Kosei Fukuda

Age–period–cohort decompositions using principal components and partial least squares

Age–period–cohort decomposition requires an identification assumption because there is a linear relationship between age, survey period, and birth cohort (age+cohort=period). This paper proposes new decomposition methods based on factor models such as principal components model and partial least squares model. Although factor models have been applied to overcome the problem of many observed variables with possible co-linearity, they are applied to overcome the perfect co-linearity among age, period, and cohort dummy variables. Since any unobserved factor in the factor model is represented as a linear combination of the observed variables, the parameter estimates for age, period, and cohort effects are automatically obtained after the application of these factor models. Simulation results suggest that in almost all cases, the performance of the proposed method is better than that of a conventional econometric method. Empirical examples are also provided.

Detection of switching cointegration rank allowing for switching lag structure: an application to money-demand function

A new method is developed for detecting regime switches between cointegration and no-cointegration at unknown times allowing for switching lag structure. In this method, time-series observations are divided into several segments, and a regression model with or without cointegration is fitted to each segment. The goodness of fit of the global model composed of these local models is evaluated using the corresponding modified information criterion, and the division which minimizes this criterion defines the best model. Simulation results suggest that the proposed method works well. Empirical results indicate that money demand is well described by the proposed method in Canada, UK and Japan.

Distribution switching of stock returns: international evidence

This article considers six alternative models–the normal model, normal model with parameter change, t model, t model with parameter change, normal and t model and the t and normal model–and the best model is selected using the Bayesian information criterion. The simulation results suggest that the proposed method works well with regard to all the models, with the exception of the t model with parameter change, which is sometimes unidentified. Empirical results show that in two out of the six countries, the monthly time series of stock returns are generated from the normal distribution before the switch point and from the t distribution after the switch point. Both the switch points are caused by international economic crises such as the turmoil in the international monetary system in 1971 or the oil shock of 1974.

A unified approach to detecting unit root and structural break

In the proposed approach, eight alternative data-generating processes (DGPs) are considered by combining a process with or without a unit root, a process with or without a trend break and a process with or without an innovation-variance break. It is determined on the basis of the selected model using the Bayesian information criterion which DGP generates the observed time series. The efficacy of the proposed approach is verified using comprehensive simulations, including comparisons with two conventional hypothesis-testing methods. The results of applying the proposed method to output time series for 20 developed countries suggest that 12 series have a trend break and 16 series have an innovation-variance break.

Distribution switching in financial time series

A new method for detecting regime switches between different probability distributions in financial time series is shown. In the proposed method, time series observations are divided into several segments, and a Gaussian model or a Cauchy model is fitted to each segment. The goodness of fit of the global model composed of these local models is evaluated using the Bayesian information criterion (BIC), and the division which minimizes this criterion defines the best model. Based on this method, for example, the specification with a Gaussian process in the first half and with a Cauchy process in the second half becomes applicable. Empirical applications and data-based simulations are presented to indicate the efficacy of the proposed method.

Monitoring unit root and multiple structural changes: An information criterion approach

An information criterion-based model selection method is proposed for monitoring unit root and multiple structural changes. In this method, a battery of possible models is considered by changing the integration order (I(0) or I(1)) and the combinations of change points. Next, the best model is selected from among alternative models via a modified Bayesian information criterion (BIC). Accordingly, on the basis of the selected model, the process that generates the observed time series is determined. The BIC is modified in order to adjust the frequency count of incorrectly selecting stationary models via the conventional BIC. The simulation results of monitoring unit root and structural change suggest that the proposed method outperforms the conventional hypothesis testing method in terms of detection accuracy and detection speed. Furthermore, the empirical results suggest that the proposed method exhibits better performances with regard to detection stability and forecastability.

Time-Series Forecast Jointly Allowing the Unit-Root Detection and the Box–Cox Transformation

ABSTRACT An information-criterion-based model-selection method is presented for forecasting that allows for the unit-root detection and the Box–Cox transformation simultaneously. In this method, a battery of alternative models with and without unit root is considered changing the order of autoregressive process and the Box–Cox parameter, and the best model is selected using information criteria. Simulation results suggest that the Bayesian information criterion (BIC) outperforms the bias-corrected Akaike information criterion (AICc) and that the augmented Dickey–Fuller test performs worse in the case of incorrect data transformation. The results of forecasting quarterly time series of industrial production indicate that the BIC-based method outperforms the other conventional methods.

Causality between corporate diversification and profitability: evidence from Japan

Prior empirical studies on the relationship between corporate diversification and firm performance have not considered data stationarity and have devoted little consideration to the dynamics of this relationship, the endogeneity problem, and causality factors. To overcome these econometric problems simultaneously, a panel vector autoregressive model is applied to product diversification data on Japanese firms. The empirical results suggest the followings. First, the panel unit-root test recommends the use of diversification, and not diversity. Second, product diversification measured by the Herfindahl index has no relationship with the other three firm performance variables, while product diversification measured by the entropy index marginally increases sales growth, leading to an increase in profitability. The empirical implications for business researchers are also provided.

Differentiating between business cycles and growth cycles: evidence from 15 developed countries

Growth cycles are often mistaken for business cycles, although these two have different statistical properties. In order to differentiate between them in a statistically satisfactory manner, the Bayesian information criterion-(BIC) based model-selection approach is presented. Business cycles are described by the cyclical trend model, and growth cycles are described by the trend-plus-cycle model. Whether the observed time series is derived from business cycles or from growth cycles is determined as a result of model selection. It is shown via data-based simulations that the proposed method works well in most situations. Empirical results obtained for 15 countries suggest that the business cycle model is selected for five countries, the growth cycle model is selected for two countries and the trend-plus-noise model is selected for eight countries.

Model-selection-based unit-root detection in unemployment rates: international evidence

A model-selection-based unit-root detection by using the Bayesian information criterion is proposed. First, six alternative model classes are obtained considering the presence or absence of a unit root and considering three kinds of deterministic terms: no constant, constant, constant and trend. Second, given the selected model class, the best model is selected from the alternative models with different lags. Third, the best of the entire model set comprising the six models obtained in the preceding step is selected. Finally, whether an observed time series contains a unit root is determined on the basis of the selected model. Simulation results suggest that the proposed method is at least comparable to and often better than the sequential testing method provided by Dolado et al . (1990). Empirical results obtained by the proposed method are more convincing than those obtained by the sequential testing method and suggest that the hysteresis hypothesis can be applied to monthly time series of the unemployment rates for all the six countries under consideration.