Long Memory Property Research Articles

Long-memory property of nonlinear transformations of break processes

Not much is known about the long-memory property of nonlinearly transformed fractionally integrated processes, let alone of occasional structural break ones. In an important work that fills this gap in the literature, Dittmann and Granger (2002) [Dittmann, I. and Granger, C.W.J., 2002. Properties of nonlinear transformations of fractionally integrated processes. Journal of Econometrics 110, 113-133] show that the estimated long-memory parameter decreases as the probability of break increases, and that it decreases only slightly with the order of the power transformation. In this note, additional results are provided that confirm the latter claim, but contradict the former one.

Renewal regime switching and stable limit laws

Abstract The paper discusses long-memory properties and large sample behavior of partial sums in a general renewal regime switching scheme. The linear model X t = μ t + a t X t - 1 + σ t ɛ t with renewal switching in levels, slope or volatility and general (possibly heavy-tailed) i.i.d. noise ɛ t is discussed in detail. Conditions on the tail behavior of interrenewal distribution and the tail index α ∈ ( 0 , 2 ] of ɛ t are obtained, in order that the partial sums process of X t is asymptotically λ -stable with index λ α .

Random coefficient autoregression, regime switching and long memory

We discuss long-memory properties and the partial sums process of the AR(1) process {X t , t ∈ 𝕫} with random coefficient {a t , t ∈ 𝕫} taking independent values A j ∈ [0,1] on consecutive intervals of a stationary renewal process with a power-law interrenewal distribution. In the case when the distribution of generic A j has either an atom at the point a=1 or a beta-type probability density in a neighborhood of a=1, we show that the covariance function of {X t } decays hyperbolically with exponent between 0 and 1, and that a suitably normalized partial sums process of {X t } weakly converges to a stable Lévy process.

Random coefficient autoregression, regime switching and long memory

We discuss long-memory properties and the partial sums process of the AR(1) process {Xt, t ∈ 𝕫} with random coefficient {at, t ∈ 𝕫} taking independent values Aj ∈ [0,1] on consecutive intervals of a stationary renewal process with a power-law interrenewal distribution. In the case when the distribution of generic Aj has either an atom at the point a=1 or a beta-type probability density in a neighborhood of a=1, we show that the covariance function of {Xt} decays hyperbolically with exponent between 0 and 1, and that a suitably normalized partial sums process of {Xt} weakly converges to a stable Lévy process.

Another example of a non-linear time series with misleading linear properties

Granger and Terasvirta provided an abstract example of a non-linear model that can generate data with the misleading linear property of long memory. They suggested that other non-linear models with this property are worth searching for. The empirical results of this article indicate that data generated from an exponential smooth transition autoregressive model can exhibit the long memory property whether in raw or temporally aggregated form.

Non-stationary Gaussian ARFIMA processes: Estimation and application

Recently, the study of time series turned the attention to the ones having long memory property. The ARFIMA (p,d,q) model shows this property when the degree of differencing d is in the interval (0.0,0.5), range where the process is stationary. In this work, we analyze the estimation of the degree d* in ARFIMA (p,d*,q) processes when d* >0.5, that is, when the processes are non-stationary but still have the property of long memory. We present a simulation study for the estimators of d* with semiparametric and parametric methods and different sample sizes. The methodology is applied to the experimental data series of UK long interest gilts.

ARCH-type bilinear models with double long memory

We discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation X t = ζ t A t + B t ,(★), where ζ t, t∈ Z are standard i.i.d. r.v.'s, and A t , B t are moving averages in X s, s<t . Stationary solution of (★) is obtained as an orthogonal Volterra expansion. In the case A t≡1, X t is the classical AR(∞) process, while B t ≡0 gives the LARCH model studied by Giraitis et al. (Ann. Appl. Probab. 10 (2000) 1002). In the general case, X t may exhibit long memory both in conditional mean and in conditional variance, with arbitrary fractional parameters 0<d 1< 1 2 and 0<d 2< 1 2 , respectively. We also discuss the hyperbolic decay of auto- and/or cross-covariances of X t and X t 2 and the asymptotic distribution of the corresponding partial sums’ processes.

