Temporal aggregation in a periodically integrated autoregressive process

A periodically integrated autoregressive process for a time series which is observed S times per year assumes the presence of S - 1 cointegration relations between the annual series containing the seasonal observations, with the additional feature that these relations are different across the seasons. This means that there is a single unit root in the vector autoregression for these annual series. In this paper it is shown that temporally aggregating such a process does not affect the presence of this unit root, i.e. the aggregated series is also periodically integrated

How Large is Average Economic Growth? Evidence from a Robust Method

This paper puts forward a method to estimate average economic growth, and its associated confidence bounds, which does not require a formal decision on potential unit root properties. The method is based on the analysis of either difference-stationary or trend-stationary time series models, implementing the robust bootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence indicates the practical relevance of the method. It is illustrated on quarterly post-war US industrial production

The Econometrics Of The Bass Diffusion Model

We propose a new empirical representation of the Bass diffusion model, in order to estimate the three key parameters, concerning innovation, imitation and maturity. The representation is based on the notion that the observed data may temporarily deviate from the mean path determined by the underlying hazard rate. Additionally, it rests on the idea that uncertainty about the cumulative process should be smaller, the closer it is to the start of the process and to the level of maturity. Taking this into account, we arrive at an extension of the basic representation proposed in Bass (1969), with an additional heteroskedastic error term. The type of heteroskedasticity can be set by the modeler, as long as it obeys certain properties. Next, we discuss the asymptotic theory for this new empirical model, that is, we focus on the properties of the estimators of the various parameters. We show that the parameters, upon standardization by their standard errors, do not have the conventional asymptotic behavior. For practical purposes, it means that the t-statistics do not have an (approximate) t-distribution. Using simulation experiments, we address the issue how these findings carry over to practical situations. In a next set of simulation experiments, we compare the new representation with that of Bass (1969) and Srinivasan and Mason (1986). We document that these last two approaches often seriously overestimate the precision of the parameter estimators. We also shed light on the effects of temporal aggregation and on the effects of a serious and persisent deviation between the actual data and their mean. Finally, we consider the various empirical representations for a monthly series on installed ATMs

Robust inference on average economic growth

We discuss a method to estimate the confidence bounds for average economic growth, which is robust to misspecification of the unit root property of a given time series. We derive asymptotic theory for the consequences of such misspecification. Our empirical method amounts to an implementation of the bootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence su

A New Multivariate Product Growth Model

To examine cross-country diffusion of new products, marketing researchers have to rely on a multivariate product growth model. We put forward such a model, and show that it is a natural extension of the original Bass (1969) model. We contrast our model with currently in use multivariate models and we show that inference is much easier and interpretation is straightforward. In fact, parameter estimation can be done using standard commercially available software. We illustrate the benefits of our model relative to other models in simulation experiments. An application to a three-country CD sales series shows the merits of our model in practice

Dynamic specification and cointegration

The article discusses the use of some Monte Carlo experiments to investigate the effects of dynamic specification on the size and power of three cointegration tests. The first test, proposed by Engle and Granger (1987), is the residual augmented Dickey-Fuller unit root test. The second is a Wald test for the significance of the error correction mechanism in an autoregressive-distributed lag model, suggested by Boswijk (1989) and further developed in Boswijk (1991). The third test is a likelihood ratio test in a vector autoregressive model, proposed by Johansen (1988) and extended in Johansen and Juselius (1990)

Periodic cointegration - Representation and Inference

This paper considers a new approach to the analysis of stable relationships between nonstationary seasonal time series. The basis of this approach is an error correction model in which both long-run effects and adjustment parameters are allowed to vary per season. First, we discuss theoretical arguments for such a periodic error correction model. We define periodic cointegration and compare this to the concept of seasonal cointegration. Next, we analyze statistical inference in the periodic error correction model A sequential procedure is proposed, consisting of a test for periodic cointegration, an estimator of the cointegration parameters and adjustment coefficients, and a class of tests for the hypothesis that some of the parameters are constant over the seasons. The finite sample behavior of the proposed test statistics is analyzed in a limited Monte Carlo exercise. We conclude the paper with an application to a model of aggregate Swedish consumption

Special issue on Time Series Econometrics

SCOPUS: ed.jinfo:eu-repo/semantics/publishe