4.6.1 Seasonal change analysis: the same period average method 季节变动分析：同期平均法在线视频

好 同学们现在我们进入
Okay, now let's start

第八讲内容
Lecture 8

季节变动的测定
measurement of seasonal variation

那在这一讲内容中
In this lecture

我们说季节变动的测定
mainly three parts are included

主要包括以下三个方面的内容
for measurement of seasonal variation

第一个内容是这个季节变动
The first part

这个测定的目的
is the purpose of measuring seasonal variation

第二个内容是
The second part is on

季节变动的分析方法与原理
the analysis methods and principles of seasonal variation

第三个内容是季节变动的一个调整
The third part is on the adjustment of seasonal variation

首先我们来看一看
First, let's look at

季节变动及其测定的目的
seasonal variation and the purpose of its measurement

那在这个长期趋势测定的过程中
In the measurement of secular trend

我们有提到
we have mentioned that

它是一个最主要的因素
secular trend is a major factor

那在这个时间数列分析过程中
As for the analysis of time series

除了长期因素以外的话
besides secular trend

我们提到第二个因素特别重要
the second factor which is particularly important

就是我们提到的
is what we've mentioned

今天这一讲中要提到的
seasonal variation, which will be discussed

季节变动这个因素
in this lecture today

那季节变动的因素
Seasonal variation

主要是指的由于这个自然季节
mainly refers to the changes with seasons

气侯条件或者人文习惯
reflecting in the natural seasonal phenomena

季节的一个变化情况
climate conditions or human habits

导致时间数列
As a result

随着这个季节更替
As the time pass

而呈现出一个周期性的
shows periodic changes

一个变化情况
with the seasons

那我们说 这个季节周期
As for seasonal cycles

在我们的意识当中
in our knowledge

主要有哪些季节周期呢
what are the major seasonal cycles

我们说通常是以年为周期
Usually the seasonal cycles are annual cycles

或者是以月 周 日 季度
based on cycles in month, week, day and quarte

为周期的一些准季节变动
or some quasi-seasonal changes

那我们注意到
Then

季节变动的特点是什么呢
what are the features of seasonal variation

它是有规律的一些变动
It is regular change

那这种季节的规律性
The regularity based on seasons

就会体现在一定周期内
is reflected in repetitive changes

经济指标的一个重复的
of economic indicators

一个变化过程
within a certain cycle

那这个重复变化过程
The process of such repetitive changes

最后展示出来
finally demonstrated

或者说显现出来就是
in each cycle

每个周期的变化大体相同
is roughly the same

最大周期为一年
The maximum period of a cycle is one year

那对于这个季节变动
The purpose of measuring seasonal variation

测定的目的
is mainly to

主要是确定现象过去的
determine the laws of seasonal variation

一个季节变化的规律
of a phenomenon in the past

消除时间数列中
to eliminate the influences of seasonal factors

一个季节因素的一个影响
in the time series

我们看看 如何来进行分析
Let's see how to

这个季节变动呢
analyze seasonal variation

我们一般是将季节变动规律
Generally, the laws of seasonal variation

归纳成一种典型的季节模型
are summarized and turned into a typical seasonal model

然后季节模型由季节指数所组成
and this model is composed of seasonal exponents

这些季节指数的平均数等于100%
The average of these seasonal exponents shall be equal to 100%

而根据这个季节指数以及平均数
The seasonal variation is determined

100%的偏差程度
based on the deviation

来测定这个季节变动的一个程度
of seasonal exponents from the average 100%

所以 如果现象没有季节变动的话
So, if there is no seasonal variation in a phenomenon

各期季节组织应该等于100%
the seasonal exponents of each period shall be equivalent to 100%

也就是意味着
which means that

如果一个月或者是季度
if there is significant seasonal variation

有明显季节变化的话
in a month or a quarter

那我们说 各期这个季节指数
then we say, the seasonal exponent of each period

就应该大于或者是小于100%
shall be greater than or less than 100%

来 我们看一看
Let's see

对于这一个季节指数
the specific steps

具体的计算的这个
for the calculation

步骤是怎么样的呢
of seasonal exponents

我们看到第一步
The first step is

它是反映季节变动的一个相对数
to figure out a relative number that reflects the seasonal variation

