Linear signal extraction with intervention techniques in non-linear time series

Seasonal adjustment is performed in some data-producing agencies according to the ARIMA-model-based signal extraction theory. A stochastic linear process parametrized in terms of an ARIMA model is first fitted to the series, and from this model the models for the trend, cycle, seasonal, and irregular component can be derived. A spectrum is associated to every component model and is used to compute the optimal Wiener–Kolmogorov filter. Since the modelling is linear, prior linearization of the series with intervention techniques is performed. This paper discusses the performance of linear signal extraction with intervention techniques in non-linear processes. In particular, the following issues are discussed: (1) the ability of intervention techniques to linearize time series which present non-linearities; (2) the stability of the linear projection giving the components estimators under non-linear misspecifications; (3) the capacity of the WK filter to preserve the linearity in some components and the non-linearities in others. Copyright © 1998 John Wiley & Sons, Ltd.     

Unobserved components in ARCH models: An application to seasonal adjustment

The paper deals with unobserved components in ARIMA models with GARCH errors, in the context of an actual application, namely seasonal adjustment of the monthly Spanish money supply series. The series shows clear evidence of (moderate) non-linearity, which does not disappear with simple outlier correction. The GARCH structure explains reasonably well the non-linearity, and this explanation is robust with respect to the GARCH specification. We look at the time variation of the standard error of the adjusted series estimator and show how it can be measured. Next, we look at the implications this variation has on short-term monetary control. The non-linearity seems to have a small effect in practice. It is further seen that the conditional variance of the GARCH process may, in turn, be decomposed into components. In fact, the conditional variance of the money supply series is the sum of a weak linear trend, a strong non-linear seasonal component, and a moderate non-linear irregular component. This information has policy implications: for example, there are periods in the year when policy can be more assertive because information is more precise. Finally, looking at the non-linear components of the money supply it is seen how linear combinations of non-linear series can produce series that behave linearly.     

Bananas and petrol: further evidence on the forecasting accuracy of the ABS ‘headline’ and ‘underlying’ rates of inflation

In the light of the still topical nature of ‘bananas and petrol’ being blamed for driving much of the inflationary pressures in Australia in recent times, the ‘headline’ and ‘underlying’ rates of inflation are scrutinised in terms of forecasting accuracy. A general structural time‐series modelling strategy is applied to estimate models for alternative types of Consumer Price Index (CPI) measures. From this, out‐of‐sample forecasts are generated from the various models. The underlying forecasts are subsequently adjusted to facilitate comparison. The Ashley, Granger and Schmalensee (1980) test is then performed to determine whether there is a statistically significant difference between the root mean square errors of the models. The results lend weight to the recent findings of Song (2005) that forecasting models using underlying rates are not systematically inferior to those based on the headline rate. In fact, strong evidence is found that underlying measures produce superior forecasts. Copyright © 2009 John Wiley & Sons, Ltd.     

Seasonal prediction of European cereal prices: good forecasts using bad models?

Because of their natural adherence to the climate and pronounced seasonal cycles, prices of field crops constitute an interesting field for exploring seasonal time series models. We consider quarterly prices of two major cereals: barley and wheat. Using traditional in‐sample fit and moving‐window techniques, we investigate whether seasonality is deterministic or unit‐root stochastic and whether seasonal cycles have converged over time. We find that seasonal cycles in the data are mainly deterministic and that evidence on common cycles across countries differs for the two commodities. Out‐of‐sample prediction experiments, however, yield a ranking with respect to accuracy that does not match the statistical in‐sample evidence. Parametric bootstrap experiments establish that the observed mismatch is indeed an inherent and systematic feature. Copyright © 2008 John Wiley & Sons, Ltd.     

Selection and estimation of component models for seasonal time series

We present a method for investigating the evolution of trend and seasonality in an observed time series. A general model is fitted to a residual spectrum, using components to represent the seasonality. We show graphically how well the fitted spectrum captures the evidence for evolving seasonality associated with the different seasonal frequencies. We apply the method to model two time series and illustrate the resulting forecasts and seasonal adjustment for one series. Copyright © 2000 John Wiley & Sons, Ltd.     

The decomposition of forecast in seasonal arima models

This paper presents a procedure to break down the forecast function of a seasonal ARIMA model in terms of its permanent and transitory components. Both depend on the initial values at the forecast origin, but their structures are fixed and independent of this origin. The permanent component is an estimate of the long-run projection of the corresponding economic variable and the transitory element describes the approach towards the permanent one. Within the permanent component a distinction is made between the factors that depend on the initial conditions of the system and those that are deterministic. The procedure is compared to other methods presented in the literature and illustrated in an example.     

Time-series Properties and Forecasts of Crude Steel Consumption in the UK

This paper makes use of simple graphical techniques, a seasonal unit root test and a structural time-series model to obtain information on the time series properties of UK crude steel consumption. It shows that steel consumption has, after the removal of some quite substantial outliers, a fairly constant seasonal pattern, and a well-defined but stochastic business cycle. The long-run movement in steel consumption also appears to be stochastic in nature. These characteristics were used to identify a structural time-series model and the ex-post forecasts obtained from it performed reasonably well. Finally, this paper presents some ex-ante quarterly forecasts for crude steel consumption to the year 1999. © 1997 by John Wiley & Sons, Ltd.     

The leading indicator approach to economic forecasting—retrospect and prospect

Our purpose in this paper is to explain briefly the theory and rationale underlying the leading, coincident and lagging indicators, describe the more important statistical procedures used, and review the evidence on how the indicators have performed in practice. The tests of performance concentrate on data not used in the selection of the indicators, in the United States and nine other countries. We conclude with some suggestions for future research and development, including the application of the approach to the analysis of inflation.     

Using the life cycle to anticipate satisfaction at work

It was hypothesized that there are important non-linear life-cycle influences upon job and organizational satisfaction. Five common life-cycle stages were identified from the literature: the phases of ‘reality shock’, ‘socialization and growth’, ‘mid-career crisis’, ‘acceptance’, and ‘pre-retirement’. The first, third and last stages were expected to show declines in job and organizational satisfaction because of the personal and job-related disappointments and crises that typically occur during these periods of life. The second and fourth stages were expected to show increases in satisfaction because of the pleasant life experiences that often occur then. All but the first stage supported these hypotheses when we controlled for the influence of sex, education, job experience, level in the hierarchy and occupational upward mobility.     

Improved business planning through an awareness of political cycles

Can business planning be improved if more attention is paid to underlying political cycles? This paper compares practitioner and researcher perspectives on this issue. While practioners stand to gain useful insights from a careful examination of past political cycles, these insights may be disconfirmed by rigorous tests carried out by researchers. In this paper we isolate and examine five hypotheses from the literature on the political-economic cycle.