In Defence of Model-Based Seasonal Adjustment: An Illustration Using Australian Data

It is argued that the X-11 seasonal adjustment procedure suffers from severe drawbacks, and so it should be abandoned in favour of model-based seasonal adjustment. Furthermore, it is argued that Harvey's structural time series model is superior to the conventional seasonal ARIMA models for the purpose of model-based seasonal adjustment. It is shown, with the help of a large number of Australian time series, that the nature of seasonality differs from one series to another, and this is why model selection is crucial for seasonal adjustment. It is further shown that model-based seasonal adjustment could produce results that are significantly different from those obtained by applying the X-11 procedure. Since the X-11 procedure is not based on an explicit model and in view of its other serious drawbacks, it is concluded that the procedure should be abandoned in favour of model-based seasonal adjustment.     

Calendar effects in structural time series models with trend and season

Calendar effects are analysed in the class of structural time series models one of the two main model based approaches in time series decomposition. While Bell and Hillmer (1983) modeled calendar variation in the ARIMA model based approach, we represent structural models in the generalized regression form which allows to apply classical estimation and test procedures. It turns out that the expected high computaional complexity 0(T ³) in the generalized regression model can be reduced to 0(T). As all parameters are estimated by maximizing the likelihood the Likelihood Ratio statistics can be used to test effects of the calendar composition.     

THE PURE CHARACTERISTICS DEMAND MODEL*

In this article, we consider a class of discrete choice models in which consumers care about a finite set of product characteristics. These models have been used extensively in the theoretical literature on product differentiation and the goal of this article is to translate them into a form that is useful for empirical work. Most recent econometric applications of discrete choice models implicitly let the dimension of the characteristic space increase with the number of products (they have “tastes for products”). The two models have different theoretical properties, and these, in turn, can have quite pronounced implications for both substitution patterns and for the welfare impacts of changes in the number and characteristics of the goods marketed. After developing those properties, we provide alternative algorithms for estimating the parameters of the pure characteristic model and compare their properties to those of the algorithm for estimating the model with tastes for products. We conclude with a series of Monte Carlo results. These are designed to illustrate: (i) the computational properties of the alternative algorithms for computing the pure characteristic model, and (ii) the differences in the implications of the pure characteristic model from the models with tastes for products.     

Fuzzy Seasonal Time Series for Forecasting the Production Value of the Mechanical Industry in Taiwan

Based on the seasonal time series ARIMA(p,d,q)(P,D,Q)_s model (SARIMA) and fuzzy regression model, we combine the advantages of two methods to propose a procedure of fuzzy seasonal time series and apply this method to forecasting the production value of the mechanical industry in Taiwan. The intention of the article is to provide the enterprises, in this era of diversified management, with a fresh method to conduct short-term prediction for the future in the hope that these enterprises can perform more accurate planning. This method includes interval models with interval parameters and provides the possibility distribution of future value. From the results of practical application to the mechanical industry, it can be shown that this method makes good forecasts. Further, this method makes it possible for decision makers to forecast the possible situations based on fewer observations than the SARIMA model and has the basis of pre-procedure for fuzzy time series.     

Seasonal fluctuations and equilibrium models of exchange rate

Most of the evidence on dynamic equilibrium exchange rate models is based on seasonally adjusted consumption data. Equilibrium models have not worked well in explaining the actual exchange rate. However, the use of seasonally adjusted data might be responsible for the spurious rejection of the model. This article presents a new equilibrium model for the exchange rates that incorporates seasonal preferences. The fit of the model to the data is evaluated for five industrialized countries using seasonally unadjusted data. Our findings indicate that a model with seasonal preferences can generate monthly time series of the exchange rate without seasonality even when the variables that theoretically determine the exchange rate show clear seasonal behaviours. Further, the model can generate theoretical exchange rates with the same order of integration than actual exchange rates, and in some cases, with the same stochastic trend.     

Intraday bidirectional volatility spillover across international stock markets: does the global financial crisis matter?

This article studies volatility spillover between the US and the three largest European stock markets (Frankfurt, London and Paris) around the time of the recent Subprime crisis. In order to investigate the impact of the latter, we break our sample down into two sub-periods: a pre-crisis period and a post-crisis period, using a structural break test that has the advantage of endogenously testing for further breaks in the data. Unlike previous studies that have frequently investigated this issue using low frequency data, our article makes use of intraday data. Accordingly, using Threshold generalized autoregressive conditional heteroscedasticity (GARCH) model estimations, we find weak evidence of volatility transmission between the two regions before the Subprime crisis. However, during the post-crisis period, we record returns and volatility spillover from US to European markets and vice versa at different times of the trading day, indicating that the two regions became more dependent during the recent Subprime crisis, a finding that supports the contagion hypothesis between the US and European stock markets.     

