Fractional Integration Parameter Research Articles

Judgment can spur long memory

We arrive at this conclusion by using a new family of models—the Long Memory Dynamic Judgmental Protocol (LMDJP)—where robust filtering and fractionally integrated auto-regressions are combined in an environment characterized by several players—namely, Forecast Producer, Forecast User, and Reality. Namely, we show that if judgment is parametrized as a deformation Likelihood function according to Lq-Likelihood methods, such a deformation affects (sometimes dramatically) the Power Spectrum, consequently inducing over-rejection in formal tests for no LM-effects based on the last. Our simulated and empirical evidence reveals that knowledge of the fractional integration parameter matters for the p-values of tests for spurious LM and, secondly, that the role of LM in belief formation is ambiguous.

Dynamics of persistence in Brazilian economic uncertainty, expectation, and confidence indexes

This study examines the persistence dynamics in Brazilian economic uncertainty, confidence, and expectation indexes, in both business and consumer sides of the economy. Using rolling window estimations of the fractional integration parameter, we assess how economic turbulence influences the persistence of these indexes. We find that economic uncertainty in Brazil is non-stationary but mean-reverting, with its persistence only transitorily affected by economic and political crises. Interestingly, confidence and expectation indexes displayed hysteretic behavior, with multiple persistence regimes linked to crises. These results may be informative for policymakers about the perceptions of the public and businessmen to economic shocks and crises.

A Comparative Study for Estimate Fractional Parameter of ARFIMA Model

Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated first, and then the fractional integration parameter is estimated from it by a relation between them. As for direct methods, the fractional integration parameter is estimated directly without relying on Hurst's parameter, and most of them are semi parametric methods. In this paper, some of the most common direct methods were used to estimate the fraction modulus namely (Geweke-Porter-Hudak, Smoothed Geweke-Porter-Hudak, Local Whittle, Wavelet and weighted wavelet), using simulation method with different value of (d) and different size of time series. The comparison between the methods was done using the mean squared error (MSE). It turns out that the best methods to estimate the fractional parameter is (Local Whittle).
 The ARFIMA model was generated by a function programmed by the MATLAB statistical program

Risk-return trade-off in the Australian Securities Exchange: Accounting for overnight effects, realized higher moments, long-run relations, and fractional cointegration

This paper examines the risk-return trade-off in the Australian Securities Exchange (ASX) using high-frequency data of related assets traded in other markets, where intra-day data are available while the ASX is closed. We consider the S&P/ASX 200 index and the ASX risk-neutral option-implied volatility (VIX) to highlight the importance of overnight information in predicting future index returns. Further, aside from the well-specified traditional approach of monitoring risk-return regressions using the second moment (volatility), we conjointly account for other higher-order moments such as the third and the fourth moments (skewness and kurtosis) to investigate the impact of overnight information corrected moments on predicting the future returns using the cointegrated fractional VAR (CFVAR) model. We find that the monthly compounded realized volatility and realized skewness adjusted with the fractional integration parameter are significantly negatively and positively related with the subsequent monthly returns, respectively. Moreover, the multivariate setting of our study implies that there exists a cointegrating relationship between the realized volatility and VIX, which can be regarded as the variance risk premium.

Persistence in the private debt-t -GDP ratio: evidence from 43 OECD countries

ABSTRACT This paper investigates the degree of persistence of the private debt-to-GDP ratio in 43 OECD countries by estimating the fractional integration parameter of each series. Almost all of them are found to be highly persistent, with orders of integration around or above 1. The only exception is Argentina, where the series appears to be mean-reverting. These results highlight the key importance of macroprudential policy as one of the pillars of macro policy.

Persistence in the Private Debt-to-GDP Ratio: Evidence from 43 OECD Countries

This paper investigates the degree of persistence of the private debt-to-GDP ratio in 43 OECE countries by estimating the fractional integration parameter of each series. Almost all of them are found to be highly persistent, with orders of integration around or above 1. The only exception is Argentina, where the series appears to be mean-reverting. These results highlight the key importance of macroprudential policy as one of the pillars of macro policy.

Are Central Bankers Inflation Nutters? An MCMC Estimator of the Long-Memory Parameter in a State Space Model

Inflation targeting is a common monetary policy regime. Inflation targets are often flexible in the sense that the central bank allows inflation to temporarily deviate from the target to avoid causing unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an autoregressive fractionally integrated moving average (ARFIMA) model. Assuming that the central bank controls the long-run inflation rate, the fractional integration order becomes a measure of how flexible the inflation target is. A higher integration order implies that inflation deviates from the target for longer periods of time and consequently, that the target is flexible. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2014) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. To resolve this issue, we first proposed a Bayesian Monte Carlo Markov Chain (MCMC) estimator for fractional integration parameters. This estimator resolves the problem of over-bias. We estimate the fractional integration order for 6 countries for the period 1993M1 to 2017M9. We found that inflation was integrated to an order of 0.8 to 0.9 indicating that the inflation targets are implemented with a high degree of flexibility.