它是以全年 月
It is figured out

或者季的资料的平均数为基础计算的
based on the average of the yearly, monthly or quarterly data

平均数等于月度的这个指数之和
The average is equivalent to the sum of monthly exponents

等于1200%
which is equal to 1200%

如果是月度的指数的话
For monthly exponents

它之和等于1200%
the sum is equivalent to 1200%

如果是季度指数之和的话
For quarterly exponents

等于400%
the sum is equivalent to 400%

我们说指数越远离其平均数
The bigger the deviation of an exponent from its average

则表现的这个季节变动的
the greater

变化程度是越大的
the seasonal variation is

而计算方法有按季度计算
It can be calculated by quarter

也有按月度计算
or by month

好 那我们看到具体的
Okay, let's see the specific

这个计算方法
calculation process

如何按月度或者是按季度
in which the seasonal exponents

来计算这个季节指数
are figured out by month or by quarter

首先我们看到第一步
First of all, let's see the first step

要根据原时间数列
Based on the original data of time series

通过简单平均计算出
we work out the monthly or quarterly average

同月或者同季的一个平均数
using the method of simple average

然后对所有的这个经济
Then, we figure out a total average

时间数列指标
of this time series

算一个总的平均数
for the economic indicator

那计算出了总的平均数
Based on the overall average and

计算出了同月或者同季平均数
the monthly or quarterly average

基础上
we can further figure out

我们进一步来计算这个季节指数
the seasonal exponent

那季节指数等于什么呢
What is the seasonal exponent equivalent to

等于同月 同季平均数
It is equal to the monthly or quarterly average

除以总的月平均数 季平均数
divided by the total monthly or quarterly average

乘以100%
and multiplied by 100%

得到就是我们的季节指数
Finally, the seasonal exponent is obtained

那我们现在看一看
Here is

具体的一个例子
a specific example

我们说某房地产商品
The sales revenue data

它一到四季度的销售额情况
of a real estate product from the first to the fourth quarter

如下所示
are shown as below

那我们看到 它的这个数值
These are the values

是一季度 二季度 三季度 四季度
for the first quarter, second quarter, third quarter and fourth quarter

首先的话 我们根据刚刚这个
First, let's follow

具体的步骤
the specific steps discussed just now

第一我们要算一个
First, we need to figure out

同季的一个平均数
the average for each quarter

那这里的话 我们看到
So here we see that

得到的同季平均数是多少呢
the quarterly averages obtained are

等于19 25 8
19, 25 and 8

而第二步的话
In the second step

我们算一个总的平均数
let's figure out

总的平均数等于多少
the total average

总的平均数等于15.75
which is equal to 15.75

在计算出了同季平均数
After working out the quarterly average

和总平均数的基础上
and total average

我们进一步来计算这个季节比率
let's we further figure out the seasonal ratio

那季节比率等于每一个季度的
The seasonal ratio is equal to

平均数除以总的平均数
the average of each quarter divided by the total average

最后得到120.63% 158.73%
and the results are 120.63%, 158.73%

50.79% 69.84%
50.79% and 69.84%

那我们观察这几个季节指数
Then we observe the seasonal exponents

一季度 二季度 三季度 四季度
for the first quarter, second quarter, third quarter and fourth quarter

