This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first provides a handbook and reference for the underlying mathematics (Part I, Chapters 1–6), statistical theory (Part II, Chapters 7–11), and stochastic process theory (Part III, Chapters 12–18). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 19–22), the central limit theorem (Part V, Chapters 23–26), and the functional central limit theorem (Part VI, Chapters 27–32). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.

Near‐epoch dependence (NED) is a generalized dependence concept for functions of mixing processes. This chapter gives definitions and examples, and considers the application to nonlinear dynamic processes. The relation to mixingales is the key theoretical result. Results on the preservation of NED under various transformations and a special result for the adapted sequence case are considered next. Finally, the related concept of approximability is defined which, unlike NED, can hold in the absence of integer moments.

A consistency theorem for kernel HAC variance estimators was originally proposed by Hansen (1992) but corrected under stronger conditions on the order of existing moments by de Jong (2000). The present result restores and also generalizes the conditions of Hansen’s result by assuming the process to be adapted to a filtration. It allows for nonstationarity, and dependence is modelled by the assumption of near-epoch dependence on a mixing process.

In Byzantium, usurpation was made possible by the conflict between hereditary-dynastic and meritocratic-republican theories of rulership. Legitimacy was founded upon subjective notions of idealized moral-behavioural norms drawn from the imperial virtues and Christian ideology. Authority could be challenged when it was perceived to deviate from these norms. Investitures transformed a usurper from a private individual to an emperor on the basis of ratification by popular consent. The historic ritual of reluctance allowed emperors to present themselves as ‘moral ideals’ at the moment of proclamation, ridding them of blame for a usurpation. Guilt and sin were inevitable byproducts of usurpation, but imperial repentance facilitated an expiation and legitimized imperial authority in relation to moral ideals. On occasion a usurper’s successors would perform repentance on his behalf, freeing the dynasty from the sins of its foundation. The treatment of defeated usurpers could take a variety of forms: reconciliations enabled a peaceful ‘healing’ of the community. Political mutilations transformed the victim’s appearance and rendered him ‘other’ in an attempt to demonstrate his immorality and illegitimacy. Degradation parades inverted recognised investiture rites in order to permanently alter a victim’s identity and reveal him to be a tyrant, acting against the interests of the people.

We propose a resampling method for stationary dependent time series, based on Rademacher wild bootstrap draws from the Fourier transform of the data. The main distinguishing feature of our method is that the bootstrap draws share their periodogram identically with the sample, implying good properties under autocorrelation of arbitrary form. A drawback of the basic procedure, that the bootstrap distribution of the mean is degenerate, is overcome by a simple Gaussian augmentation with variance estimated by a response surface fitted to preliminary simulations. Extensive Monte Carlo evidence is reported comparing alternative bootstrap methods in tests of significance and location in a regression model with autocorrelated shocks, and also of unit roots.

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. Copyright © 2015 John Wiley & Sons, Ltd.

We focus on two aspects of the links between world commodity prices and retail food price inflation: first, the effects of exchange rates and other input costs, and second; the effects of the duration of shocks on world commodity markets, not just the magnitude of price spikes (the latter often commanding most attention). The UK offers a natural and rather 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.

We focus on two aspects of the links between world commodity prices and retail food price inflation: first, the effects of exchange rates and other input costs, and second; the effects of the duration of shocks on world commodity markets, not just the magnitude of price spikes (the latter often commanding most attention). The UK offers a natural and rather 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.

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. JEL Classification: E31; Q02

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.

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.

Publihsed as chaper 2 of Essays in Nonlinear Time Series Econometrics; ed. by Niels Haldrup, Mika Meitz, and Pentti Saikkonen. Oxford University Press, 2014. ISBN-13: 9780199679959

Final version published in Handbook of Research Methods and Applications in Empirical Macroeconomics; edited by Nigar Hashimzade and Michael A. Thornton (Handbooks of Research Methods and Applications series) Edward Elgar, 2013 ISBN 9780857931016

Retail food price inflation in the UK peaked at nearly 14% in the summer of 2008, a level much higher than had been seen in the previous 10 years and, since then, food price inflation has continued to lead general inflation. An obvious factor driving domestic retail food prices is world commodity prices, but other factors matter too. In this paper, we model UK food price inflation and explore a range of potential drivers including world food prices, exchange rates, manufacturing costs, oil prices and wages. Over the period 1990-2010, we show that the major drivers of UK food price inflation are world raw food prices and the exchange rate; less important are manufacturing costs, unemployment and earnings. Oil prices matter too but indirectly via their effect on world agricultural commodity prices. We also show that the effect on domestic retail food price inflation depends on the duration of the shocks arising on world commodity markets.

Retail food price inflation in the UK peaked at nearly 14% in the summer of 2008, a level much higher than had been seen in the previous 10 years and, since then, food price inflation has continued to lead general inflation. An obvious factor driving domestic retail food prices is world commodity prices, but other factors matter too. In this paper, we model UK food price inflation and explore a range of potential drivers including world food prices, exchange rates, manufacturing costs, oil prices and wages. Over the period 1990-2010, we show that the major drivers of UK food price inflation are world raw food prices and the exchange rate; less important are manufacturing costs, unemployment and earnings. Oil prices matter too but indirectly via their effect on world agricultural commodity prices. We also show that the effect on domestic retail food price inflation depends on the duration of the shocks arising on world commodity markets. JEL Classification: E31; Q02

A Real Business Cycle model of the UK is developed to account for the behaviour of UK nonstationary macro data. The model is tested by the method of indirect inference, bootstrapping the errors to generate 95% confidence limits for a VECM representation of the data; we find the model can explain the behaviour of main variables (GDP, real exchange rate, real interest rate) but not that of detailed GDP components. We use the model to explain how 'crisis' and 'euphoria' are endemic in capitalist behaviour due to nonstationarity; and we draw some policy lessons.

We generalize Bierens’(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 but there are a number of mis-speci…cations, such as heteroskedastic errors, against which they will not typically have power. Our 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 …ts all" test. We specify a test based on a linear combination of individual components of the indicator vector 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. JEL classi…cation: C12 Keywords: speci…cation testing; quasi-maximum likelihood estimators; generalized method of moments estimators Corresponding Author: Andreea G. Halunga, Department of Economics, University of Exeter Business School, Streatham Court, Rennes Drive, Exeter EX4 4PU, UK. Email: a.g.halunga@exeter.ac.uk

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.