Modeling Persistence and Parameter Instability in Historical Crude Oil Price Data Using a Gibbs Sampling Approach

This study aims to analyze two important features of crude oil price data, namely, persistence and parameter instability. We apply an autoregressive fractionally integrated moving average model in which crude oil price persistence measured through the fractional integration parameter, conditional innovation variance and persistence change through Markov-switching dynamics. Model estimation is conducted using Gibbs sampling combined with data augmentation. Applied to monthly West Texas Intermediate crude oil price data from September 1859 to December 2017, we find evidence of four regimes. The main effect of regime switching is in the conditional variance and persistence of the innovations, but there is the possibility that regime switching also affects the fractional integration parameter. Across regimes crude oil price is very persistent with the order of integration estimated close to or slightly higher than one. Finally, discarding parameter instability leads to overestimation of the degree of persistence in the price of crude oil. It also results in inferior density forecasts.

A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter

AbstractThis paper proposes a model of time-varying fractional integration where the long-memory parameter,d$d$, in an ARFIMA model is allowed to depend ont$t$and evolve according to a Smooth Transition Regressive (STR) model advanced by Teräsvirta (1994, 1998) . To estimate the time-varying fractional integration parameter, we suggest a new multi-step estimation method based on the wavelet approach using the instantaneous least squares estimator (ILSE). We conduct some simulation experiments and we find that our estimation iterative procedure performs better than that proposed by Boutahar, Dufrénot, and Péguin-Feissolle (2008). An empirical application of this methodology to the volatility of some financial time series is used for illustration purposes. Finally, it is shown that the model proposed offers an interesting framework to describe long-range dependence in the volatility with heterogeneous persistence.

Anti-persistence and long-memory behaviour of SAREITs

PurposeThe purpose of this paper is to provide empirical evidence on the long-memory behaviour of South African real estate investment trusts (SAREITs).Design/methodology/approachThe study employs a battery of advanced techniques to examine the behaviour of returns of 29 SAREIT equities listed on the Johannesburg Stock Exchange. The authors analysed daily closing prices covering different periods up to 21 May 2016. The results provide support for long memory in majority of SAREIT returns.FindingsThe finding of negative fractional integration parameters provides evidence of anti-persistence in SAREIT returns.Practical implicationsIt is recommended that the regulatory authorities adopt technologies that allow a more effective, faster means to disseminate information, and improve the electronic trading mechanism that facilitates quicker price adjustment to news entering the market.Originality/valueThe paper determines the fractional differencing (long-memory) parameter for SAREITs and adds value to the existing body of knowledge.

On the Identification of Fractionally Cointegrated VAR Models With the Condition

ABSTRACTThis article discusses identification problems in the fractionally cointegrated system of Johansen and Johansen and Nielsen. It is shown that several equivalent reparametrizations of the model associated with different fractional integration and cointegration parameters may exist for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple nonidentified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named . This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the condition. The article also illustrates the indeterminacy between the cointegration rank and the lag-length. It is also proved that the model with rank zero and k lags may be an equivalent reparameterization of the model with full rank and k − 1 lags. This precludes the possibility to test for the cointegration rank unless a proper restriction on the fractional integration parameter is imposed.

Central bank policy rates: Are they cointegrated?

This paper analyses the stochastic properties of the bilateral linkages between the central bank policy rates of the US, the Eurozone, Australia, Canada, Japan and the UK using fractional integration and cointegration techniques respectively. The univariate analysis suggests a high degree of persistence in all cases: the fractional integration parameter d is estimated to be above 1, ranging from 1.26 (US) to 1.48 (UK), with the single exception of Japan, for which the unit root null cannot be rejected. Concerning the bivariate results, Australian interest rates are found to be cointegrated with the Eurozone and UK ones, Canadian rates with the UK and US ones, and Japanese rates with the UK ones. The increasing degree of integration of international financial markets and the coordinated monetary policy responses following the global financial crisis might both account for such linkages.

Central Bank Policy Rates: Are They Cointegrated?

This paper analyses the stochastic properties of and the bilateral linkages between the central bank policy rates of the US, the Eurozone, Australia, Canada, Japan and the UK using fractional integration and cointegration techniques respectively. The univariate analysis suggests a high degree of persistence in all cases: the fractional integration parameter d is estimated to be above 1, ranging from 1.26 (US) to 1.48 (UK), with the single exception of Japan, for which the unit root null cannot be rejected. Concerning the bivariate results, Australian interest rates are found to be cointegrated with the Eurozone and UK ones, Canadian rates with the UK and US ones, and Japanese rates with the UK ones. The increasing degree of integration of international financial markets and the coordinated monetary policy responses following the global financial crisis might both account for such linkages.

