Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on ˆ d is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a simple family of filters. The essential improvement is based on a binary decision that is asymptotically correct with probability one. The idea is closely related to the well known technique of pre-whitening.

Nonparametric estimation of time-varying covariance matrix in a slowly changing vector random walk model

A new multivariate random walk model with slowly changing parameters is introduced and investigated in detail. Nonparametric estimation of local covariance matrix is proposed. The asymptotic distributions, including asymptotic biases, variances and covariances of the proposed estimators are obtained. The properties of the estimated value of a weighted sum of individual nonparametric estimators are also studied in detail. The integrated effect of the estimation errors from the estimation for the difference series to the integrated processes is derived. Practical relevance of the model and estimation is illustrated by application to several foreign exchange rates.Multivariate time series; slowly changing vector random walk; local covariance matrix; kernel estimation; asymptotic properties; forecasting

Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors

Optimal rate of convergence, nonparametric regression, long memory, antipersistence.

Modelling Different Volatility Components in High-Frequency Financial Returns

This paper considers simultaneous modelling of seasonality, slowly changing un- conditional variance and conditional heteroskedasticity in high-frequency financial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and trend components into the GARCH model. A data-driven semiparametric algorithm is developed for estimating the model. Asymptotic properties of the proposed estimators are investigated brie y. An approximate significance test of seasonality and the use of Monte Carlo confidence bounds for the trend are proposed. Practical performance of the proposal is investigated in detail using some German stock price returns. The approach proposed here provides a useful semiparametric extension of the GARCH model.High-frequency financial data, nonparametric regression, seasonality in volatility, semiparametric GARCH model, trend in volatility

Modelling financial time series with SEMIFAR-GARCH model

A class of semiparametric fractional autoregressive GARCH models (SEMIFAR-GARCH), which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence, and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term. So that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets.Financial time series; GARCH model; SEMIFAR model; parameter estimation; kernel estimation; asymptotic property

Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors

Nonparametric regression, optimal convergence rate, long memory, antipersistence, inverse process.