We consider nonparametric generalization of various well-known financial time series models and study estimates of the trend and volatility functions and forecasts based on kernel smoothers as well as on neural networks.
We discuss how neural networks may be used to estimate conditional means, variances and quantiles of nancial time series nonparametrically. These estimates may be used to forecast, to derive trading rules and to measure market risk.
We introduce a class of models for time series of counts which include INGARCH-type models as well as log linear models for conditionally Poisson distributed data. For those processes, we formulate simple conditions for stationarity and weak dependence with a geometric rate. The coupling argument used in the proof serves as a role model for a similar treatment of integer-valued time series models based on other types of thinning operations.
In the following, we discuss a procedure for interpolating a spatial-temporal stochastic process. We stick to a particular, moderately general model but the approach can be easily transered to other similar problems. The original data, which motivated this work, are measurements of gas concentrations (SO2, NO, O2) and several meteorological parameters (temperature, sun radiation, procipitation, wind speed etc.). These date have been and are still recorded twice every hour at several irregularly located places in the forests of the state Rheinland-Pfalz as part of a program monitoring the air pollution in the forests.
In this paper we derive nonparametric stochastic volatility models in discrete time. These models generalize parametric autoregressive random variance models, which have been applied quite successfully to nancial time series. For the proposed models we investigate nonparametric kernel smoothers. It is seen that so-called nonparametric deconvolution estimators could be applied in this situation and that consistency results known for nonparametric errors- in-variables models carry over to the situation considered herein.
Kernel smoothing in nonparametric autoregressive schemes offers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the bootstrap resampling or by generating a simple regression model. Consistency of these bootstrap procedures will be shown.
In this paper, we discuss the problem of testing for a changepoint in the structure
of an integer-valued time series. In particular, we consider a test statistic
of cumulative sum (CUSUM) type for general Poisson autoregressions of order
1. We investigate the asymptotic behaviour of conditional least-squares estimates
of the parameters in the presence of a changepoint. Then, we derive the
asymptotic distribution of the test statistic under the hypothesis of no change,
allowing for the calculation of critical values. We prove consistency of the test,
i.e. asymptotic power 1, and consistency of the corresponding changepoint estimate.
As an application, we have a look at changepoint detection in daily
epileptic seizure counts from a clinical study.
Neural networks are now a well-established tool for solving classification and forecasting problems in financial applications (compare, e.g., Bol et al., 1996, Evans, 1997, Rehkugler and Zimmermann, 1994, Refenes 1995, and Refenes et al. 1996a) though many practioners are still suspicious against too evident success stories. One reason may be that the construction of an appropriate network which provides a reasonable solution to a complex data-analytic problem is rarely made explicit in the literature. In this paper, we try to contribute to filling this gap by discussing in detail the problem of dynamically allocating capital to various components of a currency portfolio in such a manner that the average gain will be larger than for certain benchmark portfolios. We base our solution on feedforward neural networks which are constructed employing various statistical model selection procedures described in, e.g., (Anders, 1997, or Refenes et al., 1996b). Neural networks which are used as the basis of trading strategies in finance should be assessed differently than in technical applications. The task is not to construct a network which provides good forecasts with respect to mean-square error of some quantities of interest or to provide good approximation of some given target values, but to achieve a good performance in economic terms. For portfolio allocation, the main goal is to achieve on the average a large return combined with a small risk. Therefore, we do not consider forecasts of the foreign exchange (FX-) rate time series using neural networks, but we try to get the allocation directly as the output of a network. Furthermore, we do not minimize some estimation or prediction error, but we try to maximize an economically meaningful performance measure, the risk-adjusted return, directly (compare also Heitkamp, 1996). In the subsequent chapter, we describe the details of the portfolio allocation problem. The following two chapters provide some technical information on how the networks were fitted to the available data and how the network inputs and outputs were selected. In chapter 5, finally, we discuss the promising results.
In this paper we deal with the problem of fitting an autoregression of order p to given data coming from a stationary autoregressive process with infinite order. The paper is mainly concerned with the selection of an appropriate order of the autoregressive model. Based on the so-called final prediction error (FPE) a bootstrap order selection can be proposed, because it turns out that one relevant expression occuring in the FPE is ready for the application of the bootstrap principle. Some asymptotic properties of the bootstrap order selection are proved. To carry through the bootstrap procedure an autoregression with increasing but non-stochastic order is fitted to the given data. The paper is concluded by some simulations.
We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t-1. We discuss an estimate which we get by inverting a kernel estimate of the conditional distribution function, and prove its asymptotic normality and uniform strong consistency. We illustrate the good performance of the estimate for light and heavy-tailed distributions of the innovations with a small simulation study.