They may be caused by various factors, such as:. Other calendar effects relate to factors that do not necessarily occur in the same month or quarter each year. They include:. Irregular fluctuations may occur due to a combination of unpredictable or unexpected factors, such as: sampling error, non-sampling error, unseasonable weather, natural disasters, or strikes.
While every member of the population is affected by general economic or social conditions, each is affected somewhat differently, so there will always be some degree of random variation in a time series. This is in marked contrast with the regular behaviour of the seasonal effects.
The trend or trend cycle represents the underlying behaviour and direction of the series. It captures the long-term behaviour of the series as well as the various medium-term business cycles.
Although there are many ways in which these components could fit together in a time series, we select one of two models:. In a multiplicative decomposition, the seasonal effects change proportionately with the trend. If the trend rises, so do the seasonal effects, while if the trend moves downward the seasonal effects diminish too. In an additive decomposition the seasonal effects remain broadly constant, no matter which direction the trend is moving in.
In practice, most economic time series exhibit a multiplicative relationship and hence the multiplicative decomposition usually provides the best fit. However, a multiplicative decomposition cannot be implemented if any zero or negative values appear in the time series. There are a variety of issues that can impact on the quality of the seasonal adjustment. These include:. Seasonal adjustment of monthly CPI can eliminate seasonal effects and make the data of different years and months be comparable.
It can also clearly reflect the basic trend of economic internal operation and the instantaneous changes of economic and the turning point of economic changes. Besides, it can be conducive to government decision-makers to seize the best time for macro-control, stabilize the price level and promote economic development. At present, Chinese domestic research on seasonal adjustment of CPI time series is still relatively scarce.
Dong Yaxiu and others studied the seasonal adjustment of the chain index of CPI and established a long-term forecasting model [7]. Luan Huide, Zhang Xiaotong proposed a method to construct mobile holiday regression by introducing dum- my variables and assigning variable weights to the three segments of the variables, which had a founding significance [8]. But in fact some of the economic variables affected by the Spring Festival are not subject to uniform distribution.
Finally, we use the adjusted time series to analyze and forecast the economy. Economic time series are usually non-stationary time series. ARIMA model is the main method on modeling non-stationary time series. In the CPI time series modeling, we should take into account the effects induced by mobile holidays such as the Spring Festival, Mid-Autumn Festival, Dragon Boat Festival , outliers, fixed seasonal effects, working days, trading days and other factors.
The regression variables mainly include all kinds of outliers, mobile holiday effect, working day effect, trading day effect and so on. The above formula is called the multiplicative seasonal model of the order.
In order to get a fully fitted sequence in the product season model, the original sequence is usually used as a logarithmic transformation, that is ; then plugging this in the product ARIMA model with regression term to make model identification, determine P, Q, p, q, d, D. Finally, estimating parameters by maximum likelihood method or least square.
After making forward prediction, backward prediction and a priori adjustment of various effects by the ARIMA model with regression term, this paper uses X seasonal adjustment method to decompose the components based on the moving average method based on multiple iterations and then completes seasonal adjustment. The regression variable mainly includes various outlier values and calendar-related factors. Calendar effects are various calendar-related factors such as leap years, trading day effects, mobile holiday effects, etc.
They will bring difficulties on judging the economic cycle, so they need to be eliminated in the ARIMA model of regression analysis. There will be a February of 29 days for every 4-year, which will have an impact on the flow of data statistics. If it is considered that the economic activity is different for each day of the week, since the number of occurrences of each day within a week is different, the variables considered will also be a corresponding change in the same calendar month for different years.
For example, if you think that the consumption level of Sunday and Monday is different, then the economic indicator variable should be correspondingly different between months with a higher number of Sundays and months have fewer Sundays but a higher number of Mondays. In the holidays, people tend to consume more and make the economic variables significantly different from non-holiday.
But the effects of mobile holiday are different from the holiday with fixed gregorian dates such as the National Day, Golden Week. For example, although the Spring Festival appears regularly, but does not necessarily appear on the same date each year.
