臺灣博碩士論文加值系統

****本研究利用機率分配的方法來探討道瓊及納士達克高頻率指數的日內效果及週間效果分析。研究發現，以日內報酬之絕對值做為道瓊及納士達克高頻率指數之波動率皆會形成U型圖，然而不同的是，道瓊指數在收盤的那一刻其波動率會略微下降，而納士達克指數仍會繼續攀升，此表示道瓊指數的投資者傾向於在收盤前十分鐘即會完成當日交易。此外，納士達克之日內報酬所形成的高斯分配，其分配寬度大於道瓊，這也意味著納士達克的交易市場其風險高於道瓊工業指數。隨後，為探討日內效果，本文將整體的樣本資料分成開盤、午餐及收盤三段期間。結果發現，無論是道瓊或納士達克指數，開盤期間的高斯分配在三段交易期間中，其中心位置最偏左、分配寬度也最寬，本文推論這是由於隔夜資訊被累積到下一個交易日早上，因此開盤期間的風險總是位居一日中之最高。
再者，本研究亦發現，單獨討論週間效果而未同時將日內與週間效果納入考慮時，容易使其中一交易期間的正負報酬被另一交易期間的報酬所稀釋，而造成整體的結論產生偏誤。當我們僅考慮週間效果時會發現，週末效果似乎已經不存在；然而若同時考量週間與日內兩種效果，將報酬分為三段交易期間來看時，卻會發現週末效果並未消失，僅是提前或延後發生而已。而利用高斯函數來配適日內報酬時發現，不論道瓊或納士達克指數，週四的分配寬度最寬、而週一與週二的寬度最窄，且週二的午餐時間其分配高度是最高的，故在日內報酬的資料中，日內效果是會影響週間效果的。相對的，利用對數常態分配來配適波動率資料時，週一與週二的平均波動率與分配最高點的機率最低、週四的平均波動率與分配最高點的機率最高，但在日內波動率資料的分配裡，日內效果是不顯著的。

****This study uses the probability distribution techniques to explore the intraday effect and weekday effect of the 10-minuate high frequency returns for the Dow Jones Industrial Average (DJIA) and NASDAQ composite indices. We find that both DJIA and NASDAQ can form a U-shaped pattern by using absolute intraday returns. However, the U-shape from the DJIA index slightly declines at the closing time, while the U-shape from the NASDAQ index still goes up at the closing time. It implies that most investors of DJIA finish their last trading strategy before ten minutes of the closing. Moreover, the width of the Gaussian distribution in NASDAQ is always wider than in DJIA. This result proves that the trading market in NASDAQ is more risky than in DJIA.
Later, as we re-group total intraday returns into the opening, lunch and closing three subgroups, we find that no matter DJIA or NASDAQ index, the lowest center and widest width of the Gaussian distribution occur at the opening trading period. This means that the overnight information is cumulated until next morning, so the opening trading period is the most risky for a whole trading day.
Furthermore, it is more likely to cause the sign of intraday returns at one specific trading period to be swamped by the sign of intraday returns at the other specific trading period when we only discuss the weekday effect without considering the intraday effect. If we only consider the weekday effect, the weekend effect seems disappearing. However, if we add the intraday effect and re-classify total intraday returns according to the trading time and the weekday, we will find that the weekend effect still exists, but the occurrence of the weekend effect may be advanced or postponed.
Besides, using the Gaussian function to refit the intraday returns, we can find that no matter DJIA or NASDAQ, Thursday has the widest width, while Monday and Tuesday have the narrowest width. Meanwhile, the lunch trading period on Tuesday has the highest height. As a result, we infer that the intraday effect will affect the weekday effect in intraday returns. Similarly, using the log-normal distribution to refit the intraday volatilities, we find that Monday and Tuesday have the lowest average volatility and the lowest peak, while Thursday has the highest average volatility and the highest peak. However, the intraday effect is not significant via observing distributions of intraday volatilities.

**Contents

1. Introduction, 1
2. Literature review, 4
3. Data and methodology, 8
3.1 Data description, 8
3.2 Methodology, 8
3.2.1 Probability distributions of intraday returns, 8
3.2.2 Probability distributions of intraday volatilities, 13
4. Panel intraday returns and panel probability distributions among opening, lunch and closing trading periods, 16
4.1 U-shaped pattern from panel intraday returns, 16
4.2 Panel distributions at three different trading periods, 21
4.3 Intraday volatilities of distributions for three different trading periods, 26
5. Panel probability distributions from Monday to Friday among opening, lunch and closing trading periods, 29
5.1 Panel intraday returns from Monday to Friday, 29
5.1.1 DJIA, 29
5.1.2 NASDAQ, 36
5.2 Panel intraday return volatilities from Monday to Friday, 42
5.2.1 DJIA, 42
5.2.2 NASDAQ, 46
6. Conclusions, 51

