Module 2: Mathematical Operations and Index Numbers Flashcards

1
Q

What does aggregation mean?

A
  • It is when you combine multiple numbers to form a single number
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2
Q

When do we use aggregation?

A
  • We usually use this with some time series to reduce the frequency: Monthly, quarterly, annual
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3
Q

How do we inform our software that our datasets are time series

A

Usually our datasets have a date column but we need to make sure they understand its for DATES

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4
Q

Before formatting our dataset what do we need to understand first about the dataset?

A

The date conventions (or dates in datasets)

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5
Q

What are the two different date conventions that can exists for time series?

A
  1. Flow + stock variables
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6
Q

What are ‘flow variables’

A
  • Flow variables are considdered to be the average flow over the period
  • This means when we set the exact time of the average flow to the center of the period
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7
Q

What are stock variables?

A
  • We consider stock variables to be the total amount at the end of the period
  • The exact time for the stock variables is at the end of the hour
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8
Q

In Macroeconomics are there many types of stock + flow variables?

A

YES

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9
Q

What’s an example of a flow variable?

A

Consumption as it accumulates the stock of goods

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10
Q

What is the units per measurement for the flow of consumptions

A

Dollars per month

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11
Q

What if we have annual/quarterly for both stock + flow variables?

A

Stock:
Annual: End of the year –> Dec 31
Quarter: end of the quarter –> March 31

Flow:
Annual: July 1
Quarterly: Feb 15 (first quarter)

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12
Q

What’s an exampl of a stock/flow vairbale that is considered neither?

A

Temperature

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13
Q

What is the dates if its neither a flow or stock?

A

Every time we have a variable that represents an average we set the date to the middle and if its for the total over till the end (stock variable)

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14
Q

Can stock variables be averages?

A

YES stats Canada does it as they publish stats that use the average population

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15
Q

How do we define our datasets as time series?

A
  • There might not be a column that has a definite date column (either fix or create one)
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16
Q

How to create a monthly time series?

A
  • Add and use the year month date provided and make a column
  • Its a monthly time series so we set the date to the middle of the month (flow variable)
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17
Q

How to name a table

A
  • Go to ‘design’ and change the ‘table name’
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18
Q

How to create an annual time series?

A
  • We create the date column
  • However the actual day we set to the middle of the year as its annual flow vraible (july 1)
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19
Q

How to add a date column in decimal format

A

Annual time series
Decimal date = Year + 0.5

Quarterly:
Decimal date = Year + 1/8 + Q-1/4

Monthly:
Decimal date = year + 1/24 + M-1/12

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20
Q

What’s a big problem when numbers are saved in text format?

A

it affects mathematical oerpations so we to change it column by column

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21
Q

What should we do if the series are in different units of measurements?

A
  • Make sure to change them into the same units
22
Q

How to change *c to *f?

A

C = (F-32) *5/9

23
Q

What are growth rates?

A

Growth rates in this context describes changes in any variable between two periods in percentage form

XT- Express the value of a variable at time T

XT -1 –> expresses the value of the same variable one period in the past
(this is dependent on the time units)

If its monthly previous month and so on

24
Q

What is the equation for the Growth rate?

A

gt = (Xt - Xt-1 / xt-1)*100

25
For growth rates do you need to only express as a %
No you can keep it as a decima;
26
When we played around with the equation what did we come to learn?
(gt+1 ) = (xt / xt-1)
27
Whats something to keep in mind about mathematical operations with gt?
Never express growth rates in % when doing mathematical operations: use decimal before converting
28
Do growth rates have measurements?
NO
29
Will growth rates in each example be constant?
NO
30
What is the growth rate of a product?
(1+ gx)*(1+gy) -1 = gx + gy --> apporximation
31
Do we wat a higher or smaller growth rate?
Smaller thats why we most likely use the approximation instead of the formula
32
What is the growth rate of ratios?
gt = (1+ gx) / (1+ gy) = gx - gy
33
Can growth rates be negative
Yes so read the question crefully
34
What is the equation for annualized growth rates (monthly data)
gt = (1+ gt)^12 -1
35
What are annualized growth rates?
Its when a monthly growth rate is annualized and calculated over one year
36
What is the equation for annualzied gt (quarterly )
gt = (1+ gt) ^4 -1
37
For any positive/neagtive numbers for log(ab)
log(ab) = Log(a) = Log(B) Log(a/b) = Log(a) - log (B)
38
How do we express log in
natural (ln)
39
How to interpret the growth rate using log?
Log(xt) - log(xt-1) = log(xt/xt-1) = log(1+gt)
40
What if we want the growth rate of the log (product version)
={ log(xt) - log(xt-1)} + {log(yt) - log(yt-1) = (gx + gy)
41
What is aggregation?
its when we combine multiple numbers to form a single number - its main usage was to reduce the frequency of a time series - Converting a monthly --> quarterly
42
How to do aggregation?
- if it's monthly to quarters you take the first three months and add them up to make 1 quarter --. yearly add everything up
43
44
When we refer to a variable in anexcel file what do we mean?
- Its when we look by the name of the table followed by the name of the varibake inside the brackets Ex: = tempdata[jjA]
44
What are the different logical operators
">=" "<" "<=" "="
44
how to take average for 3 months using sum?
=sum(tempdata[@jun] , [@jul] , [@Aug] ) / 3 = sum(tempdata[@[jun] : [Aug] ] ) /3
44
how to use round to find the average of the three months
=round(average([tempdata[@[jun] : [Aug]] , 2)
44
How do we use 'sumif'/ averageif to find the co2 emission after 1980
=sumif([co2Y[date]] , ">1980" , co2y[co2} Third argument what we want to sum First was what we wanted to restrict the observation Second was the actual restriction
45
How to restrict observations based on a date? (ex: Suppose you want the total CO2 emission before January 15th 1970.
=sumif(co2Y[date] , "<"&DATE(1970, 1 ,15) , co2Y[co2])
46
Can we impose more than one rrestriction? How? Suppose for example that we want the total CO2 emission between January 1st 1980 and March 20th 1995.
=SUMIFS(co2data[Co2], co2data[Date], "<"&DATE(1995, 3, 20), co2data[Date], ">"&DATE(1980,1,1)) 1st argument --> the variable used for the operation Second is the variable for the first criteria Third --> is the restriction fourth --> second criteria fifth --> restriction