|
on Econometric Time Series |
| By: | David F. Hendry; Grayham E. Mizon |
| Abstract: | We model expenditure on food in the USA, using an extended time series. Even when a theory is essentially ‘correct’, it can manifest serious mis-specification if just fitted to data, ignoring its observed characteristics and major external events such as wars, recessions and policy changes. When the same theory is embedded in a general framework embracing dynamics and structural breaks, it performs well even over an extended data period, as shown using Autometrics with impulse-indicator saturation. Although this particular illustration involves a simple theory, the point made is generic, and applies no matter how sophisticated the theory. |
| Keywords: | Econometric modelling, Food expenditure, Structural breaks, Impulse-indicator saturation, Autometrics |
| JEL: | C51 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:475&r=ets |
| By: | Jennifer L. Castle; Nicholas W.P. Fawcett; David F. Hendry |
| Abstract: | When location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an ‘internal’ break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an ‘external’ break with the EqCM staying constant. Both mechanistic corrections help compared to retaining a pre-break estimated model, but an estimated model of the break process could outperform. We apply the approaches to EqCMs for UK M1, compared with updating a learning function as the break evolves. |
| Keywords: | Cointegration, Equilibrium-correction, Forecasting, Location shifts, Collinearity, M1 |
| JEL: | C1 C53 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:470&r=ets |
| By: | Jennifer L. Castle; Jurgen A. Doornik; David F. Hendry |
| Abstract: | We consider model selection when there is uncertainty over the choice of variables and the occurrence and timing of multiple location shifts. General-to-simple selection is extended using Autometrics by adding an impulse indicator for every observation to the set of candidate regressors (see Hendry, Johansen and Santos, 2008, and Johansen and Nielsen, 2009). We apply that approach to a fat-tailed distribution and processes with breaks: Monte Carlo experiments show its capability of detecting up to 20 shifts in 100 observations, while jointly selecting variables. An illustration to U.S. real interest rates compares impulse-indicator saturation with the procedure in Bai and Perron (1998). |
| Keywords: | Impulse-indicator saturation, Location shifts, Model selection, Autometrics |
| JEL: | C51 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:471&r=ets |
| By: | Thomas Flury; Neil Shephard |
| Abstract: | A key ingredient of many particle filters is the use of the sampling importance resampling algorithm (SIR), which transforms a sample of weighted draws from a prior distribution into equally weighted draws from a posterior distribution. We give a novel analysis of the SIR algorithm and analyse the jittered generalisation of SIR, showing that existing implementations of jittering lead to marked inferior behaviour over the base SIR algorithm. We show how jittering can be designed to improve the performance of the SIR algorithm. We illustrate its performance in practice in the context of three filtering problems. |
| Keywords: | Importance sampling, Particle filter, Random numbers, Sampling importance resampling, State space models |
| JEL: | C14 C32 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:469&r=ets |
| By: | Ba Chu; Roman Kozhan |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:wbs:wpaper:wp09-04&r=ets |
| By: | Ingmar Nolte; Valeri Voev |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:wbs:wpaper:wp09-02&r=ets |
| By: | Giuseppe Cavaliere; David I. Harvey; Stephen J. Leybourne; A. M. Robert Taylor |
| Abstract: | In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2009) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T^-1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T^-1/2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of a one-time change in volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models. |
| Keywords: | Unit root tests; quasi difference de-trending; trend break; non-stationary volatility; wild bootstrap |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:not:notgts:09/05&r=ets |
| By: | Markus Rei\ss |
| Abstract: | The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $\sigma$. As an application, simple rate-optimal estimators of the volatility and efficient estimators of the integrated volatility are constructed. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.3006&r=ets |
| By: | B. Kaulakys; M. Alaburda; V. Gontis |
| Abstract: | We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.2639&r=ets |
| By: | Bence Toth; Fabrizio Lillo; J. Doyne Farmer |
| Abstract: | We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated to a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galvan, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.2549&r=ets |