The Excel file named $41$NDEX$-1$MIN$-05012007-02272009$ posted in Canvas has minute$-$based daily prices of the four Index Exchange Traded Funds $($ETFs$)$ DIA $($Dow Jones Industrial Average$),$ IWM $($Russell $2000),$ QQQ $($NASDAQ$-100)$ and SPY $($ S&P $500)$ between May $1,2007$ and February $27,2009.$ Note that a trading day starts at $9$:$30$AM and ends at $4$:$00$PM and there are $390$ trading minutes in a day. From our perspective, the sampling interval of the date in a given day is T$=$lmin $.$ We may also look at the daily data as a vector

of dimension NP $=391$ covering samples from $9$:$00$AM to $4$:$00$PM in one minute

sampling resolution. Hence, you may consider each column of data $($for each ticker symbol, e$.$g$.$ DIA$)$ as a rectangular matrix where each day is a column vector of dimension NP $=391$ and the number of days in data corresponds to the K rows of that rectangular data matrix.

A$)$ Let's focus on each ETF $($each data column$)$ independently and create its daily vector representation in a NP $=391$ columns x K rows $($days$)$ matrix" form. Do it for all four columns of data. Now, you have the four NpxK price

data matrices for DIA, IWM, QQQ and SPY$.$ Note that the price at $9$:$00$AM is called the opening price and at $4$:$00$PM is called the closing price of the ETF $($stock$).$

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