Adaptive ARFIMA models with applications to inflation

Many previous analyses of inflation have used either long memory or nonlinear time series models. This paper suggests a simple adaptive modification of the basic ARFIMA model, which uses a flexible Fourier form to allow for a time varying intercept. Simulation evidence suggests that the model provides a good representation of various forms of structural breaks and also that the new model can be efficiently estimated by a QMLE approach. We investigate monthly CPI inflation series for the G7 countries and find evidence of stable long memory parameters across regimes and also of significant nonlinear effects. The estimated adaptive ARFIMA models generally have less persistent long memory parameters than previous studies, with the estimated time dependent intercept being an important component. The model is also supplemented with an adaptive FIGARCH component, yielding a double nonlinear long memory model.     

Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures

Econometric issues in the estimation of persistence in macroeconomic time series are considered. In particular, the relative merits of estimates based on ARMA models, ARFIMA models and nonparametric procedures are investigated. It is shown that ARFIMA models are inappropriate for the purpose of estimating persistence. Furthermore, some of the criticism leveled in the literature against the use of ARMA models for estimating long run properties is put into perspective. Methodological issues arising in the estimation of ARMA models that are relevant to estimation of persistence are discussed. It is shown how overparameterization of an ARMA model may lead to severely downward biased estimates of persistence. The theoretical results are employed to explain some of the findings in Campbell & Mankiw (1987a) and Christiano & Eichenbaum (1990). The methodological aspects of the paper are also relevant for the problem of estimating the value of a spectral density at any given frequency. An empirical study confirms persistence estimates reported in Campbell & Mankiw (1987a), and shows that ARMA models as well as nonparametric procedures give very similar estimates of persistence if properly applied. First version received: May 1996/final version received: March 1998     

Modelling the Persistence of Unemployment in Canada

The persistence of unemployment in Canada is examined in this article by means of fractionally integrated techniques. Using Sowell's (1992) procedure of estimating ARFIMA models by maximum likelihood along with other techniques, we show that the order of integration of the series is higher than one, implying that unemployment is a highly persistent variable.     

The persistence of unemployment in the USA and Europe in terms of fractionally ARIMA models

This article examines the persistence of unemployment in the USA and four European countries by means of fractionally integrated ARMA (ARFIMA) models. In doing so, a type of flexibility in modelling low-frequency dynamics not achieved by non-fractionally ARIMA models can be provided. The results indicate that the unemployment series are much more persistent in some countries such as the UK and France, than in others including Germany or the USA.     

Fractional integration and business cycle features

We show in this article that fractionally integrated univariate models for GDP lead to a better replication of the main business cycle characteristics. We firstly show that the business cycle features are clearly affected by the degree of integration as well as by the other short run (AR, MA, etc.) components of the series. Then, we model the real GDP in the UK and the US by means of fractionally ARIMA (ARFIMA) model, and show that the time series can be specified in terms of this type of model with orders of integration higher than one but smaller than two. Comparing the ARFIMA specifications with those based on ARIMA models, we show via simulations that the former better describe the business cycles features of the data.Jel classification: C12, C15, C22The authors want to thank two anonymous referees for wise remarks. We have also benefited from questions and comments of the attendances at the econometric seminar of the Humboldt Universität zu Berlin and the ESEM2001 congress in Lausanne. Remaining errors and omissions are ours. All correspondence to: Luis A. Gil-Alana.First version received: February 2002/Final version received: December 2002     

Modelling the US real GNP with fractionally integrated techniques

The US real GNP is analysed by means of fractionally integrated techniques. LM tests proposed by Robinson for testing unit roots and other fractionally integrated hypotheses are applied to the quarterly GNP series and to its log-transformation. The maximum likelihood estimation procedure of Sowell for estimating ARFIMA models is implemented. The results indicate that the order of integration of the US real output is much higher than one, and thus, the standard approach of taking first differences may still produce series with long memory behaviour.     

Long memory and level shifts: Re-analyzing inflation rates

A key application of long memory time series models concerns inflation. Long memory implies that shocks have a long-lasting effect. It may however be that empirical evidence for long memory is caused by neglecting one or more level shifts. Since such level shifts are not unlikely for inflation, where the shifts may be caused by sudden oil price shocks, we examine whether evidence for long memory (indicated by the relevance of an ARFIMA model) in G7 inflation rates is spurious or exaggerated. Our main findings are that apparent long memory is quite resistant to level shifts, although for a few inflation rates we find that evidence for long memory disappears. First version received: March 1998/final version received: October 1998     

What can we learn from the history of gasoline crack spreads?: Long memory,structural breaks and modeling implications

