Professor James Davidson

We address the links between world commodity prices and retail food price inflation, focussing on two aspects. First, since world commodity prices represent a relatively small share of costs of retail food products, retail price behaviour may differ from world commodity prices and other factors (exchange rates and other input costs) will also matter in determining retail food inflation. Second, noting that the world price spike of 2007-2008 was different in the level and duration from the price spike experienced in 2011, we also emphasise an obvious but neglected fact that the effect on retail food price inflation depends on the duration
of the shocks on world commodity markets, not just the magnitude of price spikes (the latter often commanding most attention). Being an open economy reliant on world commodity trade, the UK offers a natural and hitherto unexplored setting for the analysis. Applying time
series methods to a sample of 259 monthly observations over the 1990(9)-2012(3) period we
find substantial and significant long term partial elasticities for domestic food price inflation with respect to world food commodity prices, the exchange rate and oil prices (the latter indirectly via a relationship with world food commodity prices). Domestic demand pressures
and food chain costs are found to be less substantial and significant over our data period.
Interactions between the main driving variables in the system tend to moderate rather than exacerbate these partial effects. Furthermore, the persistence of shocks to these variables markedly affects their effects on domestic food prices.

© 2016 John Wiley & Sons, Ltd.This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO2 and CH4. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods.

This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skip-sampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of significance of the long memory parameter, and a composite test procedure is described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependent-sample bootstrap technique to approximate short-run dependence following fractional differencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.

© 2015 Elsevier B.V.This paper derives a simple sufficient condition for strict stationarity in the ARCH(∞) class of processes with conditional heteroscedasticity. The concept of persistence in these processes is explored, and is the subject of a set of simulations showing how persistence depends on both the pattern of lag coefficients of the ARCH model and the distribution of the driving shocks. The results are used to argue that an alternative to the usual method of ARCH/GARCH volatility forecasting should be considered.

Tests for cointegration with allowance for structural breaks using the extrema of residual-based tests over subsamples of the data are considered. One motivation for the approach is to formalize the practice of data snooping by practitioners, who may examine subsamples after failing to find a predicted cointegrating relationship. Valid critical values for such multiple testing situations may be useful. The methods also have the advantage of not imposing a form for the alternative hypothesis–in particular slope vs. intercept shifts and single versus multiple breaks–and being comparatively easy to compute. A range of alternative subsampling procedures, including sample splits, incremental and rolling samples are tabulated and compared experimentally. Shiller’s annual stock prices and dividends series provide an illustration.

This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process. possibly, itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analysed in a previous paper, and the construction derived from moving average representations in the time domain. Depending on the values of the long memory parameters and choice of normalization, the limiting integral
is shown to be expressible as the sum of a constant and two itô-type integrals with respect to distinct Brownian motions. In certain cases the latter terms are of small order relative to the former. The mean is shown to match that of the harmonic representation, where the latter is defined, and satisfies the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulae are valid for the full range of the long memory parameters, and extend to non-Gaussian processes.

This paper proposes simple Hausman-type tests to check for bias in the log-periodogram regression of a time series believed to be long memory. The statistics are asymptotically standard normal on the null hypothesis that no bias is present, and the tests are consistent.

The so-called type I and type II fractional Brownian motions are limit distributions associated with the fractional integration model in which pre-sample shocks are either included in the lag structure, or suppressed. There can be substantial differences between the distributions of these two processes and of functionals derived from them, so that it becomes an important issue to decide which model to use as a basis for inference. Alternative methods for simulating the type I case are contrasted, and for models close to the nonstationarity boundary, truncating infinite sums is shown to result in a significant distortion of the distribution. A simple simulation method that overcomes this problem is described and implemented. The approach also has implications for the estimation of type I ARFIMA models, and a new conditional ML estimator is proposed, using the annual Nile minima series for illustration.

We consider Breitung’s (2002) statistic ξn which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in. distribution of ξn as n → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π2, a result that holds under
any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called “cotangent trick” associated with Cauchy’s residue theorem.

This paper compares models of fractional processes and associated weak convergence results based on moving average representations in the time domain with spectral representations. Both approaches have been applied in the literature on fractional processes. We point out that the conventional forms of these models are not equivalent, as is commonly assumed, even under a Gaussianity assumption. We show that it is necessary to distinguish between ‘two-sided’ processes depending on both leads and lags from one-sided or ‘causal’ processes, since in the case of fractional processes these models yield different limiting properties. We derive new representations of fractional Brownian motion, and show how different results are obtained for, in particular, the distribution of stochastic integrals in the multivariate context. Our results have implications for valid statistical inference in fractional integration and cointegration models.

We consider the problem of selecting the auxiliary distribution to implement the wild bootstrap for regressions featuring heteroscedasticity of unknown form. Asymptotic refinements are nominally obtained by choosing a distribution with second and third moments equal to 1. We show that this stipulation may fail in practice, due to the distortion imposed on higher moments. We propose a new class of two-point distributions and suggest using the Kolmogorov-Smirnov statistic as a selection criterion. The results are illustrated by a Monte Carlo experiment.

This paper extends the results of Byers, Davidson and Peel (1997) on long memory in support for the Conservative and Labour Parties in the UK using longer samples and additional poll series. It finds continuing support for the ARFIMA(0,d,0) model though with somewhat smaller values of the long memory parameter. We find that the move to telephone polling in the mid-1990s has no apparent effect on the estimated value of d for either party. Finally, we find that we cannot reject the hypotheses that the parties share a common long memory parameter which we estimate at around 0.65.

Two versions of a fractionally cointegrating vector error correction model (FVECM) are presented. In the case of regular cointegration, linear combinations of fractionally integrated variables are integrated to lower order. Generalized cointegration is defined as the case where the cointegrating variables may be fractional differences of the observed series. The concepts are applied to a model of poll data on approval of the performance of prime ministers and governments in the UK.

In this paper we generalize BierensÂ’(1982, 1990) approach to a wider class of models and estimators. Bierens constructs consistent moment tests in the context of linear and nonlinear
least squares, by exploiting the property of the regression residuals of having zero conditional
mean in the true model. These tests are speciÂ
c to the least squares framework and there
are a number of mis-speciÂ
cations, such as heteroskedastic errors, against which they will
not typically have power. Our extended framework is independent of the form of the model,
and covers all variants of maximum likelihood and quasi-maximum likelihood estimation and
also the generalized method of moments. It has particular applications in new cases such
as discrete data models, but the chief appeal of our approach is that it provides a "one size
Â
ts all" test, that can be computed routinely, does not need to be tailored to the particular
model, and is expected to have power against a wide class of alternatives. Although primarily
envisaged as a test of functional form, this type of moment test can also be extended to testing for omitted variables by deÂ
ning the weighting functions appropriately.