Microeconomic Models for Long Memory in the Volatility of Financial Time Series

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991) and Kirman (1993), can replicate the empirical long-memory properties of the two first-conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly or indirectly, by those of the other participants. These "field effects" generate "herding" behavior that affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I (0), the series of absolute and squared returns display strong dependence, and the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common long-memory properties in the volatility and covolatility of financial time series revealed by Teyssière (1997, 1998a). These properties are investigated by using various model-independent tests and estimators, that is, semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski et al. (1992), Robinson (1995), Lobato and Robinson (1998), and Giraitis et al. (2000, forthcoming). The relative performance of these tests and estimators for long memory in a nonstandard data-generating process is then assessed.

Microeconomic Models for Long Memory in the Volatility of Financial Time Series

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical long-memory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly,or indirectly by those of the other participants. These field effects generate herding behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I(0), the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common long-memory properties in the volatility and co-volatility of financial time series, revealed by Teyssi

Volatility persistence in asset markets: long memory in high/low prices

This study addresses the issue of volatility persistence in asset markets by analysing the behaviour of daily ratios of highest and lowest prices for a number of different assets both inter-war and post-war. These series include sterling exchange rates, S&P futures prices, the FT30 and the price of gold. It is found that each of these series can be characterized as having the property of long memory so that observations far apart in time are non-negligibly correlated. More importantly, that each series can be modelled as fractionally-integrated noise, so that its behaviour can be captured by a single parameter.

Long Memory in Stock-Market Trading Volume

This article examines consistent estimation of the long-memory parameters of stock-market trading volume and volatility. The analysis is carried out in the frequency domain by tapering the data instead of detrending them. The main theoretical contribution of the article is to prove a central limit theorem for a multivariate two-step estimator of the memory parameters of a nonstationary vector process. Using robust semiparametric procedures, the long-memory properties of trading volume for the 30 stocks in the Dow Jones Industrial Average index are analyzed. Two empirical results are found. First, there is strong evidence that stock-market trading volume exhibits long memory. Second, although it is found that volatility and volume exhibit the same degree of long memory for most of the stocks, there is no evidence that both processes share the same long-memory component.

Analysing long memory and asymmetries

The paper presents evidence on nonlinearities in Finnish financial time series. The analysis concentrates on the so-called long-memory property which is examined using, various alternative test procedures. This analysis makes use of relatively long monthly Finnish time series which cover the period 1922–1996. The results give some evidence on long memory but one cannot say that the results would overwhelmingly support the existence of long memory in Finnish time series. There are, however, considerable differences between variables and the results are quite sensitive in terms of the treatment of short memory which also applies to different ways of prefiltering the data. Clearly more work is required to obtain more affirmative results in this respect. One way, of doing that is to apply asymmetric time models to find the source of nonlinearity. When that is done with the Finnish data some weak evidence on asymmetry is obtained.

Forecasting long memory left–right political orientations

This paper considers out-of-sample forecasting of left–right political orientations of party affiliates in the Netherlands, using weekly data from 973 independent national Dutch surveys conducted between 1978 and 1996. The orientations of left-wing and right-wing party affiliates tend to converge over time in the sense that the differences between the average positions tend to decline. The left–right series also reveal long-memory properties in the sense that shocks appear to be highly persistent. We develop forecasting models that account for these data features and we derive the relevant forecast intervals.

Pitfalls in testing for long run relationships

This paper analyzes the robustness of the two most commonly used cointegration tests: the single equation based test of Engle and Granger (EG) and the system based test of Johansen. We show analytically and numerically several important situations where the Johansen LR tests tend to find spurious cointegration with probability approaching one asymptotically. The situations investigated are of two types. The first one corresponds to variables that have long-memory properties and a trending behavior, but they are not pure I(1) processes although they are difficult to tell from I(1) with standard unit root tests. The second corresponds to I(1) variables whose VAR representation has a singular or near-singular error covariance matrix. In most of the situations investigated in this paper, EG test is more robust than Johansen LR tests. This paper shows that a proper use of the LR test in applied cointegration analysis requires a deeper data analysis than the standard unit root test. We conclude by recommending to use both tests (EG and Johansen) to test for cointegration in order to avoid or to discover a pitfall.

Real and Spurious Long-Memory Properties of Stock-Market Data]: Reply

Real and Spurious Long-Memory Properties of Stock-Market Data]: Reply

Real and Spurious Long-Memory Properties of Stock-Market Data

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure of Lobato and Robinson. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment

Real and Spurious Long-Memory Properties of Stock-Market Data

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure. Spurious results can be produced by nonstationarity and aggregation.

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment

Real and Spurious Long-Memory Properties of Stock-Market Data]: Comment