Jin-Lung Lin

CAUSALITY IN THE LONG RUN

The definition of causation, discussed in Granger (1980) and elsewhere, has been widely applied in economics and in other disciplines. For this definition, a series yt is said to cause xt+l if it contains information about the forecastability for xt+l contained nowhere else in some large information set, which includes xt−j, j ≥ 0. However, it would be convenient to think of causality being different in extent or direction at seasonal or low frequencies, say, than at other frequencies. The fact that a stationary series is effectively the (uncountably infinite) sum of uncorrelated components, each of which is associated with a single frequency, or a narrow frequency band, introduces the possibility that the full causal relationship can be decomposed by frequency. This is known as the Wiener decomposition or the spectral decomposition of the series, as discussed by Hannan (1970). For any series generated by , where xt, and are both stationary, with finite variances and a(B) is a backward filterwith B the backward operator, there is a simple, well-known relationship between the spectral decompositions of the two series.

Modeling Lunar Calendar Holiday Effects in Taiwan

The three most important Chinese holidays, Chinese New Year, the Dragon-boat Festival, and Mid-Autumn Holiday have dates determined by a lunar calendar and move between two solar months. Consumption, production, and other economic behavior in countries with large Chinese population including Taiwan are strongly affected by these holidays. For example, production accelerates before lunar new year, almost completely stops during the holidays and gradually rises to an average level after the holidays. This moving holiday often creates difficulty for empirical modeling using monthly data and this paper employs an approach that uses regressors for each holiday to distinguish effects before, during and after holiday. Assuming that the holiday effect is the same for each day of the interval over which the regressor is nonzero in a given year, the value of the regressor in a given month is the proportion of this interval that falls in the month. Bell and Hillmer (1983) proposed such a regressor for Easter which is now extensively used in the U.S. and Europe. We apply the Bell and Hillmers method to analyze ten important series in Taiwan, which might be affected by moving holidays. AICC and out-of-sample forecast performance were used for selecting number of holiday regressors and their interval lengths. The results are further checked by various diagnostic checking statistics including outlier detection and sliding spans analysis. The empirical results support this approach. Adding holiday regressors can effectively control the impact of moving holidays and improves the seasonal decomposition. AICC and accumulated forecast error are useful in regressor selection. We find that unemployment rates in Taiwan have holiday effects and seasonal factors cannot be consistently estimated unless the holiday factor is included. Furthermore, as the unemployment is rising, the magnitude of holiday and seasonal factor are decreasing. Finally, we find that holiday factors are generally smaller than seasonal factors but should not be ignored.

Time aggregation effect on the correlation coefficient: added-systematically sampled framework

The aggregation of financial and economic time series occurs in a number of ways. Temporal aggregation or systematic sampling is the commonly used approach. In this paper, we investigate the time interval effect of multiple regression models in which the variables are additive or systematically sampled. The correlation coefficient changes with the selected time interval when one is additive and the other is systematically sampled. It is shown that the squared correlation coefficient decreases monotonically as the differencing interval increases, approaching zero in the limit. When two random variables are both added or systematically sampled, the correlation coefficient is invariant with time and equal to the one-period values. We find that the partial regression and correlation coefficients between two additive or systematically sampled variables approach one-period values as n increases. When one of the variables is systematically sampled, they will approach zero in the limit. The time interval for the association analyses between variables is not selected arbitrarily or the statistical results are likely affected.

Forecasting unstable processes

Previous analysis on forecasting theory either assume knowing the true parameters or assume the stationarity of the series. Not much are known on the forecasting theory for nonstationary process with estimated parameters. This paper investigates the recursive least square forecast for stationary and nonstationary processes with unit roots. We first prove that the accumulated forecast mean square error can be decomposed into two components, one of which arises from estimation uncertainty and the other from the disturbance term. The former, of the order of

Time-varying Relationship of Price Indexes in Taiwan

\log(T)

Co-integration Constraint and Forecasting: An Empirical Examination

, is of second order importance to the latter term, of the order T. However, since the latter is common for all predictors, it is the former that determines the property of each predictor. Our theorem implies that the improvement of forecasting precision is of the order of

Forecasting from non-linear models in practice

\log(T)

Is money demand in Taiwan stable

when existence of unit root is properly detected and taken into account. Also, our theorem leads to a new proof of strong consistency of predictive least squares in model selection and a new test of unit root where no regression is needed. The simulation results confirm our theoretical findings. In addition, we find that while mis-specification of AR order and under-specification of the number of unit root have marginal impact on forecasting precision, over-specification of the number of unit root strongly deteriorates the quality of long term forecast. As for the empirical study using Taiwanese data, the results are mixed. Adaptive forecast and imposing unit root improve forecast precision for some cases but deteriorate forecasting precision for other cases.

Switching ARCH Models of Stock Market Volatility in Taiwan

Price indexes are important variables in macroeconomic models. They are composed to measure various costs in an economy. For instance, a Consumer Price Index (CPI) is constructed to measure the cost of living and a Wholesale Price Index (WPI) summarizes the prices of transactions between enterprises and is intended as a measure of production cost. The price indexes of an economy are highly correlated via economic theory and index composition. The relationship is often treated as stable over time in macroeconomic modeling. In this paper we consider four monthly price indexes of Taiwan, namely the CPI, WPI, Export Price Index (PEX), and Import Price Index (PM). Our goal is to investigate the stability of the relationship between these indexes. We employ various methods, including exponentially weighted recursive least squares and parametric bootstrap methods, to show that, for Taiwan is Economy, the relationship is time-varying for the CPI and WPI. For the export price index (PEX), we found that the relationship is relatively stable after adjusting for the impact of exchange rates between the U.S. Dollar and Japanese Yen versus New Taiwan Dollar. Macroeconomic modelers should be cautioned about the time-varying relationship of price variables, and nonlinear models deserve further investigation.