The effects of a fixed holiday are already considered in the seasonal effect, so the regression variable only needs to consider moving holidays. Assuming the daily weights of the Spring Festival are different before, during and after the festival, the closer the Spring Festival, the greater the impact, hence greater weights should be given. During the festival, the variables follow the uniform distribution, therefore the daily weights are equal. The weight vector for time interval of day before the festival is.
The variable weights are the same every day during the holiday season. The weight vector for time interval of one day after the festival to day after the festival is. According to the specific distribution of the number of effective days in different months corresponding to before, during and after the Spring Festival, we can get the proportional variable by summing the weights of each day, and then normalize them respectively.
Finally, we can get regression variables , ,. From onwards, China began to use fixed base period calculation method to publish base CPI. Chinese first round base period is fixed in , that is, making the average price level in as a comparison of fixed base period, set the base index in December was Then obtained the CPI fixed base index from January to June through the chain index of forward and backward recursion.
Figure 1 is a fixed base consumer price index. One may note that it has an obvious seasonality: the price index reaches the highest peak in every year about February, March, and then decreases month by month. In the middle of the year the price index reaches the bottom, then it begins to rise.
There is a periodic change trend in the whole sequence, which indicates that there is a seasonal variation in the whole year. The program can also filter the regression variables automatically according to the t statistic and select the optimal ARIMA model according to the information criterion automatically. The effects of the Spring Festival are set to , ,. According to the above assumptions on the Spring Festival holiday regression variables, we can obtain the regression variables for periods before, during and after the Spring Festival.
Table 1 lists the regression variables of the Spring Festival after normalization Note: The Spring Festival does no effect on the month. Figure 1. Table 1. Spring-Festival Regression Variables in The regression model also includes leap year, trading day, outliers and other regression variables.
We do not list them one by one here. List of Partners vendors. The Consumer Price Index CPI is the most widely used metric for consumer inflation changes over time and utilizes data based on consumer buying habits from a broad sample set of the population. The price-change data used for the CPI is gathered and published each month as an economic time series.
Because of the frequency of its analysis, certain adjustments must be made to the data so it can be analyzed accurately over longer periods of time. The CPI, along with other broad measures of economic change, utilizes a process known as seasonal adjustment to factor out seasonal effects on the price data gathered each month to gauge increases or decreases to inflation.
This provides users with a more accurate depiction of price movements void of anomalies that can occur during specific seasons. For instance, price changes in CPI categories such as apparel or transportation may occur at an increased rate in the months leading up to a holiday due to greater consumer demand, although they may have little or no change throughout the rest of the year.
Similarly, a reduction in housing prices may occur during colder months, which may not be the case during warmer months of the year. Though the CPI adjusts for seasonality it does not adjust for substitutions; when consumers purchase cheaper substitutes when the price of the main good or service increases.
This is a limitation of the CPI. Some seasonal effects are so large that they hide other price data characteristics that provide a more accurate analysis of changes in consumer buying habits.
As such, the adjustment of information for seasonal effects is done in an effort to enhance the presentation and ultimate use of data for the long-term. To determine the adjustment, seasonal factors calculated by complex software programs are divided into the economic time series data for any given month.
The CPI data published on a broader national level is always adjusted for seasonal effects and most commonly used by those who are interested in analyzing price change trends on a grand scale.
Conversely, when CPI data is used for the purpose of escalation agreements, unadjusted data should be used instead of seasonally adjusted information.
Unadjusted data allows an analyst to measure true price changes month-to-month and is used extensively in collective bargaining contracts and pension plan calculations.
The CPI is a tool that economists, analysts, and governments use to monitor the change in prices due to inflation or deflation. The information allows for the adjustment or revision of economic policy. To make sure that the most accurate data is used, the price information is seasonally adjusted to remove price drops or increases due to seasonal factors. Even with seasonal adjustment applied, the CPI is not a perfect tool in determining shifts in consumer buying habits.
It is, however, a valuable measure of broad changes in inflation that can affect long-term economic policy and consumer behavior. Federal Reserve Bank of St.
0コメント