References, 53
Resume, 56


**Table of Contents
Table 1
Preliminary statistics of 10-min intraday returns for the entire trading time, 9
Table2
The parameters of intraday returns fitted by the Gaussian function, 10
Table 3
Preliminary statistics of 10-min intraday volatilities for the entire trading time, 14
Table 4
Summery statistics of 10-min intraday returns across different trading time in DJIA and NASDAQ, 22
Table 5
The parameters of Gaussian function in panel intraday returns among the opening, lunch and closing trading time for the DJIA index, 23
Table 6
Parameters of 10-min intraday volatilities across different trading time, 28
Table 7
Summary statistics of panel intraday returns from Monday to Friday among the opening, lunch and closing trading periods for the Dow Jones index, 30
Table 8
The Gaussian function parameters of panel intraday returns from Monday to Friday among the opening, lunch and closing trading periods for the Dow Jones index, 34
Table 9
Summary statistics of panel intraday returns from Monday to Friday among the opening, lunch and closing trading periods for the NASDAQ index, 37
Table 10
The Gaussian function parameters of panel intraday returns from Monday to Friday among the opening, lunch and closing trading periods for the NASDAQ index, 39
Table 11
Summary statistics of panel intraday volatilities from Monday to Friday among the opening, lunch and closing trading periods for the Dow Jones index, 42
Table 12
Summary statistics of panel intraday volatilities from Monday to Friday among the opening, lunch and closing trading periods for the NASDAQ index, 47


**Figure of Contents
Figure 1
Probability distribution of 10-min intraday return for entire trading time, 12
Figure 2
Probability distribution of 10-min intraday volatility for entire trading time, 14
Figure 3(a)
Average intraday DJIA absolute 10-min returns including initial returns, 17
Figure 3(b)
Average intraday DJIA absolute 10-min returns excluding initial returns, 17
Figure 4(a)
Average intraday NASDAQ absolute 10-min returns including initial returns, 19
Figure 4(b)
Average intraday NASDAQ absolute 10-min returns excluding initial returns, 19
Figure 5(a)
Boxplot of average absolute intraday DJIA 10-min returns, 20
Figure 5(b)
Boxplot of average absolute intraday NASDAQ 10-min returns, 20
Figure 6
Probability distributions of 10-min intraday returns across opening, lunch and closing trading time for the DJIA index, 24
Figure 7
Probability distributions of 10-min intraday returns across opening, lunch and closing trading time for the NASDAQ index, 25
Figure 8
Probability distributions of 10-min intraday volatilities across opening, lunch and closing trading time, 28
Figure 9(a)
Bar chart of the average intraday return from Monday to Friday for the DJIA index, 31
Figure 9(b)
3-dimension intraday returns from Monday to Friday among opening, lunch and closing trading periods for the DJIA index, 31
Figure 9(c)
Skewness from Monday to Friday among entire, opening, lunch, and closing trading periods for the DJIA index, 31
Figure 10
Panel probability distributions of DJIA intraday return from Monday to Friday among opening, lunch and closing trading periods, 35
Figure 11(a)
Bar chart of the average intraday return from Monday to Friday for the NASDAQ index, 38
Figure 11(b)
3-dimension intraday returns from Monday to Friday among opening, lunch and closing trading periods for the NASDAQ index, 38
Figure 11(c)
Skewness from Monday to Friday among entire, opening, lunch, and closing trading periods for the NASDAQ index, 38
Figure 12
Panel probability distributions of NASDAQ intraday return from Monday to Friday among opening, lunch and closing trading periods, 40
Figure 13(a)
Bar chart of the average volatility from Monday to Friday for the DJIA index, 43
Figure 13(b)
3-dimension weekday volatilities from Monday to Friday among opening, lunch and closing trading periods for the DJIA index, 43
Figure 14
Panel probability distributions of DJIA intraday volatility for the entire trading period, 44
Figure 15
Panel probability distributions of DJIA intraday volatility from Monday to Friday among opening, lunch and closing trading periods, 45
Figure 16(a)
Bar chart of the average volatility from Monday to Friday for the NASDAQ index, 48
Figure 16(b)
3-dimension weekday volatilities from Monday to Friday among opening, lunch and closing trading periods for the NASDAQ index, 48
Figure 17
Panel probability distributions of NASDAQ intraday volatility for the entire trading period, 49
Figure 18
Panel probability distributions of NASDAQ intraday volatility from Monday to Friday among opening, lunch and closing trading periods, 50

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