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This chapter extends the univariate forecasting method proposed by Wang, Luc, and Hsiao (2013) to forecast the multivariate long memory model subject to structural breaks. The approach does not need to estimate the parameters of this multivariate system nor need to detect the structural breaks. The only procedure is to employ a VAR(k) model to approximate the multivariate long memory model subject to structural breaks. Therefore, this approach reduces the computational burden substantially and also avoids estimation of the parameters of the multivariate long memory model, which can lead to poor forecasting performance. Moreover, when there are multiple breaks, when the breaks occur close to the end of the sample or when the breaks occur at different locations for the time series in the system, our VAR approximation approach solves the issue of spurious breaks in finite samples, even though the exact orders of the multivariate long memory process are unknown. Insights from our theoretical analysis are confirmed by a set of Monte Carlo experiments, through which we demonstrate that our approach provides a substantial improvement over existing multivariate prediction methods. Finally, an empirical application to the multivariate realized volatility illustrates the usefulness of our forecasting procedure.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

This paper shows that volatility persistence in GARCH models and spurious long memory in autoregressive models may arise if the possibility of structural changes is not incorporated in the time series model. It also describes a tractable hidden Markov model (HMM) in which the regression parameters and error variances may undergo abrupt changes at unknown time points, while staying constant between adjacent change-points. Applications to real and simulated financial time series are given to illustrate the issues and methods.

The purpose of this paper is to re-examine the long-run relationship between radiative forcing (including emissions of carbon dioxide, sulphur oxides, methane and solar radiation) and temperatures from a structural time series modelling perspective. The authors assess whether forcing measures are cointegrated with global temperatures using the structural time series approach.

A Bayesian approach is used to obtain estimates that represent the uncertainty regarding this relationship. The estimated structural time series model enables alternative model specifications to be consistently compared by evaluating model performance.

The results confirm that cointegration between radiative forcing and temperatures is consistent with the data. However, the results find less support for cointegration between forcing and temperature data than found previously.

Given considerable debate within the literature relating to the “best” way to statistically model this relationship and explain results arising as well as model performance, there is uncertainty regarding our understanding of this relationship and resulting policy design and implementation. There is a need for further modelling and use of more data.

There is divergence of views as to how best to statistically capture, explain and model this relationship. Researchers should avoid being too strident in their claims about model performance and better appreciate the role of uncertainty.

The results of this study make a contribution to the literature by employing a theoretically motivated framework in which a number of plausible alternatives are considered in detail, as opposed to simply employing a standard cointegration framework.

This paper examines the time‐series behaviour of house prices for the four Asian markets, namely, Hong Kong, Singapore, Tokyo and Taipei, by using structural time‐series methodology. The paper assumes two types of trend models to characterise and compare the long‐run movement of house prices. It also examines the cyclical pattern hidden in the series. The long‐run trend rate in these markets ranged between approximately 1.6 and 3.2 per cent per annum. Hong Kong, Singapore and Taipei have relatively higher figures, which could be expected in light of the rapidly growing economies. Surprisingly, their cyclical patterns were fairly similar, although causes of the cycles differed. The markets were found to have stochastic cycles of around one year, two to four years and seven to ten years, which were consistent with previous findings on real business cycles commonly observed internationally in other macroeconomic time series. However, the found stochastic nature suggests all these markets are not in a steady state and is still changing.

The global financial crisis (GFC) of 2008‐2009 has highlighted the need for understanding fluctuations in housing variables and how, as such, they contribute to understanding how housing markets work. The contention of this paper is to present a univariate structural time series analysis of the Australian Housing Finance Commitments (HFCs) covering the period 1988:6‐2009:5. The empirical analysis aims to focus on establishing whether monthly HFCs exhibit the expected cyclical and seasonal variations. The presence of a monthly seasonal pattern in HFCs is to be ascertained by way of testing possible hypotheses that explain such a pattern.

A structural time series framework approach, used in this paper, is in line with that promulgated by Harvey. Such models can be interpreted as regressions on functions of time in which the parameters are time‐varying. This makes them a natural vehicle for handling changing seasonality of a complex form. The structural time series model is applied to seasonally unadjusted monthly HFCs, between 1988:6 and 2009:5. The data have been sourced from the ABS. For consistency, the sample for each variable is standardised to start with the first available July observation and end with the latest available June observation.

The modelling results confirm the presence of cyclicality in HFCs. The magnitude of the observed cycle‐related changes is A$817m. A structural time series model incorporating trigonometric specification reveals that seasonality is also present and that it is stochastic (as implied by the inconsistency of the monthly seasonal factors over the sample period). The magnitude of monthly seasonal changes is A$435.8m. The results show the presence of statistically significant factors for January, February, March, April, May, September, October and November, which are attributed to “spring”, “summer” and “autumn” seasonal effects.

Empirical evidence of variations in housing‐related variables is relatively limited. A study of the literature uncovered that most studies focus on house prices and found no empirical research focusing on fluctuations in HFCs. Consequently, this research aims to be the first to explain the presence of seasonal and cyclical fluctuations in such an important housing variable as HFCs. Moreover, the paper aims to enhance the practice of modelling seasonal influences on housing variables.

Online advertising such as Google AdWords gives small and medium-sized enterprises access to new markets at reduced costs. The purpose of this paper is to analyse the visibility and performance of a website and to test the effectiveness of online marketing using the data provided by Google Analytics.

The authors use a class of econometric time series models with unobservable components, Structural Time Series Models (STSM). The authors allow for time-varying trends to take into account the non-stationary behaviour displayed by time series. The authors illustrate the model using daily data from a local tourist website. Three specific questions are addressed: do paid keywords campaigns increase the volume and quality of search traffic? Do paid keywords affect the volume and quality of the unpaid traffic? How do paid and unpaid keywords perform?

The results for the case study show that: first, online campaigns affect traffic volume positively but their effectiveness on traffic quality is uncertain; second, paid keywords do not affect the volume and quality of unpaid traffic; third, the increase in traffic volume is not always due to the paid keywords and the lowest quality visits come from paid traffic.

This analysis may help webmasters to design successful online advertising strategies.

This study contributes to the development of user-friendly methodologies to monitor website performance. The analysis shows that STSM is a suitable methodology to test the effectiveness of online campaigns and to assess the changes over time in the performance of a website.