In this paper, we investigate the long-range auto-correlations of crack spreads using a nonparametric method, named detrended moving average (MF-DMA). We find that the auto-correlations display multiscaling behaviors and are dominated by the anti-persistence (mean-reversion) in the long-term. Moreover, the auto-correlations are multifractal, indicating that various small and large fluctuations display different scaling behaviors. Using a technique of rolling windows, we find that some extreme events can drive the degree of anti-persistence and the multifractality (complexity) to rise up. In other words, these events have negative impacts on market efficiency. However, the effects of these events are not alike. We also detect long-range auto-correlations in crack spread volatilities and find a strong persistent behavior and multifractality. Finally, we discuss the modeling implications of the findings on long-range auto-correlated patterns. Our results indicate that ARFIMA-GARCH models can capture the major dynamics of large fluctuations. For small fluctuations, they are misspecified. Interestingly, we find that the strong long-range auto-correlated behaviors do not imply that ARFIMA model which takes long memory into account can outperform random walk model in the sense of out-of-sample prediction. The major reason may be that market complexity exploited in this paper causes the low predictability of ARFIMA model.     

Pricing Nikkei 225 Options Using Realized Volatility

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non‐trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. The main results using put options on the Nikkei 225 index are that: (i) the ARFIMAX model performs best; (ii) the Hansen and Lunde (2005a) adjustment for non‐trading hours improves the performance; (iii) methods for reducing microstructure noise‐induced bias yield better performance, while if the Hansen–Lunde adjustment is used, the other methods are not necessarily needed; and (iv) the performance is unaffected by removing large jumps from realized volatility.     

Asymptotics of trend stationary fractionally integrated ARMA models

The main contribution of this study is to provide asymptotic results for MLE applied to the trend stationary ARFIMA model and to implement a detailed simulation study. For small sample sizes, the bias for the fractional parameter, d, can be quite substantial when the other parameters are also estimated simultaneously.     

The dynamics of inflation: a study of a large number of countries

Over the last twenty years the statistical properties of inflation persistence has been the subject of intense investigation and debate without reaching a unanimous conclusion yet. In this article we attempt to shed further light to this debate using a battery of econometric techniques in order to provide robust evidence on the degree of inflation persistence and whether this has changed during the period in which several countries have followed inflation-targeting regimes or new monetary regimes. We consider the inflation rates of thirty developed and emerging economies using quarterly data for the period 1958 to 2007 which include alternative monetary policy regimes. The coefficient of the inflation parameter is estimated by Ordinary Least Squares (OLS), Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. Furthermore, the grid-bootstrap Median Unbiased (MUB) estimator approach developed by Hansen (1999) is used to estimate the finite sample OLS estimates coupled with the 95% symmetric confidence interval. We also examine parameter stability of persistence coefficients by estimating a model with time-varying parameters.     

Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.     

Long memory and structural breaks in the returns and volatility of gold: evidence from Turkey

This article examines the long-memory properties and structural breaks in spot and futures gold returns and volatility in Turkey. The data cover the period from 2008 through 2013 in which gold prices hit an all-time high. ARFIMA–FIGARCH model provides evidence of dual long memory in spot series and a lack of long-memory property in futures returns. Anti-persistence in spot returns is indicative of an overreaction of gold prices to new information, thus disconfirming the weak form of market efficiency. The findings further provide evidence of one structural break, which is associated with correction in the gold prices during the post-global financial crisis. The analyses suggest that the long memory is true, not spurious. This implies that long memory is a feature of the data instead of an outcome of structural changes.     

Monetary policy in steering the EONIA and POLONIA rates in the Eurosystem and Poland: a comparative analysis

The effectiveness of the monetary policies of the European Central Bank (ECB) and the Narodowy Bank Polski (NBP) is compared directly in terms of influencing the spread between the interbank overnight rate and the main rates of the central banks during periods of different economic conditions, i.e. the global financial crisis of 2008, the European sovereign debt crisis and the period of relative stability. Three categories of determinants of the Euro Overnight Index Average/Polish Overnight Index Average (EONIA/POLONIA) spreads are considered: (1) monetary policy instruments such as open market operations, standing facilities and minimum reserve requirements; (2) measures of liquidity conditions; and (3) market expectations and risk measures. Applying the ARFIMA–GARCH models, we show that the statistical and economic properties of the EONIA and POLONIA spreads are quite different. The EONIA spread has a long memory while the POLONIA spread is characterized by a short memory. This difference is important from the viewpoint of a stabilizing monetary policy. The impact of shocks on the future levels of the spread was stronger for the POLONIA spread, but it was short-lived in comparison with the EONIA spread. Most of the analysed variables significantly influenced the spreads during the financial crisis, while the biggest differences in the impact of determinants between the EONIA and POLONIA spreads occurred during the period of relative stability. Substantial differences also exist between the volatilities of both spreads.     