Multiple time series analysis of simultaneous equations model specification

This paper presents an extension of the Zellner-Palm methodology using the multiple time series representation of an underlying structural econometric model. The multiple time series approach avoids the problem of cancellation of common factors that has made it difficult to infer structural model characteristics from univariate time series models. In addition the correspondence between the structural model and the multiple time series model provides structural content to the tests for Granger-causality. The approach is illustrated with applications to small macroeconomic models of Friedman and Sargent and Wallace.     

Adaptive ARFIMA models with applications to inflation

Many previous analyses of inflation have used either long memory or nonlinear time series models. This paper suggests a simple adaptive modification of the basic ARFIMA model, which uses a flexible Fourier form to allow for a time varying intercept. Simulation evidence suggests that the model provides a good representation of various forms of structural breaks and also that the new model can be efficiently estimated by a QMLE approach. We investigate monthly CPI inflation series for the G7 countries and find evidence of stable long memory parameters across regimes and also of significant nonlinear effects. The estimated adaptive ARFIMA models generally have less persistent long memory parameters than previous studies, with the estimated time dependent intercept being an important component. The model is also supplemented with an adaptive FIGARCH component, yielding a double nonlinear long memory model.     

Measuring sustainability performance for China: A sequential generalized directional distance function approach

This paper aims to present certain composite sustainability efficiency indicators for China based on a sequential generalized directional distance function. This approach can measure the sustainability performance of a country with diverse outputs, nature of technologies, and non-radial slacks. First, we propose the concept of a generalized directional distance function under a sequential environmental production technology. Second, we develop several standardized composite indicators related to sustainability performance. We then estimate the sequential generalized directional distance function based on a series of sequential data envelopment analysis models. Finally, we empirically examine regions in China using the proposed model and present some implications based on the empirical results.     

Seasonal fractional components in macroeconomic time series

Seasonal fractional models are shown in this article to be alternative credible ways of modelling the seasonal component in macroeconomic time series. A testing procedure that allows one to test different orders of integration at zero and at each of the seasonal frequencies is described. This procedure is then applied to the Italian consumption and income series, the results being very sensitive to the way of modelling the I(0) disturbances.     

Modelling seasonality in innovation diffusion

The ability to forecast new product growth is especially important for innovative firms that compete in the marketplace. Today many new products exhibit very strong seasonal behaviour, which may deserve specific modelling, both for producing better forecasts in the short term and for better explaining special market dynamics and related managerial decisions. By considering seasonality as a deterministic component to be estimated jointly with the trend through Nonlinear Least Squares methods, we have developed two extensions of the Guseo–Guidolin model that are able to simultaneously describe trend and seasonality. Such models are based on two different but equally reasonable approaches: in one case we consider a simple additive decomposition of a time series and design a model in which seasonality is directly added to the trend and jointly estimated with it; in the other we design a more complex structure, mimicking that of a Generalized Bass model and embed two separate seasonal perturbations within the dynamic market potential and the corresponding adoption process. The different characteristics of two products, a pharmaceutical drug and an IT device, make it possible to appreciate empirically various modelling options and performances. Both models are quite simple to implement and to interpret from a managerial point of view.     

Modelling the domestic and foreign tourist arrivals to Tamil Nadu (India)

In recent years, due to the Indian Federal Government's and Tamil Nadu State Government's various initiatives and promotional activities, foreign and domestic tourist arrivals in Tamil Nadu are on the increase. This article aims to model the monthly tourist arrivals (foreign as well as domestic) in Tamil Nadu for monthly time series data during the period 1998 to 2002 using univariate time-series models. As both time series show strong seasonal patterns, we also investigate the possibility of seasonal unit roots in the domestic and foreign tourist arrivals series. The results show that significant growth in domestic and foreign arrivals takes place during the months December to January. Growth rate for domestic tourist arrivals is positive during April and May, but is negative for the foreign tourist arrivals during April and insignificant during May. Such information would be very useful to the Tamil Nadu government and the tourism industry in maximizing the usage of available tourist spot infrastructure and to provide high quality service.     

Volatility–volume co-movements: evidence from China metal markets

This article investigates the interactional relationship between price volatility and futures trading activity for three heavily traded metal products on the Shanghai Metal Exchange and the Shanghai Futures Exchange. Using models based on vector autoregression and generalized method of moments, we show, in particular, that futures trading activity has a strong impact on both spot and futures price volatility in copper and aluminium markets. Futures trading activity leads spot market volatility in copper and aluminium markets which suggests that futures markets have a destabilizing effect. In order to disentangle the effect of different traders’ types on asset price movements, we decompose futures trading into speculators’ and hedgers’ trading and investigate their contributions to volatility. As a robustness check, we investigate the impact of endogenous structural breaks on the interactional relationship between price volatility and futures trading.     