回到刚刚我们的定义当中
Let's return to its definition

或者刚刚那个特点当中
or its characteristics

我们知道
As we know

这个每个季度的季节指数
the quarterly seasonal exponents

它是否存在说
may have a very large deviation

有一个非常大的一个变化幅度呢
from the average seasonal exponent

我们说 刚刚有提到
As we've just mentioned

如果说季度比值的话
if the quarterly ratio

是等于100%的话
is equal to 100%

我们认为什么呢
that is, if the ratio of the quarterly seasonal exponent to

我们认为如果季节指数
the average seasonal exponent

季度指数它等于100%
is equal to 100%

我们认为它是没有一个变化的趋势
we believe that the trend is flat

如果它大于100%
If the ratio is greater than 100%

或小于100%的话
or less than 100%

我们都认为
we'll think that

它有一个季节因素影响在里面
there is seasonal variation in it

那计算出这四个指数
After figuring out the four exponents

把它一相加 我们发现
we add them together

它有一个
and then we find

非常大的一个问题是什么呢
there is a very big problem

我们发现最后加总它这个数字
We see that the final sum

它不等于400%
is not equal to 400%

这跟我们刚刚所提到的
There is a deviation

由季节同季 计算出来的指数
from the total exponent which is

加总应该等于400%
the sum of all exponents in the same season

它出现一个偏差
which should be 400%

那就回到我们最后一部分内容
Now we go back to the last part of this lecture

叫调整
which is about adjustment

如果说季节指数
When the seasonal exponent

它不等于400%或者说月度指数
is not equal to 400%, or the monthly exponent

它不等于1200%的时候
is not equal to 1200%

我们做一个什么处理呢
what shall we do

那我们要通过这个
In this case, we need to make adjustments

下一个内容调整系数
through the adjustment coefficient

来进行调整
which we are going to discuss next

调整系数调整以后的话
After making adjustment via the adjustment coefficient

我们会发现
we see

它根据调整系数的公式是什么呢
the formula has changed after using the adjustment coefficient

它等于原来的这个平均指数
It is now equal to the original average exponent

乘以调整系数得到的
multiplied by the adjustment coefficient

就是调整过后的这个季节指数
which actually is the seasonal exponent after adjustment

对于月度资料
For monthly data

如果全年12个月的季节指数之和
if the sum of seasonal exponents for the 12 months of the year

不等于1200%
is not equivalent to 1200%

则应计算调整系数进行调整
then adjustment shall be made by using the adjustment coefficient

而对于季度资料
For quarterly data

如果四个季度指数之和
if the sum of exponents for the four quarters

不等于400%
is not equivalent to 400%

也应进行调整
then adjustment shall be made, too

我们看到调整系数的公式
We see the formula for the adjustment coefficient

等于1200%或者400%除以
is equivalent to 1200% or 400% divided by

各月或各季季节比例之和
the sum of the seasonal ratios of each month or season

假定现在资料计算的
We assume that the sum

12个月的这个季节指数之和
of seasonal exponents of 12 months figured out

不等于1200%
is not equivalent to 1200%

则每个月的季节指数
then the seasonal exponents of each month

要分别进行调整
shall be adjusted separately

若其中一个月的原季节指数为A
If the original seasonal exponent of one of the months is A

则调整完的季节指数为A′
then the seasonal exponent after adjustment is A′

那我们说A′与原季节指数A
What is the association of A′ with the original seasonal exponent A

及调整系数的关系为什么呢
and the adjustment coefficient

（公式如上）
(formula as the above)