我国短期利率序列均值过程和波动率过程的长期记忆性测度与检验

我们使用我国1996年1月至2008年6月期间的银行同业拆借利率,对我国利率均值过程及其波动过程的长期记忆性进行测度和检验。利用ARFIMA模型和FIGARCH模型的检验结果说明,我国利率序列的一阶矩中不存在长期记忆性,而二阶矩中存在显著的长期记忆性;进一步运用ARFIMA-FIGARCH模型对利率均值过程及其波动过程的双长期记忆性进行检验时发现,我国利率序列均值过程中不存在明显的长期记忆性,但波动率序列中存在非常显著且较强的长期记忆性特征;通过考虑Student-t分布进一步说明,我国利率序列中明显存在"尖峰厚尾"分布特征。     

中国股市长期记忆效应的实证研究

股票市场长期记忆效应问题一直是金融经济学家们倍感兴趣的一个研究热点。本文针对中国股票市场中价格指数与个股的日收益序列 ,在已有研究文献主要采用的经典R S分析方法基础上 ,引入修正R S分析与ARFIMA模型进行了实证研究。从研究结果来看 ,2 2个样本序列并不满足传统的正态分布假设 ,序列呈现出尖峰、肥尾、右偏等有偏特征以及独特的自相关与偏自相关结构 ,这些迹象预示着非线性动态系统的存在。而进一步的研究却表明 ,中国股市中代表市场总体的股价指数不存在长期记忆效应 ,而个股收益序列的分布特征存在着较大差异 ,仅少数个股存在长期记忆行为。这一结论明显地有别于以往那些由经典R S分析所得到的研究结果。     

Does final energy demand in Portugal exhibit long memory? A fractional integration analysis

In this paper, we measure the degree of fractional integration in final energy demand in Portugal using an ARFIMA model with and without adjustments for seasonality. We consider aggregate energy demand as well as final demand for petroleum, electricity, coal, and natural gas. Our findings suggest the presence of long memory in all of the components of energy demand. All fractional-difference parameters are positive and lower than 0.5 indicating that the series are stationary, although with mean reversion patterns slower than in the typical short-run processes. These results have important implications for the design of energy policies. As a result of the long-memory in final energy demand, the effects of temporary policy shocks will tend to disappear slowly. This means that even transitory shocks have long lasting effects. Given the temporary nature of these effects, however, permanent effects on final energy demand require permanent policies. This is unlike what would be suggested by the more standard, but much more limited, unit root approach, which would incorrectly indicate that even transitory policies would have permanent effects.     

Estimating persistence in Canadian unemployment: evidence from a Bayesian ARFIMA

The degree of persistence in aggregate Canadian unemployment is estimated within a Bayesian ARFIMA class of models. The results conclude that unemployment exhibits persistence in the short and intermediate run. The evidence of persistence is stronger than previously reported by Koustas and Veloce (1996 Koustas, Z and Veloce, W. 1996. Unemployment hysteresis in Canada: an approach based on long-memory time series models. Applied Economics, 28: 823–31. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). This persistence cast a vital implication regarding disinflation policies, Based on the unemployment rate, these policies will prove very costly in terms of lost output and – if implemented – they considerably lengthen recessions.     

DISCRIMINATING SHORT AND LONG MEMORY IN FINITE SAMPLES USING SENSITIVITY ANALYSIS: AN APPLICATION TO GROWTH CONVERGENCE

The standard linear model where u_t is generated from an ARFIMA process, is considered. The sensitivity of the predictor and sensitivity of variance estimates of the linear model to long memory are investigated by constructing the statistical measures B_L/S and D_L/S , respectively. B_L/S and D_L/S is interpreted as a sensitivity measure for the long‐memory process without the short‐memory effects. As an application, the memory characteristics of per capita GDP of 30 countries are investigated from the Maddison GDP dataset. It is found that per‐capita GDP exhibits long memory characteristics, and the long‐run growth estimates are sensitive to the long memory characteristics.     

Structural stability and model design

The paper introduces the concept of structural stability and proposes that it should be considered a necessary property of scientifically valid models. Formalization of the concept is considered in both linear and non-linear models. A strong preference in favour of the wider use of non-linear models is supported by consideration of the dangers of linearization in dynamic models. The importance of structural stability is demonstrated with reference to dynamic rational expectations models which exhibit the saddle-point property. In such cases convergence to equilibrium is shown to be a structurally unstable property which can be forced by restrictive auxillary assumptions, which are highlighted.