1,720,992 research outputs found
First Stage Estimation of Fractional Cointegration
No full textIn a fractionally cointegrated model, we analyze, both theoretically and by means of a Monte Carlo experiment, the performance of the most popular first stage estimation methods, including ordinary and narrow band least squares (Robinson, 1994), difference taper narrow band least squares (Chen and Hurvich, 2003a), instrumental variables (Robinson and Gerolimetto, 2006), and compare it with the behavior of a new proposal, the integrated ordinary least squares. An appropriate version of this latter estimator (and also of the instrumental variables one) achieves in all circumstances the fastest convergence rate (among other first stage methods) and performs well in finite samples. The use of improved first stage methods is most important in cases of low collective memory of regressor and cointegrating error. This is particularly relevant in multivariate settings, where the key parameters which rule the convergence properties of the estimators are the memories of adjacent cointegrating subspace
Nonparametric detection of a time-varying mean
No full textWe propose a nonparametric portmanteau test for detecting changes in the unconditional mean of a univariate time series which may display either long or short memory.
Our approach is designed to have power against, among other things, cases where the mean component of the series displays abrupt level shifts, deterministic trending behaviour, or is subject to some form of time-varying, continuous change. The test we propose is simple to compute, being based on ratios of periodogram ordinates, has a pivotal limiting null distribution of known form which reduces to the multiple of a χ2 random variable in the case where the series is short memory, and has power against a wide class of time-varying mean models. A Monte Carlo simulation study into the finite sample behaviour of the test shows it to have both good size properties under the null for a range of long and short memory series and to exhibit good power against
a variety of plausible time-varying mean alternatives. Because of its simplicity, we recommend our periodogram ratio test as a routine portmanteau test for whether the mean component of a time series can reasonably be treated as constant
Testing for equal predictive accuracy with strong dependence
Full text linkWe analyse the properties of the Diebold and Mariano (1995) test in the presence of autocorrelation in the loss differential. We show that the power of the Diebold and Mariano (1995) test decreases as the dependence increases, making it more difficult to obtain statistically significant evidence of superior predictive ability against less accurate benchmarks. We also find that, after a certain threshold, the test has no power and the correct null hypothesis is spuriously rejected. Taken together, these results
caution to seriously consider the dependence properties of the loss differential before the application of the Diebold and Mariano (1995) test
Local Whittle estimation of the memory parameter in presence of deterministic components
No full textWe discuss the estimation of the order of integration of a fractional process that may be contaminated by a time-varying deterministic trend or by a break in the mean. We show that in some cases the estimate may still be consistent and asymptotically normally distributed even when the order of magnitude of the spectral density of the fractional process does not dominate the one of the periodogram of the contaminating term. If trimming is introduced, stronger deterministic components may be neglected. The performance of the estimate in small samples is studied in a Monte Carlo experiment. Copyright Copyright 2009 Blackwell Publishing Ltd
Comparing predictive ability in presence of instability over a very short time
Full text linkWe consider forecast comparison in the presence of instability when this
affects only a short period of time. We demonstrate that global tests do not perform well in this case, as they were not designed to capture very short-lived instabilities, and their power vanishes altogether when the magnitude of the shock is very large. We then propose and discuss approaches that are more suitable to detect such situations, such as nonparametric methods like the S test from Andrews (2003) or the MAX procedure from Harvey et al. (2021). We illustrate these results in a Monte Carlo exercise and in a comparison of the nowcast of the quarterly US nominal GDP from the Survey of Professional Forecasters (SPF) against a naive benchmark of no growth, over a period that includes the GDP instability brought by the COVID-19 crisis. We recommend that the forecaster does not pool the sample, but excludes the short periods of high local instability from the evaluation exercise
Spatial effects in a common trend model of US city-level CPI
No full textThis paper studies relative movements in price indices of 17 US cities. We employ an unobserved common trend model where the trend can be stochastic or deterministic with possible breaks or other nonlinearities. To accommodate the spatial nature of the data we allow for spatially correlated short-run shocks. In this way, the speed of convergence to the equilibrium implied by the law of one price is estimated taking into account the effect of distances across cities. The parameters of the model are estimated using a generalized method of moments (GMM) method which incorporates moment conditions corresponding to a generalized least squares-like within estimator of regression parameters. We find a slow rate of convergence of the price levels and strong evidence of spatial effects
Small-b and fixed-b asymptotics for weighted covariance estimation in fractional cointegration
Full text linkIn a standard cointegrating framework, Phillips (1991) introduced the weighted covariance (WC) estimator of cointegrating parameters. Later, Marinucci (2000) applied this estimator to fractional circumstances and, like Phillips (1991), analysed the so-called small-b asymptotic approximation to its sampling distribution. Recently, an alternative limiting theory (fixed-b asymptotics) has been successfully employed to approximate sampling distributions. With the purpose of comparing both approaches, we derive here the fixed-b limit of WC estimators in a fractional setting, filling also some gaps in the traditional (small-b) theory. We also provide some Monte Carlo evidence that suggests that the fixed-b limit is more accurate
Semiparametric Tests for the Order of Integration in the Possible Presence of Level Breaks
Full text linkLobato and Robinson (1998) develop semiparametric tests for the null hypothesis
that a series is weakly autocorrelated, or I(0), about a constant level, against frac-
tionally integrated alternatives. These tests have the advantage that the user is not
required to specify a parametric model for any weak autocorrelation present in the
series. We extend this approach in two distinct ways. First we show that it can be
generalised to allow for testing of the null hypothesis that a series is I(d) for any
d lying in the usual stationary and invertible region of the parameter space. The
second extension is the more substantive and addresses the well known issue in the
literature that long memory and level breaks can be mistaken for one another, with
unmodelled level breaks rendering fractional integration tests highly unreliable. To
deal with this inference problem we extend the Lobato and Robinson (1998) ap-
proach to allow for the possibility of changes in level at unknown points in the se-
ries. We show that the resulting statistics have standard limiting null distributions,
and that the tests based on these statistics attain the same asymptotic local power
functions as infeasible tests based on the unobserved errors, and hence there is no
loss in asymptotic local power from allowing for level breaks, even where none is
present. We report results from a Monte Carlo study into the finite-sample be-
haviour of our proposed tests, as well as several empirical examples
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