我们再看一个新的例子
Here is another example

我们会发现
Let's see

如果这个时候
Here if

房地产商品的
the sales revenue of real estate commodities

这个三年的销售情况如下
for three years is as the following

然后让我们来计算一个
and we are required to figure out the

季节指数的话
seasonal exponents

我们发现 第一步的话
we see, the first step is to

同样还是算这个同季的平均
figure out the average for each quarter

就我们发现同季平均中
We see the average

第一个季度是6.33
for the first quarter is 6.33

第二个季度是8
for the second quarter is 8

第三个季度16.33
for the third quarter is 16.33

第四个季度是20
and for the fourth quarter, it is 20

最后我们发现
Finally, we can

总的平均数是多少
figure out the total average

在这里我们看到
Here we see

这个图表中有多少个数据
how many data are there in this graph

我们说三年四季度
There are totally 12 data corresponding to

总共有12个数据
4 quarters per year for three years

那所以在总个的
So we have the sum

这个经济指标之和基础上
of the total economic indicator

除以12得到它这个平均数
divided by 12 and we obtain

等于12.67
an average of 12.67

那我们看到
We see

在这样的一个基础上
based on this

再求这个季节指数的话
we can figure out

我们得到的这个季节指数
the seasonal exponents

四个季度季节指数
The four quarterly seasonal exponents

分别如下所示
are shown as below

那我们在前一个基础上我们看看
Based on this, let's see

它这个季节指数
if the sum of these quarterly seasonal exponents

加总是否等于400呢
is equivalent to 400

我们去进行加总发现
After adding them together

它也出现一个问题
we see there is a problem

是399.84%
that the result we get is 399.84%

它跟400也是有一段距离的
There is also a deviation from 400

那是否也需要通过
Shall we make an adjustment

调整系数来进行调整
using the adjustment coefficient

那我们说每一个季节指数
We say, the general steps

它调整的一般步骤是
for making adjustment for exponent of each quarter

原始的这个指数比上x
is the ratio of the original exponent to X

x就是我们假定调整后的这个指数
and X is the assumed exponent after adjustment

等于什么呢
So here

等于399.84%比上400%
it is the ratio of 399.84% to 400%

那我们说
So, we say that

这个X求出来以后的话
this X is the new exponent

就是我们提到的
after adjustment

新的调整过后的指数
as we've mentioned

我们发现 调整完以后
We see, after the adjustment

下面表格中
the red column

红色这一列显示的
of the table below

就告诉我们 调整完以后
shows that the total exponent

我们最后加总起来
after adjustment

得到就是400%
is 400%

好 那我们如果是
Okay, so what if it is a monthly indicator

碰到这个月度指标也同样如此
It shall be the same

只不过月度指标的话
Only that for monthly indicator

我们发现
we see

我们不是跟400%进行比较
it is not compared with 400%

我们就应该跟什么进行比较呢
So, what shall it be compared with

我们说月份的话
We say, for monthly indicator

是一共有12个月
there are 12 months in total

所以我们就应该
So here we shall

跟1200%来进行比较
compare it with to 1200%

那我们看到
So, here

在这里有一个总结
let's make a summary

我们说对于这个季节指数和分析
For seasonal exponent and its analysis

一般来讲
generally speaking

对于这种季节指数
when seasonal exponent is used for

分析的时间序列的话
analyzing a time series

它是不存在长期趋势和循环变动的
the secular trend and cyclical variation are not considered

如果说资料它存在这个
If the data shows

上升的长期趋势的话
an upward secular trend

则我们说
then we say that

季节指数在年末的季节指数
the seasonal exponent at the end of the year

它要明显大于年初
is significantly greater than that at the beginning of the year

如果说资料
If the data

它存在一个下降的趋势的话
shows a downward trend

那我们说
then we say that

它有一个年末
the exponent at the end of the year

要明显小于年初这样一个趋势
is significantly smaller than that at the beginning of the year.

那我们看看
Let's see

现在我们这个例子当中
in this example

我们能不能观察一下看
Let's observe and see

它究竟是一个上升趋势
whether it is an upward trend

还是一个下降趋势
or a downward trend

那我们发现
As we can see

它这个一季度 二季度 三季度 四季度
the changing process of the indicator

这个指数的一个变化过程
in the first quarter, second quarter, third quarter and fourth quarter

它明显是一个上升趋势
shows an obvious upward trend

好 这是我们看到的
Well, this is all for

这个季节指数测定的所有内容
the determination of seasonal exponent