Dynamical Linkage among Economic Conditions, Exchange Rates, and Prices

We apply a complex Hilbert principal component analysis (CHPCA) to a set of Japanese economic data collected over the last 30 years, comprising individual price indices of middle classification level (imported goods, producer goods, consumption goods and services), indices of business conditions (leading, coincident, lagging), and yen-U.S. dollar exchange rate. The CHPCA enables us to delve into dynamical linkage of price movements with economic conditions and foreign exchange rates. Adopting a random rotational shuffling (RRS) method as a null hypothesis, we extract statistically meaningful correlations out of the noisy data; the RRS destroys only cross correlations preserving autocorrelations involved in multivariate time series. The statistical test identifies two significant eigenmodes with the largest and second largest eigenvalues. The lead-lag relations among domestic prices in the two modes are quite similar. This fact indicates there exists a collective motion of individual prices arising from mutual interactions between them. However, the collective motion is driven differently in the two modes, namely, its driver is the exchange rate at the upper stream side in the first mode and the demand at the lower stream side in the second mode.