Masking of volatility by seasonal adjustment methods

We report that the X-12 ARIMA and TRAMO–SEATS seasonal adjustment methods consistently underestimate the variability of the differenced seasonally adjusted series. We show that underestimation is due to a non-zero estimation error in estimating the seasonal component at each time period, which is the result of the use of low order seasonal filter in X12-ARIMA for estimating the seasonal component. Hence, we propose the use of high order seasonal filter for estimating the seasonal component, which helps reducing the estimation error noticeably, helps amending the underestimation problem, and helps improving the forecasting accuracy of the series. In TRAMO–SEATS, Airline model is found to deliver the best seasonal filter among other ARIMA models.     

The price of owning a car: an analysis of auction quota premium in Singapore

Faced with dilemmas parallel to countries besieged by road congestions and limited land resources, Singapore has chosen to adapt a Vehicle Quota System (VQS) whereby car owners are required to bid for a licence in an auction before their vehicles are allowed onto the road. In this study, the behaviour of VQS auction prices is examined using a structural time series approach. For outliers that are not observable from innovations, auxiliary residuals with dummy variables are used to supplement the analysis. In general, prices exhibit a fairly constant seasonal pattern. The inclusion of monthly VQS quotas released by the transport regulatory body and the national stock market index is not useful in explaining the observed price behaviour. Interestingly, a basic structural model with stochastic components seems to fit the data best.     

Forecasting business and consumer surveys indicators–a time-series models competition

The objective of this article is to compare different time-series methods for the short-run forecasting of Business and Consumer Survey Indicators. We consider all available data taken from the Business and Consumer Survey Indicators for the Euro area between 1985 and 2002. The main results of the forecast competition are offered not only for raw data but we also consider the effects of seasonality and removing outliers on forecast accuracy. In most cases, the univariate autoregressions were not outperformed by the other methods. As for the effect of seasonal adjustment methods and the use of data from which outliers have been removed, we obtain that the use of raw data has little effect on forecast accuracy. The forecasting performance of qualitative indicators is important since enlarging the observed time series of these indicators with forecast intervals may help in interpreting and assessing the implications of the current situation and can be used as an input in quantitative forecast models.     

Was the recent downturn in US real GDP predictable?

This article uses a small set of variables – real GDP, the inflation rate and the short-term interest rate – and a rich set of models – atheoretical (time series) and theoretical (structural), linear and nonlinear, as well as classical and Bayesian models – to consider whether we could have predicted the recent downturn of the US real GDP. Comparing the performance of the models to the benchmark random-walk model by root mean-square errors, the two structural (theoretical) models, especially the nonlinear model, perform well on average across all forecast horizons in our ex post, out-of-sample forecasts, although at specific forecast horizons certain nonlinear atheoretical models perform the best. The nonlinear theoretical model also dominates in our ex ante, out-of-sample forecast of the Great Recession, suggesting that developing forward-looking, microfounded, nonlinear, dynamic stochastic general equilibrium models of the economy may prove crucial in forecasting turning points.     

Models of mortality rates – analysing the residuals

The area of mortality modelling has received significant attention over the last 25 years owing to the need to quantify and forecast improving mortality rates. This need is driven primarily by the concern of governments, insurance and actuarial professionals and individuals to be able to fund their old age. In particular, to quantify the costs of increasing longevity we need suitable model of mortality rates that capture the dynamics of the data and forecast them with sufficient accuracy to make them useful. In this article, we test several of the leading time series models by considering the fitting quality and in particular, testing the residuals of those models for normality properties. In a wide ranging study considering 30 countries we find that almost exclusively the residuals do not demonstrate normality. Further, in Hurst tests of the residuals we find evidence that structure remains that is not captured by the models.     

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model–GARCH (ARMA–GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA–GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA–GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.     

Forecasting Brazilian inflation by its aggregate and disaggregated data: a test of predictive power by forecast horizon

This work aims to compare the forecast efficiency of different types of methodologies applied to Brazilian consumer inflation (Índice de Preços ao Consumidor Amplo; IPCA). We will compare forecasting models using disaggregated and aggregated data from IPCA over 12 months ahead. We used IPCA in a monthly basis, over the period between January 1996 and March 2012. Out-of-sample analysis will be made through the period of January 2008 to March 2012. The disaggregated models were estimated by Seasonal Autoregressive Integrated Moving Average (SARIMA) and will have different levels of disaggregation from IPCA as groups and items, as well as disaggregation with more economic sense used by Brazilian Central Bank as: (1) services, monitored prices, food and industrials and (2) durables, non-durables, semi-durables, services and monitored prices. Aggregated models will be estimated by time series techniques as SARIMA, state-space structural models and Markov-switching. The forecasting accuracy among models will be made by the selection model procedure known as Model Confidence Set developed by Peter Hansen, Asger Lunde and James Nason. We were able to find evidence of forecast accuracy gains in models using more disaggregated rather than aggregate data.