Central Bank Policy Rates: Are They Cointegrated?

This paper analyses the stochastic properties of and the bilateral linkages between the central bank policy rates of the US, the Eurozone, Australia, Canada, Japan and the UK using fractional integration and cointegration techniques respectively. The univariate analysis suggests a high degree of persistence in all cases: the fractional integration parameter d is estimated to be above 1, ranging from 1.26 (US) to 1.48 (UK), with the single exception of Japan, for which the unit root null cannot be rejected. Concerning the bivariate results, Australian interest rates are found to be cointegrated with the Eurozone and UK ones, Canadian rates with the UK and US ones, and Japanese rates with the UK ones. The increasing degree of integration of international financial markets and the coordinated monetary policy responses following the global financial crisis might both account for such linkages.

Time-varying persistence of inflation: evidence from a wavelet-based approach

AbstractWe propose a new stochastic long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a “one-size-fits-all” monetary policy is unlikely to work in all circumstances. The empirical results are consistent with newly developed tests of wavelet-based unit root and fractional Brownian motion.

Inference on the long-memory properties of time series with non-stationary volatility

Time-varying volatility is often present in time series data and can have adverse effects when inferring about the persistence properties of examined series. This note analyzes the effects of such nonstationarity on periodogram-based inference for the fractional integration parameter. Based on asymptotic arguments and Monte Carlo simulations, we show that the log-periodogram regression estimator remains consistent, but has asymptotic distribution whose variance depends on the variation of the volatility of the series.

Time-Varying Persistence of Inflation: Evidence from a Wavelet-Based Approach

We propose a new long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a one-size-fits-all monetary policy is unlikely to work in all circumstances.

A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets

AbstractIn this paper, we apply the recently developed fractionally cointegrated vector autoregressive (FCVAR) model to analyze price discovery in the spot and futures markets for five non‐ferrous metals (aluminum, copper, lead, nickel, and zinc). The FCVAR model allows for long memory (fractional integration) in the equilibrium errors, and, following Figuerola‐Ferretti and Gonzalo (2010), we allow for the existence of long‐run backwardation or contango in the equilibrium as well, that is, a non‐unit cointegration coefficient. Price discovery can be analyzed in the FCVAR model by a relatively straightforward examination of the adjustment coefficients. In our empirical analysis, we use the data from Figuerola‐Ferretti and Gonzalo (2010), who conduct a similar analysis using the usual (non‐fractional) CVAR model. Our first finding is that, for all markets except copper, the fractional integration parameter is highly significant, showing that the usual, non‐fractional model is not appropriate. Next, when allowing for fractional integration in the long‐run equilibrium relations, fewer lags are needed in the autoregressive formulation, further stressing the usefulness of the fractional model. Compared to the results from the non‐fractional model, we find slightly more evidence of price discovery in the spot market. Specifically, using standard likelihood ratio tests, we do not reject the hypothesis that price discovery takes place exclusively in the spot (futures) market for copper, lead, and zinc (aluminum and nickel). © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:339–356, 2015

Exponential Smoothing, Long Memory and Volatility Prediction

Extracting and forecasting the volatility of financial markets is an important empirical problem. Time series of realized volatility or other volatility proxies, such as squared returns, display long range dependence. Exponential smoothing (ES) is a very popular and successful forecasting and signal extraction scheme, but it can be suboptimal for long memory time series. This paper discusses possible long memory extensions of ES and finally implements a generalization based on a fractional equal root integrated moving average (FerIMA) model, proposed originally by Hosking in his seminal 1981 article on fractional differencing. We provide a decomposition of the process into the sum of fractional noise processes with decreasing orders of integration, encompassing simple and double exponential smoothing, and introduce a lowpass real time filter arising in the long memory case. Signal extraction and prediction depend on two parameters: the memory (fractional integration) parameter and a mean reversion parameter. They can be estimated by pseudo maximum likelihood in the frequency domain. We then address the prediction of volatility by a FerIMA model and carry out a recursive forecasting experiment, which proves that the proposed generalized exponential smoothing predictor improves significantly upon commonly used methods for forecasting realized volatility.

The Weekend Effect: A Trading Robot and Fractional Integration Analysis

This paper provides some new empirical evidence on the weekend effect, one of the most recognized anomalies in financial markets. Two different methods are used: (i) a trading robot approach to examine whether or not there is such an anomaly giving rise to exploitable profit opportunities by replicating the actions of traders; (ii) a fractional integration technique for the estimation of the (fractional) integration parameter d. The results suggest that trading strategies aimed at exploiting the weekend effect can generate extra profits but only in a minority of cases in the gold and stock markets, whist they appear to be profitable in most cases in the FOREX. Further, the lowest orders of integration are generally found on Mondays, which can be seen as additional evidence for a weekend effect.