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What are methods for compiling business cycle indicators? How does composite index differ from trend-adjusted index?

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(I) Methods for Compiling Business Cycle Indicators

  1. Data Processing of the Component Series

(1) Seasonal adjustment: Seasonal components undergo adjustment through X-13ARIMA-SEATS to avoid seasonal factors having an impact on the determination of economic situations.

(2) De-trending and smoothing: For de-trending and smoothing, the two-stage HP (Hodrick-Prescott, 1997) computation method is adopted. First we remove the long term trend by setting λ to a high value, and we preserve the business cycle frequencies and the high frequency components. Second, we apply the HP filter with a smaller λ, meaning that the cut-off frequencies are much higher, and so, preserve the cycle part of the filter results. The first step de-trends the second step smoothes.

(3) Normalization: Naturally, even after the above steps have been conducted, the different component series used in the construction of a single composite indicator will be expressed in different units or scales. As such, the various component series that are used in the construction of a trend-adjusted index are first normalised. This normalisation process is achieved by subtracting from ‘filtered’ observations the mean of the series, and dividing this by the mean absolute deviation of the series, and, finally, by adding 100 to each observation.

  1. Composite Business Cycle Indicators

(1) Weighted average of components. After each component undergoes processing mentioned above, the same weight is used to carry out weighted average composition.

(2) The amplitude adjusted index rescales this ‘averaged’ index to match the amplitudes of the reference series.

(3) Carry out trend restoration to derive at composite index: In order for all communities to grasp the long-term economic trend, we carry out long-term trend restoration of trend-adjusted index to derive at composite index of business cycle indicators.

(II)   The Difference between Composite Index and Trend-adjusted Index

        Since the characteristics of different economies vary, two concepts are generally used for measuring business cycles, namely, classic cycles used to measure increases or declines in absolute values (levels values) of economic activates and growth cycles used to measure economic changes after de-trending. Currently, both Taiwan and OECD adopt the concept of growth cycles.

        In terms of methods for compiling business cycle indicators, the “trend-adjusted index” obtained after magnitude adjustment of composite business cycle indicators refers to business cycle indicators presented through the concept of growth cycles, which covers only economic cycle fluctuation components. As for the “composite index” obtained after the trend restoration of the trend-adjusted index, it is presented through the concept of classic cycles, including the long-term economic trend.

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