$3.[$Total $20$ marks$]$

Suppose you are given the historical daily closing prices of $1000$ stocks, covering a period of $20$ years, as exemplified below.

Table V$.$ An Exemplified Time Series Dataset of $1000$ Stocks from $2002$ to $2021$

$($a$)$ If clustering is applied to the stock time series above, you are asked to comment on the followings. Make necessary assumption$($s$).$

i$)$ Is it necessary to normalize the data before clustering? If so$,$ how to do it$?$ If not, justify it$.$

ii$)$ Is it reasonable to cluster the $1000$ stocks with respect to a history of $20$ years, i$.$e$.,$ using all daily closing prices from $2002$ to $2021?$ Justify your answer.

iii$)$ Is it meaningful to carry out intra$-$stock clustering $($i$.$e$.,$ clustering the extracted data of a specific stock$)?$ Justify your answer.

$(10$ marks$)$

$($b$)$ If classification is applied to the stock time series dataset above, you are asked to comment on the followings. Make necessary assumption$($s$).$

i$)$ Is it necessary to normalize the data before classification? If so$,$ how to do it$?$ If not, justify it$.$

ii$)$ Name a class attribute that can be extracted from Table V$.$ For this picked class attribute, suggest the features$/$attributes that should be used to carry out an effective classification task.

iii$)$ For your answer in part $($b$-$ii$)$ above, how should the extracted data be split for training and testing?