table of Contents

Seasonally adjusted methodology
Reading "theme tune of measurement methods quarter bond market study: Theory and Practice"
Reading "seasonal adjustment model and forecast inflation"

Seasonally adjusted methodology

Reading "theme tune of measurement methods quarter bond market study: Theory and Practice"

Seasonal adjustment principle

Decomposed into trend factors, cycle factors, seasonal factors and irregular factors.

Trend factors reflect the long-term evolution of the direction of economic phenomena.
Cycle performance factor is the ongoing cyclical fluctuations, also known as cyclical factors. A complete cycle (cycle) into expansion, recession, depression, recovery in four different stages.
Seasonal factors represents the periodic change a regular pattern appears the same time in different years and seasons.
It means irregular factor is a factor due to an error or random generated other than the above three laws unexplained.

Seasonal adjustment refers to the process to be amended seasonality time series of economic indicators right. Seasonally adjusted series should contain the trend factor synthesis cycle factors and irregular factors. Its main purpose is a true reflection of the direction of the trend and cycle represent, clearly reveals the movement of the economic cycle.

Additive model: \ (= T_T Y_t S_T + + + C_T I_t, A_T C_T + + = T_T I_t \)
乘法模型：\(Y_t =T_t \times C_t \times S_t\times I_t ,A_t =T_t\times C_t\times I_t\)

Wherein \ (the Y \) is the original sequence, \ (T \) is trend factor, \ (C \) is a cyclic factor, \ (S \) is the seasonal factors, \ (the I \) is irregular factors, \ (A \) is the seasonally adjusted series.

For a time series, if the above-described four factors are independent of each other, using the additive model better; if four factors are interrelated, better use of the multiplicative model. And if the scale of seasonal factors remained unchanged, with the growth of the original sequence does not grow, then use the additive model; if the horizontal size of the original sequence of seasonal factors proportional change, use the multiplicative model.

Seasonal adjustment method

Seasonal adjustment method is divided into two theorists: Experience (empiricail-based) and based on model (model-based) basis.

Based on empirical methods include moving average, and X-11 model as we know.

Moving Average:

Composite simple moving average
Henderson moving average
Musgrave asymmetric moving average

Model-based methods mainly refers to the ARIMA model.

Analysis of problems encountered in practice seasonally adjusted

Only an

According to seasonally adjusted method requires, such data can not be seasonally adjusted. But theory and practical application in the presence of each month using the base period are set to the phenomenon of post-100 method to calculate the seasonally adjusted chain.

Missing data

You should first consider how to do a good job of filling in missing data, so that data is filled with the raw data fit best on the trend.

Spring Festival effect

Now, most of the Chinese New Year seasonally adjusted method from the X-12-ARIMA of Easter model , is the influence of the ratio of the number of days allocated across all months in accordance with the set holiday to construct the regression variables, variables and then return the original sequence of regression, the Chinese New Year effect, the effect of excluding Chinese New Year from the original sequence, the sequence is obtained after the Spring Festival factor correction.

The model assumes that: the first before the Spring Festival from \ (WN \) days beginning on economic activity produced a change in consistency to continue after the Spring Festival \ (N \) days to restore the situation before the Spring Festival. Which all affect the number of days is \ (W \) days, before the Spring Festival \ (WN \) days after the Spring Festival \ (N \) days. Of course, after the completion of the calculation for all months of the season return variable, but also centers of treatment to eliminate its seasonal ensure that the sum of the original sequence before the annual return variable annual sum roughly equal to the resulting adjusted, otherwise the adjustment will have the original sequence sequence shifted.

Different economic activities by the different way the Chinese New Year effect, leading \ (W \) and \ (N \) choice is not the same.

Production class economic activity in the New Year with less influence, generally before a holiday (ie two days before the Spring Festival) in the 28th lunar month, the first month and before one week (seven days after the Spring Festival) are the traditional New Year holiday visiting relatives time, period of time almost stagnant production activities. Thus for industrial added value, fixed asset investment index for \ (= W is 10 \) , \ (N =. 7 \) .
For consumer economic indicators, the hot season before the Spring Festival shopping, stocking and gifts in every possible way, by the end of the settlement and other factors lead to increased consumption of the more obvious, and over the New Year with relatives and start the plant, consumption gradually return to normal. So for retail sales, M0 index for \ (W = 20 \) , \ (N = 7 \) .

Reading "seasonal adjustment model and forecast inflation"

Forecasting inflation

Univariate model is the CPI forecast based approach .
Phillips curve model and the monetarist theory of inflation is predicted basic theory .
Using high frequency data timeliness and accuracy of the model predictions can be improved.

Seasonally adjusted inflation forecast

CPI has a significant effect New Year

A time-series seasonal trend can be decomposed into a long T, cyclic component C, component S seasonal and irregular component I.

Calendar effect can be divided into seven categories: fixed seasonal effects, leap year effect, length effect in January, quarter length effect, trading day effect, working day effects and moving holiday effects.

China Mobile Holidays include Spring Festival, Mid-Autumn Festival, Dragon Boat Festival and Ching Ming Festival. Where the greatest impact, the Spring Festival.

Typically, time series are seasonally adjusted on the basis of the fixed base index performed.

Spring Festival effect of food items in the CPI significantly higher than non-food items; Spring Festival effect service items significantly higher than items of consumer goods.

Consider the effect of seasonal adjustment Spring Festival

To determine the effect of the Chinese New Year

Effect of preganglionic \ (TB \) , the influence of the section \ (TD \) and postganglionic Effect of \ (TA \) , corresponding to the introduction of three dummy variables \ (D_ {I, J} (TB) \) , \ (d_ {i, j} (td) \) and \ (D_ {I, J} (TA) \) . For a given year \ (I \) , the interval length is determined impact festival \ (TB \) after a month of j, which is affected by the holiday period accounts \ (TB \) ratio is the \ (d_ { I, J} (TB) \) . Similarly, define \ (d_ {i, j} (td) \) and \ (D_ {I, J} (TA) \) . In less than a month holiday impact, the dummy variable value of 0.

Effect Effect preganglionic number of days to 7 days, the number of days impact effect section is 7 days long holiday, the holiday effect affect the number of days to 10 days.

The seasonally adjusted CPI

After determining the Spring Festival effect variables, add it as a new variable in the regression model. Multiplicative decomposition model.

Seasonally adjusted CPI forecast based

After separating the long-term trend of CPI factors, seasonal factors and irregular factors, CPI sequences can be predicted based on the prediction value and the multiplicative decomposition model of the three components.

Three predicted components are questionable practice.

Correction of inflation (to deal with the impact of African swine fever)

Time series model can not take into account the impact of unexpected events, such as African swine fever makes this Chinese pork prices rose.

CPI pork out for separation of the individual items seasonally adjusted predicted binding frequency data and the correction of the predicted value of the CPI.

According to the National Bureau of Consumer residents of China in February 2019 issued price announcements: pork prices fell 4.8%, affecting the CPI decreased by about 0.12% , can be calculated weights pork CPI weight accounts for 2.5% (= 0.12 / 4.8) .

Revised CPI forecast

According to 22 provinces and the average pork price (weekly) , March pork prices rose as high as 23.32%, far higher than the -1.67% forecast. Accordingly, to deal with CPI predictive value increased by 24% * 2.5% = 0.6%, in March 2019 CPI forecast of 2.5%.