11 The trend cycle component t T is the underlying path of the series It

11 the trend cycle component t t is the underlying

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identified (and estimated) from the observed time series using a signal extraction technique. 11. The trend-cycle component ( t T ) is the underlying path of the series. It includes both the long-term trend and the business-cycle movements in the data. The long-term trend can be associated with structural changes in the economy, such as population growth and progress in technology and productivity. Business cycle variations are related to the periodic oscillations of different phases of the economy (i.e., recession, recovery, growth, and decline), which generally repeat themselves with a period between two to eight years. 12. The seasonal component ( t S ) includes those seasonal fluctuations that repeat themselves with similar annual timing, direction, and magnitude. 7 Possible causes of seasonal movements relate to climatic factors, administrative or legal rules, and social/cultural traditions and conventions - including calendar effects that are stable in annual timing (e.g., public holidays, or other national festivities). Each of these causes (or a combination of them) can affect expectations in such a way that seasonality is indirectly induced. Similarly, changes in any of these causes may change the properties of the seasonal pattern. 13. The calendar component ( t C ) comprises effects that are related to the different characteristics of the calendar from period to period. Calendar effects are both seasonal and nonseasonal. Only the “nonseasonal” part should be included in the calendar component and treated separately, as the “seasonal” one is already caught by the seasonal component. 8 The most used calendar effects include the following: x Trading-day or working-day effects. The trading-day effect detects the different number of each day of the week within a specific quarter relative to the standard weekday composition of a quarter. The working-day effect 7 Seasonality may be gradually changing over time. This phenomenon is called “moving seasonality”. 8 For example, the effect due to the different average number of days in each quarter is part of the seasonal effects.
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7 catches the difference between the number of working days (e.g., Monday through Friday) and the number of weekend days (e.g., Saturday and Sunday) in a quarter. The trading-day effect assumes an underlying pattern associated with each day of the week; the working-day effect postulates different behavior between the groups of weekdays and weekend days. 9 Both the trading-day and working-day effects should incorporate the effects of national holidays (e.g., when Christmas falls on Monday, that Monday should not be counted as a trading/working day). x Moving holiday effect . A moving holiday is associated with events of religious or cultural significance within a country that change date from year to year (e.g., Easter or Ramadan). x Leap year effect. This effect is needed to account for the extra day in February of a leap year, which may generate a four-year cycle with a peak in the first quarter of leap years.
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  • Spring '16
  • Business, Regression Analysis, ........., Autoregressive integrated moving average, X-13A-S

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