Modelling time series properties of Australian lending interest rates

The purpose of this paper is to examine the time series properties of Australian residential mortgage interest rates, and in doing so, establish whether or not selected home loan rates （product-level monthly home loan interest rates for CBA） exhibit the expected cyclical and seasonal variations and whether seasonality, if present, is stochastic or deterministic. In particular, due to a well established presence of cyclicality in financial markets＇ interest rates and strong correlation between financial markets＇ interest rates and home loan interest rates, the paper presumes that cyclicality is also to be found in home loan interest rates. Furthermore, the paper tests the hypothesis that home loan interest rates, for selected products, exhibit the three identified （＂Spring＂, ＂Autumn＂ and ＂The end of the Financial Year＂） season-related interest rate reductions. The paper uses a structural time series modelling approach and product-level home loan interest rates data from one of the biggest banks in Australia, Commonwealth Bank of Australia （CBA）. As expected, the results overall confirm the existence of cyclicality in home loan interest rates. With respect to the seasonality of home loan interest rate, although most of the analysed variables show the presence of statistically significant seasonal factors, the majority of the statistically significant seasonal factors observed cannot be attributed to any of the three considered seasonal effects.     

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.First version received: September 2002/Final version received : October 2003I would like to thank Cees Diks, Cars Hommes and an anonymous referee for useful comments that significantly improved the paper.     

Forecasting nonlinear economic time series: A simple test to accompany the nearest neighbor approach

This paper is based on a recent nonparametric forecasting approach by Sugihara, Grenfell and May (1990) to improve the short term prediction of nonlinear chaotic processes. The idea underlying their forecasting algorithm is as follows: For a nonlinear low-dimensional process, a state space reconstruction of the observed time series exhibits spatial correlation, which can be exploited to improveshort term forecasts by means of locally linear approximations. Still, the important question of evaluating the forecast perfomance is very much an open one, if the researcher is confronted with data that are additionally disturbed by stochastic noise. To account for this problem, a simple nonparametric test to accompany the algorithm is suggested here. To demonstrate its practical use, the methodology is applied to observed price series from commodity markets. It can be shown that the short term predictability of the best fitting linear model can be improved upon significantly by this method.     

A modified logit model for time series with an application to the pricing behaviour of manufacturing firms in Australia

The modified logit model (Amemiya and Nold, 1975) is generalised to the case where the error term is autocorrelated. The asymptotic distribution (as n →∞ and T →∞) of a feasible GLS estimator of β is derived. Tests of linear restrictions on β and the significance of ρ are presented. The results of the applied work suggest that the factors which explain the pricing behaviour of manufacturing firms, as reported in the tendency survey conducted by the Australian Chamber of Commerce and Industry and the Westpac Banking Corporation, include historical inflation rates of up to 7 quarters and capacity utilisation. First version received: March 2001/Final version received: July 2002 RID="*" ID="*"  The first draft of this paper was written while the author was on study leave at the Department of Econometrics, University of Sydney, Australia.     

甘肃省经济发展态势分析——基于时序主成分分析

本文利用时序主成分分析法，对甘肃的经济发展态势进行了分析，时序全局主成分分析的方法是时序分析和全局主成分分析方法的结合，从文中的实证部分来看，时序主成分分析法得到的分析结果与甘肃省的现实经济状况相吻合。     

A system approach for measuring the euro area NAIRU

This paper addresses the issue of measuring the NAIRU for the euro area and assessing the robustness and precision of the obtained estimates. The empirical framework adopted is based on systems combining an Okun-type relationship between cyclical unemployment and the output gap with a Phillips curve and stochastic laws of motion for the NAIRU and potential output. Such systems have been estimated using Kalman-filter techniques. The results obtained point to an estimate of the area-wide NAIRU that is robust to changes in the underlying models. This robustness is shown to hold both in terms of the mean – i.e., the shape of the resulting NAIRU – and the variance of the process. The latter is derived through bootstrap exercises using the models alone or pooled together. The evidence found suggests that the increase in the aggregate NAIRU that took place in the early part of the sample period has come to a halt and may be about to be reversed.Jel classification: C11, C15, E31, E32The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the Institutions they belong to. The authors are grateful to Per Jansson for providing parts of the econometric RATS code and to Gonzalo Camba-Mendez and Frank Smets of the ECB for useful comments. Comments and recommendations by two anonimous referees are also gratefully acnowledged. All the remaining errors are the authors responsibility. All correspondence to Ricardo Mestre.First version received: January 2002/Final version received December 2002     

Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost

A main drawback of existing fuzzy time series forecasting methods is that they lack persuasiveness in determining universe of discourse and the length of intervals. Two approaches are proposed for overcoming the problem, and the proposed approaches are more objective and reasonable to improve the persuasiveness in determining the universe of discourse, length of intervals and membership functions of fuzzy time series. The first approach is using Minimize Entropy Principle Approach (MEPA) to partition the universe of discourse and build membership functions, and the second is using Trapezoid Fuzzification Approach (TFA). Monthly amount data of IT project expenditure of a company are used to evaluate the performance of the proposed approaches. The forecasting accuracies of the proposed approaches are better than those of previous methods.     

Calculating Value-at-Risk for high-dimensional time series using a nonlinear random mapping model

In this study, we propose a non-linear random mapping model called GELM. The proposed model is based on a combination of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and the Extreme Learning Machine (ELM), and can be used to calculate Value-at-Risk (VaR). Alternatively, the GELM model is a non-parametric GARCH-type model. Compared with conventional models, such as the GARCH models, ELM, and Support Vector Machine (SVM), the computational results confirm that the GELM model performs better in volatility forecasting and VaR calculation in terms of efficiency and accuracy. Thus, the GELM model can be an essential tool for risk management and stress testing.     

A new methodology for the logistic analysis of evolutionary S-shaped processes: Application to historical time series and forecasting

A new multi-logistic methodology to analyze long range time series of evolutionary S-shaped processes is presented. It conceptually innovates over the traditional logistic approach. The ansatz includes computing the residuals to an optimized multi-logistic trend curve least squares fitted to the time-series data. The elements of the residuals series are checked for autocorrelations and once detected the residuals series is further analyzed to search for eventual presence of underlying periodic structures using a truncated Fourier sine series. The method foundations ensures both a universal applicability and a capacity to disclose the existence of active clocks that can be possibly traced to the driving motors of the evolutionary character of the time series, due to the responsiveness of corresponding process to the development of economic cycles. On associating these two views, it is found that the methodology has a strong potential to improve the quality of short-term forecasts. These findings have been put to test through applications of the methodology to studying the time evolution of two commodities of strong economic and social importance (corn and steel) and good results were consistently obtained for both the analytical and forecasting aspects.