WEEK 9

Question 1

time series TIME DEPENDABLE VARIABLES

Answer 1

collect data on one subject over many time periods e.g. ice cream sales each week, daily number of flights or monthly job applications , we care about trends, patterns and changes over time

Question 2

DATA WE USUALLY ANALYSE IS CALLD CROSS SECTION OF DATA and its a data that is collected

Answer 2

at one single point of time

eg a survey of 1000 people about their income

Question 2

predictions about the future

Answer 2

forecasting

Question 3

flactuations can happend due to

Answer 3

seasonality (over year)

Question 4

time series characteristics - decompositions due to the nature of the time series data evolving over time we assume that our data is subject to the most common characteristics

Answer 4

trend - the overall long run average movement in the data, increasing, decreasing or constant

seasonality - related to the period fluctuation that repeats themselves at fixed intervals of the time (season) use visual graph or theory to understand it

cyclic behaviour - represents the generic ups and downs of the economy or industry that occurs over longer intervals of time

randomness - in the real world there is always variation in the data that cannot be explained

Question 5

once we assume that the data is subject to these 4 factors we can try to identify the and use them to create a statistical model for forecasting. time series models which incorporate there characteristics are known as the decomposition model the step to carry this out are

Answer 5

1 identify the trend
2 identify seasonality
3 identify cyclical behaviour
4 combine these 3 a certain way to create a model
5 assess model error
6 use the model to make forecasts

Question 6

randomness is the only

Answer 6

non systematic term

Question 7

we need to keep doing the moel unit we achieve

Answer 7

a low error model to allow us to use randomness trend

Question 8

low error model is a

Answer 8

model that leaves a very little amount of variation (randomness) and most of the variation of time series is explained by the systematic part (the first 3 ) which creates more accurate forecast

Question 9

trend can be hard to see due to

Answer 9

the fluctuation caused by seasonality and/or cyclical behaviour

Question 10

to identify general trend of our data we need to first

Answer 10

smooth or remove the effect of the seasonal fluctuations

Question 11

the method to smooth is called moving average

Answer 11

which considers the avarege value of our data at different point in time (moving)

Question 12

there are 2 ways use the moving average

Answer 12

simple moving average and centred moving average

Question 13

simple moving average

Answer 13

k-period SMA is an average taken over the previous k periods and plotted at that period, we then shift everything along by 1 period to the the next average and so on, the idea is to smooth out the seasonal effect or spikes in the data making the trend much easier to identify an
d then use to forecast future values

k = 2 basically take first 2 periods calculate average of the 2 and we put is as SMA for period 3, then we do 2nd and 3rd period average and put it on the 4th period

if we do k = 3 then we do first 3 do average then its 4th period SMA then we do 2,3,4 and add average then its 5th period SMA

diss - use past values

Question 13

we take the average by adding all then

Answer 13

dividing by how much data points there are

in excel we do =AVERAGE(D2:D4)

Question 14

centred moving average

Answer 14

average taken over k periods which is then plotted in the centre of those values, we then shift everything along by 1 period to take the next average and so on

the adv is that it removes the ‘lag’ from moving average, but it does present an issue that SMA doesn’t, that is the calculations differ depending on whether k is odd or even

so basically

Question 15

CMA odd k

Answer 15

odd like 3, 5 ,7 more straightforward

if k=3 we take average of 3 observations and plot this for 2nd period then take period 2,3,4 average and put it on number 3

if k=7 we do it under period 4 is middle cuz its 3 period before and 3 after

Question 16

CMA even k = 4

in excel -(D2+2*(SUM(D3:D5))+D6)/8

Answer 16

k= 24,6 more complicated if there is 4 period which one is middle

so we take averages of averages so if we take average of first 4 then take the average of observations 2-5 and take average of these 2 we get 2.5 and 3.5 and the middle the is 3

so basically first4 average THEN TAKE average from 2nd period to 5th so 4 period again and then take average of these 2 averages so add them and divide by 2